{"id":235,"date":"2021-07-23T09:19:22","date_gmt":"2021-07-23T13:19:22","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/calorimetry\/"},"modified":"2024-04-10T17:27:58","modified_gmt":"2024-04-10T21:27:58","slug":"calorimetry","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/calorimetry\/","title":{"raw":"5.2 Calorimetry","rendered":"5.2 Calorimetry"},"content":{"raw":"<strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em;background-color: #cbd4b6;color: #000000\">Learning Objectives<\/span><\/strong>\r\n<div class=\"textbox textbox--learning-objectives\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Explain the technique of calorimetry<\/li>\r\n \t<li>Calculate and interpret heat and related properties using typical calorimetry data<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"fs-idm52788928\">One technique we can use to measure the amount of heat involved in a chemical or physical process is known as <strong>calorimetry<\/strong>. Calorimetry is used to measure amounts of heat transferred to or from a substance. To do so, the heat is exchanged with a calibrated object (calorimeter). The temperature change measured by the calorimeter is used to derive the amount of heat transferred by the process under study. The measurement of heat transfer using this approach requires the definition of a <strong>system <\/strong>(the substance or substances undergoing the chemical or physical change) and its <strong>surroundings <\/strong>(all other matter, including components of the measurement apparatus, that serve to either provide heat to the system or absorb heat from the system).<\/p>\r\n<p id=\"fs-idm64462704\">A <strong>calorimeter <\/strong>is a device used to measure the amount of heat involved in a chemical or physical process. For example, when an exothermic reaction occurs in solution in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. When an endothermic reaction occurs, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HeatMeas\">(Figure)<\/a>). The temperature change, along with the specific heat and mass of the solution, can then be used to calculate the amount of heat involved in either case.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_HeatMeas\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">In a calorimetric determination, either (a) an exothermic process occurs and heat, <em data-effect=\"italics\">q<\/em>, is negative, indicating that thermal energy is transferred from the system to its surroundings, or (b) an endothermic process occurs and heat, <em data-effect=\"italics\">q<\/em>, is positive, indicating that thermal energy is transferred from the surroundings to the system.<\/div>\r\n<span id=\"fs-idp17874784\" data-type=\"media\" data-alt=\"Two diagrams labeled a and b are shown. Each is made up of two rectangular containers with a thermometer inserted into the top right and extending inside. There is a right facing arrow connecting each box in each diagram. The left container in diagram a depicts a pink and green swirling solution with the terms \u201cExothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms pointing to \u201cq.\u201d The labels \u201cSolution\u201d and \u201cSurroundings\u201d are written at the bottom of the container. The right container in diagram a has the term \u201cSolution\u201d written at the bottom of the container and a red arrow facing up near the thermometer with the phrase \u201cTemperature increased\u201d next to it. The pink and green swirls are more blended in this container. The left container in diagram b depicts a purple and blue swirling solution with the terms \u201cEndothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms and \u201cSolution\u201d and \u201cSurroundings\u201d written at the bottom. The arrows point away from the letter \u201cq.\u201d The right container in diagram b has the term \u201cSolution\u201d written at the bottom and a red arrow facing down near the thermometer with the phrase \u201cTemperature decreased\u201d next to it. The blue and purple swirls are more blended in this container.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HeatMeas-1.jpg\" alt=\"Two diagrams labeled a and b are shown. Each is made up of two rectangular containers with a thermometer inserted into the top right and extending inside. There is a right facing arrow connecting each box in each diagram. The left container in diagram a depicts a pink and green swirling solution with the terms \u201cExothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms pointing to \u201cq.\u201d The labels \u201cSolution\u201d and \u201cSurroundings\u201d are written at the bottom of the container. The right container in diagram a has the term \u201cSolution\u201d written at the bottom of the container and a red arrow facing up near the thermometer with the phrase \u201cTemperature increased\u201d next to it. The pink and green swirls are more blended in this container. The left container in diagram b depicts a purple and blue swirling solution with the terms \u201cEndothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms and \u201cSolution\u201d and \u201cSurroundings\u201d written at the bottom. The arrows point away from the letter \u201cq.\u201d The right container in diagram b has the term \u201cSolution\u201d written at the bottom and a red arrow facing down near the thermometer with the phrase \u201cTemperature decreased\u201d next to it. The blue and purple swirls are more blended in this container.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm75322144\">Scientists use well-insulated calorimeters that all but prevent the transfer of heat between the calorimeter and its environment, which effectively limits the \u201csurroundings\u201d to the nonsystem components with the calorimeter (and the calorimeter itself). This enables the accurate determination of the heat involved in chemical processes, the energy content of foods, and so on. General chemistry students often use simple calorimeters constructed from polystyrene cups (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_Calorim\">(Figure)<\/a>). These easy-to-use \u201ccoffee cup\u201d calorimeters allow more heat exchange with the outside environment, and therefore produce less accurate energy values.<\/p>\r\n\r\n<div id=\"CNX_Chem_05_02_Calorim\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">A simple calorimeter can be constructed from two polystyrene cups. A thermometer and stirrer extend through the cover into the reaction mixture.<\/div>\r\n<span id=\"fs-idm11505008\" data-type=\"media\" data-alt=\"Two Styrofoam cups are shown nested in one another with a cover over the top. A thermometer and stirring rod are inserted through the cover and into the solution inside the cup, which is shown as a cut-away. The stirring rod has a double headed arrow next to it facing up and down. The liquid mixture inside the cup is labeled \u201cReaction mixture.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_Calorim-1.jpg\" alt=\"Two Styrofoam cups are shown nested in one another with a cover over the top. A thermometer and stirring rod are inserted through the cover and into the solution inside the cup, which is shown as a cut-away. The stirring rod has a double headed arrow next to it facing up and down. The liquid mixture inside the cup is labeled \u201cReaction mixture.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm10930512\">Commercial solution calorimeters are also available. Relatively inexpensive calorimeters often consist of two thin-walled cups that are nested in a way that minimizes thermal contact during use, along with an insulated cover, handheld stirrer, and simple thermometer. More expensive calorimeters used for industry and research typically have a well-insulated, fully enclosed reaction vessel, motorized stirring mechanism, and a more accurate temperature sensor (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_Calorim2\">(Figure)<\/a>).<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_Calorim2\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">Commercial solution calorimeters range from (a) simple, inexpensive models for student use to (b) expensive, more accurate models for industry and research.<\/div>\r\n<span id=\"fs-idm53300432\" data-type=\"media\" data-alt=\"Two diagrams are shown and labeled a and b. Diagram a depicts a thermometer which passes through a disk-like insulating cover and into a metal cylinder which is labeled \u201cmetal inner vessel,\u201d which is in turn nested in a metal cylinder labeled \u201cmetal outer vessel.\u201d The inner cylinder rests on an insulating support ring. A stirrer passes through the insulating cover and into the inner cylinder as well. Diagram b shows an inner metal vessel half full of liquid resting on an insulating support ring and nested in a metal outer vessel. A precision temperature probe and motorized stirring rod are placed into the solution in the inner vessel and connected by wires to equipment exterior to the set-up.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_Calorim2-1.jpg\" alt=\"Two diagrams are shown and labeled a and b. Diagram a depicts a thermometer which passes through a disk-like insulating cover and into a metal cylinder which is labeled \u201cmetal inner vessel,\u201d which is in turn nested in a metal cylinder labeled \u201cmetal outer vessel.\u201d The inner cylinder rests on an insulating support ring. A stirrer passes through the insulating cover and into the inner cylinder as well. Diagram b shows an inner metal vessel half full of liquid resting on an insulating support ring and nested in a metal outer vessel. A precision temperature probe and motorized stirring rod are placed into the solution in the inner vessel and connected by wires to equipment exterior to the set-up.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm10925216\">Before discussing the calorimetry of chemical reactions, consider a simpler example that illustrates the core idea behind calorimetry. Suppose we initially have a high-temperature substance, such as a hot piece of metal (M), and a low-temperature substance, such as cool water (W). If we place the metal in the water, heat will flow from M to W. The temperature of M will decrease, and the temperature of W will increase, until the two substances have the same temperature\u2014that is, when they reach thermal equilibrium (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HeatTrans2\">(Figure)<\/a>). If this occurs in a calorimeter, ideally all of this heat transfer occurs between the two substances, with no heat gained or lost by either its external environment. Under these ideal circumstances, the net heat change is zero:<\/p>\r\n\r\n<div id=\"fs-idm194903168\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>substance M<\/sub> + <em>q<\/em><sub>substance W<\/sub> =0<\/div>\r\n<p id=\"fs-idp41620800\">This relationship can be rearranged to show that the heat gained by substance M is equal to the heat lost by substance W:<\/p>\r\n\r\n<div id=\"fs-idm280055136\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>substance M <\/sub>= -<em>q<\/em><sub>substance W<\/sub><\/div>\r\n<p id=\"fs-idm129199216\">The magnitude of the heat is therefore the same for both substances, and the negative sign merely shows that <em data-effect=\"italics\">q<\/em><sub>substance M<\/sub> and <em data-effect=\"italics\">q<\/em><sub>substance W<\/sub> are opposite in direction of heat flow (gain or loss) but does not indicate the arithmetic sign of either <em data-effect=\"italics\">q<\/em> value (that is determined by whether the matter in question gains or loses heat, per definition). In the specific situation described, <em data-effect=\"italics\">q<\/em><sub>substance M<\/sub> is a negative value and <em data-effect=\"italics\">q<\/em><sub>substance W<\/sub> is positive, since heat is transferred from M to W.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_HeatTrans2\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">In a simple calorimetry process, (a) heat, <em data-effect=\"italics\">q<\/em>, is transferred from the hot metal, M, to the cool water, W, until (b) both are at the same temperature.<\/div>\r\n<span id=\"fs-idm50825408\" data-type=\"media\" data-alt=\"Two diagrams are shown and labeled a and b. Each diagram is composed of a rectangular container with a thermometer inserted inside from the top right corner. Both containers are connected by a right-facing arrow. Both containers are full of water, which is depicted by the letter \u201cW,\u201d and each container has a square in the middle which represents a metal which is labeled with a letter \u201cM.\u201d In diagram a, the metal is drawn in brown and has three arrows facing away from it. Each arrow has the letter \u201cq\u201d at its end. The metal is labeled \u201csystem\u201d and the water is labeled \u201csurroundings.\u201d The thermometer in this diagram has a relatively low reading. In diagram b, the metal is depicted in purple and the thermometer has a relatively high reading.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HeatTrans2-1.jpg\" alt=\"Two diagrams are shown and labeled a and b. Each diagram is composed of a rectangular container with a thermometer inserted inside from the top right corner. Both containers are connected by a right-facing arrow. Both containers are full of water, which is depicted by the letter \u201cW,\u201d and each container has a square in the middle which represents a metal which is labeled with a letter \u201cM.\u201d In diagram a, the metal is drawn in brown and has three arrows facing away from it. Each arrow has the letter \u201cq\u201d at its end. The metal is labeled \u201csystem\u201d and the water is labeled \u201csurroundings.\u201d The thermometer in this diagram has a relatively low reading. In diagram b, the metal is depicted in purple and the thermometer has a relatively high reading.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idp13199280\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm94530896\"><strong>Heat Transfer between Substances at Different Temperatures:<\/strong><\/p>\r\nA 360.0-g piece of rebar (a steel rod used for reinforcing concrete) is dropped into 425 mL of water at 24.0 \u00b0C. The final temperature of the water was measured as 42.7 \u00b0C. Calculate the initial temperature of the piece of rebar. Assume the specific heat of steel is approximately the same as that for iron (<a class=\"autogenerated-content\" href=\"\/contents\/fae98e81-a194-4023-9468-aafca1dc4674#fs-idm68801008\">(Figure)<\/a>), and that all heat transfer occurs between the rebar and the water (there is no heat exchange with the surroundings).\r\n<p id=\"fs-idp13157184\"><strong>Solution:<\/strong><\/p>\r\nThe temperature of the water increases from 24.0 \u00b0C to 42.7 \u00b0C, so the water absorbs heat. That heat came from the piece of rebar, which initially was at a higher temperature. Assuming that all heat transfer was between the rebar and the water, with no heat \u201clost\u201d to the outside environment, then <em data-effect=\"italics\">heat given off by rebar = \u2212heat taken in by water<\/em>, or:\r\n<div id=\"fs-idm107179568\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>rebar <\/sub>= -<em>q<\/em><sub>water<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp46728032\">Since we know how heat is related to other measurable quantities, we have:<\/p>\r\n\r\n<div id=\"fs-idm52673840\" style=\"text-align: center\" data-type=\"equation\">(<em>c<\/em> \u00d7 <em>m<\/em> <span style=\"font-size: 1em\">\u00d7 \u0394<em>T<\/em>)<sub>rebar<\/sub> = -(<em>c<\/em> \u00d7 <em>m<\/em>\u00d7 \u0394<em>T<\/em>)<sub>water<\/sub><\/span><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp47392976\">Letting f = final and i = initial, in expanded form, this becomes:<\/p>\r\n\r\n<div id=\"fs-idp7508656\" style=\"text-align: center\" data-type=\"equation\"><em>c<span style=\"font-size: 1em\"><sub>rebar<\/sub><\/span><\/em> \u00d7 <em>m<span style=\"font-size: 1em\"><sub>rebar<\/sub><\/span><\/em> <span style=\"font-size: 1em\">\u00d7 (<em>T<\/em><sub>f,rebar<\/sub> - <em>T<\/em><sub>i,rebar<\/sub>) = -<em>c<sub>water<\/sub><\/em> \u00d7 <em>m<sub>water<\/sub><\/em>\u00d7 (<em>T<\/em><sub>f,water<\/sub> - <em>T<\/em><sub>i,water<\/sub>)<\/span><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm100431536\">The density of water is 1.0 g\/mL, so 425 mL of water = 425 g. Noting that the final temperature of both the rebar and water is 42.7 \u00b0C, substituting known values yields:<\/p>\r\n\r\n<div id=\"fs-idm160292560\" style=\"text-align: center\" data-type=\"equation\">(0.449 J\/g \u00b0C)(360.0 g)(42.7\u00b0C - T<sub>i,rebar<\/sub>)=-(4.184 J\/g \u00b0C)(425 g)(42.7\u00b0C -24.0\u00b0C)<\/div>\r\n<div id=\"fs-idp7310352\" data-type=\"equation\"><img class=\"alignnone wp-image-1268 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-300x32.png\" alt=\"\" width=\"375\" height=\"40\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm56113136\">Solving this gives <em data-effect=\"italics\">T<\/em><sub>i,rebar<\/sub>= 248 \u00b0C, so the initial temperature of the rebar was 248 \u00b0C.<\/p>\r\n<p id=\"fs-idm82711952\"><strong>Check Your Learning:<\/strong><\/p>\r\nA 248-g piece of copper is dropped into 390. mL of water at 22.6 \u00b0C. The final temperature of the water was measured as 39.9 \u00b0C. Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water.\r\n\r\n&nbsp;\r\n<div id=\"fs-idm20275344\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm12419600\">The initial temperature of the copper was 336 \u00b0C.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<p id=\"fs-idp12008976\"><strong>Check Your Learning:<\/strong><\/p>\r\nA 248-g piece of copper initially at 314 \u00b0C is dropped into 390. mL of water initially at 22.6 \u00b0C. Assuming that all heat transfer occurs between the copper and the water, calculate the final temperature.\r\n\r\n&nbsp;\r\n<div id=\"fs-idm17192400\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm84058400\">The final temperature (reached by both copper and water) is 38.7 \u00b0C.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idm1809184\">This method can also be used to determine other quantities, such as the specific heat of an unknown metal.<\/p>\r\n\r\n<div id=\"fs-idm80667088\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm92661904\"><strong>Identifying a Metal by Measuring Specific Heat:<\/strong><\/p>\r\nA 59.7 g piece of metal that had been submerged in boiling water was quickly transferred into 60.0 mL of water initially at 22.0 \u00b0C. The final temperature is 28.5 \u00b0C. Use these data to determine the specific heat of the metal. Use this result to identify the metal.\r\n<p id=\"fs-idm56342080\"><strong>Solution:<\/strong><\/p>\r\nAssuming perfect heat transfer, <em data-effect=\"italics\">heat given off by metal = \u2212heat taken in by water<\/em>, or:\r\n<div id=\"fs-idm199710176\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>metal <\/sub>= -<em>q<\/em><sub>water<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\nIn expanded form, this is:\r\n<p style=\"text-align: center\"><em>c<\/em><sub>metal<\/sub> \u00d7 <em>m<sub>metal<\/sub><\/em>\u00a0<span style=\"font-size: 1em\">\u00d7 (<em>T<\/em><sub>f,metal<\/sub>\u00a0- <em>T<\/em><sub>i,metal<\/sub>) = -<em>c<sub>water<\/sub><\/em> \u00d7 <em>m<sub>water<\/sub><\/em>\u00d7 (<em>T<\/em><sub>f,water<\/sub> - <em>T<\/em><sub>i,water<\/sub>)<\/span><\/p>\r\n<p id=\"fs-idm9602288\">Noting that since the metal was submerged in boiling water, its initial temperature was 100.0 \u00b0C; and that for water, 60.0 mL = 60.0 g; we have:<\/p>\r\n\r\n<div id=\"fs-idm127022128\" style=\"text-align: center\" data-type=\"equation\">(<em>c<\/em><sub>metal<\/sub>)(59.7 g)(28.5\u00b0C - 100.0\u00b0C)=-(4.184 J\/g \u00b0C)(60.0 g)(28.5\u00b0C -22.0\u00b0C)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm4520800\">Solving this:<\/p>\r\n<img class=\"alignnone wp-image-1269 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-300x38.png\" alt=\"\" width=\"332\" height=\"42\" \/>\r\n<p id=\"fs-idm61018208\">Comparing this with values in the table of specific heat capacities, our experimental specific heat is closest to the value for copper (0.39 J\/g \u00b0C), so we identify the metal as copper.<\/p>\r\n<p id=\"fs-idm42342688\"><strong>Check Your Learning:<\/strong><\/p>\r\nA 92.9-g piece of a silver\/gray metal is heated to 178.0 \u00b0C, and then quickly transferred into 75.0 mL of water initially at 24.0 \u00b0C. After 5 minutes, both the metal and the water have reached the same temperature: 29.7 \u00b0C. Determine the specific heat and the identity of the metal. (Note: You should find that the specific heat is close to that of two different metals. Explain how you can confidently determine the identity of the metal).\r\n\r\n&nbsp;\r\n<div id=\"fs-idm64160064\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm19048032\"><em data-effect=\"italics\">c<\/em><sub>metal<\/sub>= 0.13 J\/g \u00b0C<\/p>\r\n<p id=\"fs-idm40554112\">This specific heat is close to that of either gold or lead. It would be difficult to determine which metal this was based solely on the numerical values. However, the observation that the metal is silver\/gray in addition to the value for the specific heat indicates that the metal is lead.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idp8565200\">When we use calorimetry to determine the heat involved in a chemical reaction, the same principles we have been discussing apply. The amount of heat absorbed by the calorimeter is often small enough that we can neglect it (though not for highly accurate measurements, as discussed later), and the calorimeter minimizes energy exchange with the outside environment. Because energy is neither created nor destroyed during a chemical reaction, the heat produced or consumed in the reaction (the \u201csystem\u201d), <em data-effect=\"italics\">q<\/em><sub>reaction<\/sub>, plus the heat absorbed or lost by the solution (the \u201csurroundings\u201d), <em data-effect=\"italics\">q<\/em><sub>solution<\/sub>, must add up to zero:<\/p>\r\n\r\n<div id=\"fs-idm289467200\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> + <em>q<\/em><sub>solution<\/sub> = 0<\/div>\r\n<p id=\"fs-idm98090832\">This means that the amount of heat produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution:<\/p>\r\n\r\n<div id=\"fs-idm208991056\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = -<em>q<\/em><sub>solution<\/sub><\/div>\r\n<p id=\"fs-idm68084048\">This concept lies at the heart of all calorimetry problems and calculations.<\/p>\r\n\r\n<div id=\"fs-idm19242032\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm66182640\"><strong>Heat Produced by an Exothermic Reaction:<\/strong><\/p>\r\nWhen 50.0 mL of 1.00 M HCl(<em data-effect=\"italics\">aq<\/em>) and 50.0 mL of 1.00 M NaOH(<em data-effect=\"italics\">aq<\/em>), both at 22.0 \u00b0C, are added to a coffee cup calorimeter, the temperature of the mixture reaches a maximum of 28.9 \u00b0C. What is the approximate amount of heat produced by this reaction?\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idm32936848\" style=\"text-align: center\" data-type=\"equation\">HCl(<em>aq<\/em>) + NaOH(<em>aq<\/em>) \u27f6 NaCl(<em>aq<\/em>)+ H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm73607008\"><strong>Solution:<\/strong><\/p>\r\nTo visualize what is going on, imagine that you could combine the two solutions so quickly that no reaction took place while they mixed; then after mixing, the reaction took place. At the instant of mixing, you have 100.0 mL of a mixture of HCl and NaOH at 22.0 \u00b0C. The HCl and NaOH then react until the solution temperature reaches 28.9 \u00b0C.\r\n<p id=\"fs-idm74180672\">The heat given off by the reaction is equal to that taken in by the solution. Therefore:<\/p>\r\n\r\n<div id=\"fs-idm259063904\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = -<em>q<\/em><sub>solution<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm11281888\">(It is important to remember that this relationship only holds if the calorimeter does not absorb any heat from the reaction, and there is no heat exchange between the calorimeter and the outside environment.)<\/p>\r\n<p id=\"fs-idm12358560\">Next, we know that the heat absorbed by the solution depends on its specific heat, mass, and temperature change:<\/p>\r\n\r\n<div id=\"fs-idm174034752\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>solution<\/sub> = (<em>c<\/em> \u00d7 <em>m<\/em> \u00d7 \u0394<em>T<\/em>)<sub>solution<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp12432\">To proceed with this calculation, we need to make a few more reasonable assumptions or approximations. Since the solution is aqueous, we can proceed as if it were water in terms of its specific heat and mass values. The density of water is approximately 1.0 g\/mL, so 100.0 mL has a mass of about 1.0 \u00d7 10<sup>2<\/sup> g (two significant figures). The specific heat of water is 4.184 J\/g \u00b0C, so we use that for the specific heat of the solution. Substituting these values gives:<\/p>\r\n\r\n<div id=\"fs-idm261390032\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>solution<\/sub> = (4.184 J\/g \u00b0C) \u00d7 (1.0 x 10<sup>2<\/sup> g)(28.9\u00b0C -22.0\u00b0C) = 2.9 \u00d7 10<sup>3 <\/sup>J<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm6689328\">Finally, since we are trying to find the heat of the reaction, we have:<\/p>\r\n\r\n<div id=\"fs-idm178566000\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = -<em>q<\/em><sub>solution <\/sub>=-2.9 \u00d7 10<sup>3 <\/sup>J<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm66484944\">The negative sign indicates that the reaction is exothermic. It produces 2.9 kJ of heat.<\/p>\r\n<p id=\"fs-idm55750416\"><strong>Check Your Learning:<\/strong><\/p>\r\nWhen 100 mL of 0.200 M NaCl(<em data-effect=\"italics\">aq<\/em>) and 100 mL of 0.200 M AgNO<sub>3<\/sub>(<em data-effect=\"italics\">aq<\/em>), both at 21.9 \u00b0C, are mixed in a coffee cup calorimeter, the temperature increases to 23.5 \u00b0C as solid AgCl forms. How much heat is produced by this precipitation reaction? What assumptions did you make to determine your value?\r\n\r\n&nbsp;\r\n<div id=\"fs-idm9227984\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm94618544\">1.34 \u00d7 10<sup>3<\/sup> J; assume no heat is absorbed by the calorimeter, no heat is exchanged between the calorimeter and its surroundings, and that the specific heat and mass of the solution are the same as those for water<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm9530672\" class=\"chemistry everyday-life\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Thermochemistry of Hand Warmers<\/strong><\/div>\r\n<p id=\"fs-idm19355440\">When working or playing outdoors on a cold day, you might use a hand warmer to warm your hands (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HandWarmer\">(Figure)<\/a>). A common reusable hand warmer contains a supersaturated solution of NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> (sodium acetate) and a metal disc. Bending the disk creates nucleation sites around which the metastable NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> quickly crystallizes (a later chapter on solutions will investigate saturation and supersaturation in more detail).<\/p>\r\n<p id=\"fs-idm213136\">The process NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) \u27f6NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub>(<em>s<\/em>) is exothermic, and the heat produced by this process is absorbed by your hands, thereby warming them (at least for a while). If the hand warmer is reheated, the NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> redissolves and can be reused.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_HandWarmer\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">Chemical hand warmers produce heat that warms your hand on a cold day. In this one, you can see the metal disc that initiates the exothermic precipitation reaction. (credit: modification of work by Science Buddies TV\/YouTube)<\/div>\r\n<span id=\"fs-idm20337008\" data-type=\"media\" data-alt=\"A series of three photos is shown. There are two right-facing arrows connecting one photo to the next. The first photo shows a chemical hand warmer. It is a bag that contains a clear, colorless liquid. There is a white disk located to the right inside the bag. The second photo shows the same thing, except the white disc has become a white, cloudy substance. The third photo shows the entire bag filled with this white substance.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HandWarmer-1.jpg\" alt=\"A series of three photos is shown. There are two right-facing arrows connecting one photo to the next. The first photo shows a chemical hand warmer. It is a bag that contains a clear, colorless liquid. There is a white disk located to the right inside the bag. The second photo shows the same thing, except the white disc has become a white, cloudy substance. The third photo shows the entire bag filled with this white substance.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm15246800\">Another common hand warmer produces heat when it is ripped open, exposing iron and water in the hand warmer to oxygen in the air. One simplified version of this exothermic reaction is 2Fe(<em>s<\/em>) + (3\/2)O<sub>2<\/sub>(<em>g<\/em>) \u27f6 Fe<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>). Salt in the hand warmer catalyzes the reaction, so it produces heat more rapidly; cellulose, vermiculite, and activated carbon help distribute the heat evenly. Other types of hand warmers use lighter fluid (a platinum catalyst helps lighter fluid oxidize exothermically), charcoal (charcoal oxidizes in a special case), or electrical units that produce heat by passing an electrical current from a battery through resistive wires.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm79691632\" class=\"chemistry link-to-learning\" data-type=\"note\">\r\n<p id=\"fs-idm81095744\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16Handwarmer\">link<\/a> shows the precipitation reaction that occurs when the disk in a chemical hand warmer is flexed.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"fs-idp325184\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm52519632\"><strong>Heat Flow in an Instant Ice Pack:<\/strong><\/p>\r\nWhen solid ammonium nitrate dissolves in water, the solution becomes cold. This is the basis for an \u201cinstant ice pack\u201d (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_IcePack\">(Figure)<\/a>). When 3.21 g of solid NH<sub>4<\/sub>NO<sub>3<\/sub> dissolves in 50.0 g of water at 24.9 \u00b0C in a calorimeter, the temperature decreases to 20.3 \u00b0C.\r\n<p id=\"fs-idp41329920\">Calculate the value of <em data-effect=\"italics\">q<\/em> for this reaction and explain the meaning of its arithmetic sign. State any assumptions that you made.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_IcePack\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">An instant cold pack consists of a bag containing solid ammonium nitrate and a second bag of water. When the bag of water is broken, the pack becomes cold because the dissolution of ammonium nitrate is an endothermic process that removes thermal energy from the water. The cold pack then removes thermal energy from your body.<\/div>\r\n<span id=\"fs-idm30928704\" data-type=\"media\" data-alt=\"A diagram depicts a rectangular pack containing a white, solid substance and an interior bag full of water. The white solid is labeled \u201cammonium nitrate.\u201d The top of the packet has the words \u201cInstant Cold Pack\u201d written on it. It also has three pictograms, which from right to left, show a hand squeezing the pack, agitating the pack and placing the pack on a person\u2019s body. The bottom of the pack has printed words that read \u201csingle use only.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_IcePack-1.jpg\" alt=\"A diagram depicts a rectangular pack containing a white, solid substance and an interior bag full of water. The white solid is labeled \u201cammonium nitrate.\u201d The top of the packet has the words \u201cInstant Cold Pack\u201d written on it. It also has three pictograms, which from right to left, show a hand squeezing the pack, agitating the pack and placing the pack on a person\u2019s body. The bottom of the pack has printed words that read \u201csingle use only.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idp364256\"><strong>Solution:<\/strong><\/p>\r\nWe assume that the calorimeter prevents heat transfer between the solution and its external environment (including the calorimeter itself), in which case:\r\n<div id=\"fs-idm127206368\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = -<em>q<\/em><sub>soln<\/sub><\/div>\r\n<p id=\"fs-idm76420496\">with \u201crxn\u201d and \u201csoln\u201d used as shorthand for \u201creaction\u201d and \u201csolution,\u201d respectively.<\/p>\r\n<p id=\"fs-idm52847712\">Assuming also that the specific heat of the solution is the same as that for water, we have:<\/p>\r\n\r\n<div id=\"fs-idm183045408\" style=\"text-align: left\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = -<em>q<\/em><sub>soln <\/sub>= -(<em>c<\/em> \u00d7 <em>m<\/em> \u00d7 \u0394<em>T<\/em>)<sub>soln<\/sub><\/div>\r\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 = \u2212(4.184 J\/g \u00b0C)(53.2 g)(20.3\u00b0C -24.9\u00b0C)<\/div>\r\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 =\u2212(4.184 J\/g \u00b0C)(53.2\u00a0 g)(-4.6\u00b0C)<\/div>\r\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 =+1.0 \u00d7 <i>10<sup>3 <\/sup><\/i>J<i> = +1.0 <\/i>kJ<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp8566608\">The positive sign for <em data-effect=\"italics\">q<\/em> indicates that the dissolution is an endothermic process.<\/p>\r\n<p id=\"fs-idm6778640\"><strong>Check Your Learning:<\/strong><\/p>\r\nWhen a 3.00-g sample of KCl was added to 3.00 \u00d7 10<sup>2<\/sup> g of water in a coffee cup calorimeter, the temperature decreased by 1.05 \u00b0C. How much heat is involved in the dissolution of the KCl? What assumptions did you make?\r\n\r\n&nbsp;\r\n<div id=\"fs-idm9544544\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm5945296\">1.33 kJ; assume that the calorimeter prevents heat transfer between the solution and its external environment (including the calorimeter itself) and that the specific heat of the solution is the same as that for water<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idm33984192\">If the amount of heat absorbed by a calorimeter is too large to neglect or if we require more accurate results, then we must take into account the heat absorbed both by the solution and by the calorimeter.<\/p>\r\n<p id=\"fs-idm75111136\">The calorimeters described are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow accompanying processes that occur in solution. A different type of calorimeter that operates at constant volume, colloquially known as a <strong>bomb calorimeter<\/strong>, is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions. (The term \u201cbomb\u201d comes from the observation that these reactions can be vigorous enough to resemble explosions that would damage other calorimeters.) This type of calorimeter consists of a robust steel container (the \u201cbomb\u201d) that contains the reactants and is itself submerged in water (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_BombCalor\">(Figure)<\/a>). The sample is placed in the bomb, which is then filled with oxygen at high pressure. A small electrical spark is used to ignite the sample. The energy produced by the reaction is absorbed by the steel bomb and the surrounding water. The temperature increase is measured and, along with the known heat capacity of the calorimeter, is used to calculate the energy produced by the reaction. Bomb calorimeters require calibration to determine the heat capacity of the calorimeter and ensure accurate results. The calibration is accomplished using a reaction with a known <em data-effect=\"italics\">q<\/em>, such as a measured quantity of benzoic acid ignited by a spark from a nickel fuse wire that is weighed before and after the reaction. The temperature change produced by the known reaction is used to determine the heat capacity of the calorimeter. The calibration is generally performed each time before the calorimeter is used to gather research data.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_BombCalor\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">(a) A bomb calorimeter is used to measure heat produced by reactions involving gaseous reactants or products, such as combustion. (b) The reactants are contained in the gas-tight \u201cbomb,\u201d which is submerged in water and surrounded by insulating materials. (credit a: modification of work by \u201cHarbor1\u201d\/Wikimedia commons)<\/div>\r\n<span id=\"fs-idp22458144\" data-type=\"media\" data-alt=\"A picture and a diagram are shown, labeled a and b, respectively. Picture a depicts a bomb calorimeter. It is a cube-shaped machine with a cavity in the top, a metal cylinder that is above the cavity, and a read-out panel attached to the top-right side. Diagram b depicts a cut away figure of a cube with a cylindrical container full of water in the middle of it. Another container, labeled \u201cbomb,\u201d sits inside of a smaller cylinder which holds a sample cup and is nested in the cylindrical container surrounded by the water. A black line extends into the water and is labeled \u201cPrecision thermometer.\u201d Two wires labeled \u201cElectrodes\u201d extend away from a cover that sits on top of the interior container. A read-out panel is located at the top right of the cube.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_BombCalor-1.jpg\" alt=\"A picture and a diagram are shown, labeled a and b, respectively. Picture a depicts a bomb calorimeter. It is a cube-shaped machine with a cavity in the top, a metal cylinder that is above the cavity, and a read-out panel attached to the top-right side. Diagram b depicts a cut away figure of a cube with a cylindrical container full of water in the middle of it. Another container, labeled \u201cbomb,\u201d sits inside of a smaller cylinder which holds a sample cup and is nested in the cylindrical container surrounded by the water. A black line extends into the water and is labeled \u201cPrecision thermometer.\u201d Two wires labeled \u201cElectrodes\u201d extend away from a cover that sits on top of the interior container. A read-out panel is located at the top right of the cube.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idm2366288\" class=\"chemistry link-to-learning\" data-type=\"note\">\r\n<p id=\"fs-idp41066256\">Click on this <a href=\"http:\/\/openstaxcollege.org\/l\/16BombCal\">link<\/a> to view how a bomb calorimeter is prepared for action.<\/p>\r\n<p id=\"fs-idm11069408\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16Calorcalcs\">site<\/a> shows calorimetric calculations using sample data.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm49773520\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp23917952\"><strong>Bomb Calorimetry:<\/strong><\/p>\r\nWhen 3.12 g of glucose, C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>, is burned in a bomb calorimeter, the temperature of the calorimeter increases from 23.8 \u00b0C to 35.6 \u00b0C. The bomb calorimeter assembly, which <em>includes<\/em> the water, has a heat capacity of 4.13 kJ\/\u00b0C. How much heat was produced by the combustion of the glucose sample?\r\n<p id=\"fs-idm103829360\"><strong>Solution:<\/strong><\/p>\r\nThe combustion produces heat that is primarily absorbed by the bomb calorimetry assembly. (The amounts of heat absorbed by the reaction products and the unreacted excess oxygen are relatively small and dealing with them is beyond the scope of this text. We will neglect them in our calculations.)\r\n<p id=\"fs-idm51439440\">The heat produced by the reaction is absorbed by the water and the bomb:<\/p>\r\n\r\n<div id=\"fs-idm137623248\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = -<em>q<\/em><sub>calorimeter <\/sub><\/div>\r\n<div data-type=\"equation\">=-(4.31 kJ\/\u00b0C)(35.6\u00b0C - 23.8\u00b0C)<\/div>\r\n<div data-type=\"equation\">=-(4.31 kJ\/\u00b0C)(11.8\u00b0C)<\/div>\r\n<div data-type=\"equation\">=-50.8 kJ<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm51688848\">This reaction released 50.8 kJ of heat when 3.12 g of glucose was burned.<\/p>\r\n<p id=\"fs-idm39952704\"><strong>Check Your Learning:<\/strong><\/p>\r\nWhen 0.963 g of benzene, C<sub>6<\/sub>H<sub>6<\/sub>, is burned in a bomb calorimeter, the temperature of the calorimeter increases by 8.39 \u00b0C. The bomb calorimetry assembly has a heat capacity of 4.65 kJ\/\u00b0C.. How much heat was produced by the combustion of the glucose sample?\r\n\r\n&nbsp;\r\n<div id=\"fs-idm11360480\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm88592432\">39.0 kJ<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idm30236928\">Since the first one was constructed in 1899, 35 calorimeters have been built to measure the heat produced by a living person.<sup data-type=\"footnote-number\"><a href=\"#footnote1\" data-type=\"footnote-link\">1<\/a><\/sup> These whole-body calorimeters of various designs are large enough to hold an individual human being. More recently, whole-room calorimeters allow for relatively normal activities to be performed, and these calorimeters generate data that more closely reflect the real world. These calorimeters are used to measure the metabolism of individuals under different environmental conditions, different dietary regimes, and with different health conditions, such as diabetes. In humans, metabolism is typically measured in Calories per day. A <span data-type=\"term\">nutritional calorie (Calorie)<\/span> is the energy unit used to quantify the amount of energy derived from the metabolism of foods; one Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 \u00b0C.<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm19033248\" class=\"chemistry everyday-life\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Measuring Nutritional Calories<\/strong><\/div>\r\n<p id=\"fs-idm130611536\">The macronutrients in food are proteins, carbohydrates, and fats or oils. Proteins provide about 4 Calories per gram, carbohydrates also provide about 4 Calories per gram, and fats and oils provide about 9 Calories\/g. Nutritional labels on food packages show the caloric content of one serving of the food, as well as the breakdown into Calories from each of the three macronutrients (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_FoodLabel\">(Figure)<\/a>).<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_05_02_FoodLabel\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">(a) Macaroni and cheese contain energy in the form of the macronutrients in the food. (b) The food\u2019s nutritional information is shown on the package label. In the US, the energy content is given in Calories (per serving); the rest of the world usually uses kilojoules. (credit a: modification of work by \u201cRex Roof\u201d\/Flickr)<\/div>\r\n<span id=\"fs-idm70103536\" data-type=\"media\" data-alt=\"Two pictures are shown and labeled a and b. Picture a shows a close-up of a bowl of macaroni and cheese. Picture b is a food label that contains highlighted information in a table format. The top of the label reads \u201cSample label for macaroni and cheese.\u201d Below this are the words \u201cNutrition facts.\u201d Below this are two lines of highlighted text that read \u201cServing size one cup (228 g)\u201d and \u201cServings per container 2.\u201d A label to the left of these lines reads \u201cStart here\u201d and a right-facing arrow is beside these words. Below this are the words \u201ccheck calories\u201d which lie to the left of the phrases \u201cAmount per serving\u201d which is above the words \u201cCalories 250\u201d and \u201cCalories from fat 210.\u201d The next segment of the label is highlighted and contains five phrases \u201cTotal fat 12 g,\u201d \u201cSaturated fat 3 g,\u201d \u201cTrans fat 3 g,\u201d \u201cCholesterol 30 m g,\u201d and \u201cSodium 470 m g.\u201d The phrase \u201cLimit these nutrients\u201d lies to the left of these five phrases. The phrase below these is \u201cTotal carbohydrates 31 g\u201d and is followed by a highlighted phrase, \u201cDietary fiber 0 g.\u201d Below this are the phrases \u201cSugars 5 g\u201d and \u201cProteins 5 g.\u201d Below this is a highlighted portion containing the phrases \u201cVitamin A,\u201d \u201cVitamin C,\u201d \u201cCalcium,\u201d and \u201cIron.\u201d A label to the left of these terms states \u201cGet enough of these nutrients.\u201d The bottom of the label is labeled \u201cFootnote\u201d and reads \u201cPercent daily values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.\u201d Each of the highlighted terms in the table are in line with a percentage value to the right of the table. A note on the outer right of the table states \u201cQuick guide to % DV\u201d, \u201c5% or less is low\u201d and \u201c20% or more is high. The daily value for total fat is 18%, for saturated fat is 15%, for cholesterol is 10%, for sodium is 20%, for total carbohydrates is 10%, for dietary fiber is 0%, for vitamin A is 4%, for vitamin C is 2%, for calcium is 20%, and for iron is 4%.\u201d At the very bottom is a table that indicates calories at 2,000 and 2,500. For total fat the table indicates less than 65 g for 2,000 calories and 80 g from 2,500 calories. For saturated fat the table indicates less than 20 g for 2,000 calories and 25 g for 2,500 calories. For cholesterol the table indicates less than 300 m g for 2,000 calories and 300 m g for 2,500 calories. For sodium the table indicates less than 2,400 m g for 2,000 calories and 2,400 m g for 2,500 calories. For total carbohydrate the table indicates 300 g for 2,000 calories and 375 g for 2,500 calories. For dietary fiber the table indicates 25 g for 2,000 calories and 30 g for 2,500 calories.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_FoodLabel-1.jpg\" alt=\"Two pictures are shown and labeled a and b. Picture a shows a close-up of a bowl of macaroni and cheese. Picture b is a food label that contains highlighted information in a table format. The top of the label reads \u201cSample label for macaroni and cheese.\u201d Below this are the words \u201cNutrition facts.\u201d Below this are two lines of highlighted text that read \u201cServing size one cup (228 g)\u201d and \u201cServings per container 2.\u201d A label to the left of these lines reads \u201cStart here\u201d and a right-facing arrow is beside these words. Below this are the words \u201ccheck calories\u201d which lie to the left of the phrases \u201cAmount per serving\u201d which is above the words \u201cCalories 250\u201d and \u201cCalories from fat 210.\u201d The next segment of the label is highlighted and contains five phrases \u201cTotal fat 12 g,\u201d \u201cSaturated fat 3 g,\u201d \u201cTrans fat 3 g,\u201d \u201cCholesterol 30 m g,\u201d and \u201cSodium 470 m g.\u201d The phrase \u201cLimit these nutrients\u201d lies to the left of these five phrases. The phrase below these is \u201cTotal carbohydrates 31 g\u201d and is followed by a highlighted phrase, \u201cDietary fiber 0 g.\u201d Below this are the phrases \u201cSugars 5 g\u201d and \u201cProteins 5 g.\u201d Below this is a highlighted portion containing the phrases \u201cVitamin A,\u201d \u201cVitamin C,\u201d \u201cCalcium,\u201d and \u201cIron.\u201d A label to the left of these terms states \u201cGet enough of these nutrients.\u201d The bottom of the label is labeled \u201cFootnote\u201d and reads \u201cPercent daily values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.\u201d Each of the highlighted terms in the table are in line with a percentage value to the right of the table. A note on the outer right of the table states \u201cQuick guide to % DV\u201d, \u201c5% or less is low\u201d and \u201c20% or more is high. The daily value for total fat is 18%, for saturated fat is 15%, for cholesterol is 10%, for sodium is 20%, for total carbohydrates is 10%, for dietary fiber is 0%, for vitamin A is 4%, for vitamin C is 2%, for calcium is 20%, and for iron is 4%.\u201d At the very bottom is a table that indicates calories at 2,000 and 2,500. For total fat the table indicates less than 65 g for 2,000 calories and 80 g from 2,500 calories. For saturated fat the table indicates less than 20 g for 2,000 calories and 25 g for 2,500 calories. For cholesterol the table indicates less than 300 m g for 2,000 calories and 300 m g for 2,500 calories. For sodium the table indicates less than 2,400 m g for 2,000 calories and 2,400 m g for 2,500 calories. For total carbohydrate the table indicates 300 g for 2,000 calories and 375 g for 2,500 calories. For dietary fiber the table indicates 25 g for 2,000 calories and 30 g for 2,500 calories.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm42605520\">For the example shown in (b), the total energy per 228-g portion is calculated by:<\/p>\r\n\r\n<div id=\"fs-idm196775520\" style=\"text-align: center\" data-type=\"equation\">(5 g protein \u00d74 Calories\/g) + (31 g carb \u00d7 4 Calories\/g) + (12 g fat \u00d7 9 Calories\/g) = 252 Calories<\/div>\r\n<p id=\"fs-idm63696\">So, you can use food labels to count your Calories. But where do the values come from? And how accurate are they? The caloric content of foods can be determined by using bomb calorimetry; that is, by burning the food and measuring the energy it contains. A sample of food is weighed, mixed in a blender, freeze-dried, ground into powder, and formed into a pellet. The pellet is burned inside a bomb calorimeter, and the measured temperature change is converted into energy per gram of food.<\/p>\r\n<p id=\"fs-idm53626320\">Today, the caloric content on food labels is derived using a method called the <span class=\"no-emphasis\" data-type=\"term\">Atwater system<\/span> that uses the average caloric content of the different chemical constituents of food, protein, carbohydrate, and fats. The average amounts are those given in the equation and are derived from the various results given by bomb calorimetry of whole foods. The carbohydrate amount is discounted a certain amount for the fiber content, which is indigestible carbohydrate. To determine the energy content of a food, the quantities of carbohydrate, protein, and fat are each multiplied by the average Calories per gram for each and the products summed to obtain the total energy.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm72852528\" class=\"chemistry link-to-learning\" data-type=\"note\">\r\n<p id=\"fs-idm56857472\">Click on this <a href=\"http:\/\/openstaxcollege.org\/l\/16USDA\">link<\/a> to access the US Department of Agriculture (USDA) National Nutrient Database, containing nutritional information on over 8000 foods.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm31992064\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idm25518976\">Calorimetry is used to measure the amount of thermal energy transferred in a chemical or physical process. This requires careful measurement of the temperature change that occurs during the process and the masses of the system and surroundings. These measured quantities are then used to compute the amount of heat produced or consumed in the process using known mathematical relations.<\/p>\r\n<p id=\"fs-idm11014384\">Calorimeters are designed to minimize energy exchange between their contents and the external environment. They range from simple coffee cup calorimeters used by introductory chemistry students to sophisticated bomb calorimeters used to determine the energy content of food.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"fs-idm18398304\" class=\"exercises\" data-depth=\"1\">\r\n<div id=\"fs-idp47244464\" data-type=\"exercise\">\r\n<div id=\"fs-idp47244720\" data-type=\"problem\">\r\n<p id=\"fs-idp47244976\"><strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em\">Footnotes<\/span><\/strong><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div data-type=\"footnote-refs\">\r\n<ul data-list-type=\"bulleted\" data-bullet-style=\"none\">\r\n \t<li data-type=\"footnote-ref\"><a href=\"#footnote-ref1\" data-type=\"footnote-ref-link\">1<\/a><span data-type=\"footnote-ref-content\">Francis D. Reardon et al. \u201cThe Snellen human calorimeter revisited, re-engineered and upgraded: Design and performance characteristics.\u201d <em data-effect=\"italics\">Medical and Biological Engineering and Computing<\/em> 8 (2006)721\u201328, http:\/\/link.springer.com\/article\/10.1007\/s11517-006-0086-5.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\r\n<dl id=\"fs-idm56360448\">\r\n \t<dt>bomb calorimeter<\/dt>\r\n \t<dd id=\"fs-idm56360064\">device designed to measure the energy change for processes occurring under conditions of constant volume; commonly used for reactions involving solid and gaseous reactants or products<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm56359488\">\r\n \t<dt>calorimeter<\/dt>\r\n \t<dd id=\"fs-idm56359104\">device used to measure the amount of heat absorbed or released in a chemical or physical process<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm56358720\">\r\n \t<dt>calorimetry<\/dt>\r\n \t<dd id=\"fs-idm56358336\">process of measuring the amount of heat involved in a chemical or physical process<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp41853040\">\r\n \t<dt>surroundings<\/dt>\r\n \t<dd id=\"fs-idp41853424\">all matter other than the system being studied<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp41853808\">\r\n \t<dt>system<\/dt>\r\n \t<dd id=\"fs-idp41854192\">portion of matter undergoing a chemical or physical change being studied<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<p><strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em;background-color: #cbd4b6;color: #000000\">Learning Objectives<\/span><\/strong><\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Explain the technique of calorimetry<\/li>\n<li>Calculate and interpret heat and related properties using typical calorimetry data<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-idm52788928\">One technique we can use to measure the amount of heat involved in a chemical or physical process is known as <strong>calorimetry<\/strong>. Calorimetry is used to measure amounts of heat transferred to or from a substance. To do so, the heat is exchanged with a calibrated object (calorimeter). The temperature change measured by the calorimeter is used to derive the amount of heat transferred by the process under study. The measurement of heat transfer using this approach requires the definition of a <strong>system <\/strong>(the substance or substances undergoing the chemical or physical change) and its <strong>surroundings <\/strong>(all other matter, including components of the measurement apparatus, that serve to either provide heat to the system or absorb heat from the system).<\/p>\n<p id=\"fs-idm64462704\">A <strong>calorimeter <\/strong>is a device used to measure the amount of heat involved in a chemical or physical process. For example, when an exothermic reaction occurs in solution in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. When an endothermic reaction occurs, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HeatMeas\">(Figure)<\/a>). The temperature change, along with the specific heat and mass of the solution, can then be used to calculate the amount of heat involved in either case.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_HeatMeas\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">In a calorimetric determination, either (a) an exothermic process occurs and heat, <em data-effect=\"italics\">q<\/em>, is negative, indicating that thermal energy is transferred from the system to its surroundings, or (b) an endothermic process occurs and heat, <em data-effect=\"italics\">q<\/em>, is positive, indicating that thermal energy is transferred from the surroundings to the system.<\/div>\n<p><span id=\"fs-idp17874784\" data-type=\"media\" data-alt=\"Two diagrams labeled a and b are shown. Each is made up of two rectangular containers with a thermometer inserted into the top right and extending inside. There is a right facing arrow connecting each box in each diagram. The left container in diagram a depicts a pink and green swirling solution with the terms \u201cExothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms pointing to \u201cq.\u201d The labels \u201cSolution\u201d and \u201cSurroundings\u201d are written at the bottom of the container. The right container in diagram a has the term \u201cSolution\u201d written at the bottom of the container and a red arrow facing up near the thermometer with the phrase \u201cTemperature increased\u201d next to it. The pink and green swirls are more blended in this container. The left container in diagram b depicts a purple and blue swirling solution with the terms \u201cEndothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms and \u201cSolution\u201d and \u201cSurroundings\u201d written at the bottom. The arrows point away from the letter \u201cq.\u201d The right container in diagram b has the term \u201cSolution\u201d written at the bottom and a red arrow facing down near the thermometer with the phrase \u201cTemperature decreased\u201d next to it. The blue and purple swirls are more blended in this container.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HeatMeas-1.jpg\" alt=\"Two diagrams labeled a and b are shown. Each is made up of two rectangular containers with a thermometer inserted into the top right and extending inside. There is a right facing arrow connecting each box in each diagram. The left container in diagram a depicts a pink and green swirling solution with the terms \u201cExothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms pointing to \u201cq.\u201d The labels \u201cSolution\u201d and \u201cSurroundings\u201d are written at the bottom of the container. The right container in diagram a has the term \u201cSolution\u201d written at the bottom of the container and a red arrow facing up near the thermometer with the phrase \u201cTemperature increased\u201d next to it. The pink and green swirls are more blended in this container. The left container in diagram b depicts a purple and blue swirling solution with the terms \u201cEndothermic process\u201d and \u201cSystem\u201d written in the center with arrows facing away from the terms and \u201cSolution\u201d and \u201cSurroundings\u201d written at the bottom. The arrows point away from the letter \u201cq.\u201d The right container in diagram b has the term \u201cSolution\u201d written at the bottom and a red arrow facing down near the thermometer with the phrase \u201cTemperature decreased\u201d next to it. The blue and purple swirls are more blended in this container.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm75322144\">Scientists use well-insulated calorimeters that all but prevent the transfer of heat between the calorimeter and its environment, which effectively limits the \u201csurroundings\u201d to the nonsystem components with the calorimeter (and the calorimeter itself). This enables the accurate determination of the heat involved in chemical processes, the energy content of foods, and so on. General chemistry students often use simple calorimeters constructed from polystyrene cups (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_Calorim\">(Figure)<\/a>). These easy-to-use \u201ccoffee cup\u201d calorimeters allow more heat exchange with the outside environment, and therefore produce less accurate energy values.<\/p>\n<div id=\"CNX_Chem_05_02_Calorim\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">A simple calorimeter can be constructed from two polystyrene cups. A thermometer and stirrer extend through the cover into the reaction mixture.<\/div>\n<p><span id=\"fs-idm11505008\" data-type=\"media\" data-alt=\"Two Styrofoam cups are shown nested in one another with a cover over the top. A thermometer and stirring rod are inserted through the cover and into the solution inside the cup, which is shown as a cut-away. The stirring rod has a double headed arrow next to it facing up and down. The liquid mixture inside the cup is labeled \u201cReaction mixture.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_Calorim-1.jpg\" alt=\"Two Styrofoam cups are shown nested in one another with a cover over the top. A thermometer and stirring rod are inserted through the cover and into the solution inside the cup, which is shown as a cut-away. The stirring rod has a double headed arrow next to it facing up and down. The liquid mixture inside the cup is labeled \u201cReaction mixture.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm10930512\">Commercial solution calorimeters are also available. Relatively inexpensive calorimeters often consist of two thin-walled cups that are nested in a way that minimizes thermal contact during use, along with an insulated cover, handheld stirrer, and simple thermometer. More expensive calorimeters used for industry and research typically have a well-insulated, fully enclosed reaction vessel, motorized stirring mechanism, and a more accurate temperature sensor (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_Calorim2\">(Figure)<\/a>).<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_Calorim2\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Commercial solution calorimeters range from (a) simple, inexpensive models for student use to (b) expensive, more accurate models for industry and research.<\/div>\n<p><span id=\"fs-idm53300432\" data-type=\"media\" data-alt=\"Two diagrams are shown and labeled a and b. Diagram a depicts a thermometer which passes through a disk-like insulating cover and into a metal cylinder which is labeled \u201cmetal inner vessel,\u201d which is in turn nested in a metal cylinder labeled \u201cmetal outer vessel.\u201d The inner cylinder rests on an insulating support ring. A stirrer passes through the insulating cover and into the inner cylinder as well. Diagram b shows an inner metal vessel half full of liquid resting on an insulating support ring and nested in a metal outer vessel. A precision temperature probe and motorized stirring rod are placed into the solution in the inner vessel and connected by wires to equipment exterior to the set-up.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_Calorim2-1.jpg\" alt=\"Two diagrams are shown and labeled a and b. Diagram a depicts a thermometer which passes through a disk-like insulating cover and into a metal cylinder which is labeled \u201cmetal inner vessel,\u201d which is in turn nested in a metal cylinder labeled \u201cmetal outer vessel.\u201d The inner cylinder rests on an insulating support ring. A stirrer passes through the insulating cover and into the inner cylinder as well. Diagram b shows an inner metal vessel half full of liquid resting on an insulating support ring and nested in a metal outer vessel. A precision temperature probe and motorized stirring rod are placed into the solution in the inner vessel and connected by wires to equipment exterior to the set-up.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm10925216\">Before discussing the calorimetry of chemical reactions, consider a simpler example that illustrates the core idea behind calorimetry. Suppose we initially have a high-temperature substance, such as a hot piece of metal (M), and a low-temperature substance, such as cool water (W). If we place the metal in the water, heat will flow from M to W. The temperature of M will decrease, and the temperature of W will increase, until the two substances have the same temperature\u2014that is, when they reach thermal equilibrium (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HeatTrans2\">(Figure)<\/a>). If this occurs in a calorimeter, ideally all of this heat transfer occurs between the two substances, with no heat gained or lost by either its external environment. Under these ideal circumstances, the net heat change is zero:<\/p>\n<div id=\"fs-idm194903168\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>substance M<\/sub> + <em>q<\/em><sub>substance W<\/sub> =0<\/div>\n<p id=\"fs-idp41620800\">This relationship can be rearranged to show that the heat gained by substance M is equal to the heat lost by substance W:<\/p>\n<div id=\"fs-idm280055136\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>substance M <\/sub>= &#8211;<em>q<\/em><sub>substance W<\/sub><\/div>\n<p id=\"fs-idm129199216\">The magnitude of the heat is therefore the same for both substances, and the negative sign merely shows that <em data-effect=\"italics\">q<\/em><sub>substance M<\/sub> and <em data-effect=\"italics\">q<\/em><sub>substance W<\/sub> are opposite in direction of heat flow (gain or loss) but does not indicate the arithmetic sign of either <em data-effect=\"italics\">q<\/em> value (that is determined by whether the matter in question gains or loses heat, per definition). In the specific situation described, <em data-effect=\"italics\">q<\/em><sub>substance M<\/sub> is a negative value and <em data-effect=\"italics\">q<\/em><sub>substance W<\/sub> is positive, since heat is transferred from M to W.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_HeatTrans2\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">In a simple calorimetry process, (a) heat, <em data-effect=\"italics\">q<\/em>, is transferred from the hot metal, M, to the cool water, W, until (b) both are at the same temperature.<\/div>\n<p><span id=\"fs-idm50825408\" data-type=\"media\" data-alt=\"Two diagrams are shown and labeled a and b. Each diagram is composed of a rectangular container with a thermometer inserted inside from the top right corner. Both containers are connected by a right-facing arrow. Both containers are full of water, which is depicted by the letter \u201cW,\u201d and each container has a square in the middle which represents a metal which is labeled with a letter \u201cM.\u201d In diagram a, the metal is drawn in brown and has three arrows facing away from it. Each arrow has the letter \u201cq\u201d at its end. The metal is labeled \u201csystem\u201d and the water is labeled \u201csurroundings.\u201d The thermometer in this diagram has a relatively low reading. In diagram b, the metal is depicted in purple and the thermometer has a relatively high reading.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HeatTrans2-1.jpg\" alt=\"Two diagrams are shown and labeled a and b. Each diagram is composed of a rectangular container with a thermometer inserted inside from the top right corner. Both containers are connected by a right-facing arrow. Both containers are full of water, which is depicted by the letter \u201cW,\u201d and each container has a square in the middle which represents a metal which is labeled with a letter \u201cM.\u201d In diagram a, the metal is drawn in brown and has three arrows facing away from it. Each arrow has the letter \u201cq\u201d at its end. The metal is labeled \u201csystem\u201d and the water is labeled \u201csurroundings.\u201d The thermometer in this diagram has a relatively low reading. In diagram b, the metal is depicted in purple and the thermometer has a relatively high reading.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idp13199280\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm94530896\"><strong>Heat Transfer between Substances at Different Temperatures:<\/strong><\/p>\n<p>A 360.0-g piece of rebar (a steel rod used for reinforcing concrete) is dropped into 425 mL of water at 24.0 \u00b0C. The final temperature of the water was measured as 42.7 \u00b0C. Calculate the initial temperature of the piece of rebar. Assume the specific heat of steel is approximately the same as that for iron (<a class=\"autogenerated-content\" href=\"\/contents\/fae98e81-a194-4023-9468-aafca1dc4674#fs-idm68801008\">(Figure)<\/a>), and that all heat transfer occurs between the rebar and the water (there is no heat exchange with the surroundings).<\/p>\n<p id=\"fs-idp13157184\"><strong>Solution:<\/strong><\/p>\n<p>The temperature of the water increases from 24.0 \u00b0C to 42.7 \u00b0C, so the water absorbs heat. That heat came from the piece of rebar, which initially was at a higher temperature. Assuming that all heat transfer was between the rebar and the water, with no heat \u201clost\u201d to the outside environment, then <em data-effect=\"italics\">heat given off by rebar = \u2212heat taken in by water<\/em>, or:<\/p>\n<div id=\"fs-idm107179568\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>rebar <\/sub>= &#8211;<em>q<\/em><sub>water<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp46728032\">Since we know how heat is related to other measurable quantities, we have:<\/p>\n<div id=\"fs-idm52673840\" style=\"text-align: center\" data-type=\"equation\">(<em>c<\/em> \u00d7 <em>m<\/em> <span style=\"font-size: 1em\">\u00d7 \u0394<em>T<\/em>)<sub>rebar<\/sub> = -(<em>c<\/em> \u00d7 <em>m<\/em>\u00d7 \u0394<em>T<\/em>)<sub>water<\/sub><\/span><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp47392976\">Letting f = final and i = initial, in expanded form, this becomes:<\/p>\n<div id=\"fs-idp7508656\" style=\"text-align: center\" data-type=\"equation\"><em>c<span style=\"font-size: 1em\"><sub>rebar<\/sub><\/span><\/em> \u00d7 <em>m<span style=\"font-size: 1em\"><sub>rebar<\/sub><\/span><\/em> <span style=\"font-size: 1em\">\u00d7 (<em>T<\/em><sub>f,rebar<\/sub> &#8211; <em>T<\/em><sub>i,rebar<\/sub>) = &#8211;<em>c<sub>water<\/sub><\/em> \u00d7 <em>m<sub>water<\/sub><\/em>\u00d7 (<em>T<\/em><sub>f,water<\/sub> &#8211; <em>T<\/em><sub>i,water<\/sub>)<\/span><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm100431536\">The density of water is 1.0 g\/mL, so 425 mL of water = 425 g. Noting that the final temperature of both the rebar and water is 42.7 \u00b0C, substituting known values yields:<\/p>\n<div id=\"fs-idm160292560\" style=\"text-align: center\" data-type=\"equation\">(0.449 J\/g \u00b0C)(360.0 g)(42.7\u00b0C &#8211; T<sub>i,rebar<\/sub>)=-(4.184 J\/g \u00b0C)(425 g)(42.7\u00b0C -24.0\u00b0C)<\/div>\n<div id=\"fs-idp7310352\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1268 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-300x32.png\" alt=\"\" width=\"375\" height=\"40\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-300x32.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-768x81.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-225x24.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a-350x37.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2a.png 949w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm56113136\">Solving this gives <em data-effect=\"italics\">T<\/em><sub>i,rebar<\/sub>= 248 \u00b0C, so the initial temperature of the rebar was 248 \u00b0C.<\/p>\n<p id=\"fs-idm82711952\"><strong>Check Your Learning:<\/strong><\/p>\n<p>A 248-g piece of copper is dropped into 390. mL of water at 22.6 \u00b0C. The final temperature of the water was measured as 39.9 \u00b0C. Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm20275344\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm12419600\">The initial temperature of the copper was 336 \u00b0C.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p id=\"fs-idp12008976\"><strong>Check Your Learning:<\/strong><\/p>\n<p>A 248-g piece of copper initially at 314 \u00b0C is dropped into 390. mL of water initially at 22.6 \u00b0C. Assuming that all heat transfer occurs between the copper and the water, calculate the final temperature.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm17192400\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm84058400\">The final temperature (reached by both copper and water) is 38.7 \u00b0C.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idm1809184\">This method can also be used to determine other quantities, such as the specific heat of an unknown metal.<\/p>\n<div id=\"fs-idm80667088\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm92661904\"><strong>Identifying a Metal by Measuring Specific Heat:<\/strong><\/p>\n<p>A 59.7 g piece of metal that had been submerged in boiling water was quickly transferred into 60.0 mL of water initially at 22.0 \u00b0C. The final temperature is 28.5 \u00b0C. Use these data to determine the specific heat of the metal. Use this result to identify the metal.<\/p>\n<p id=\"fs-idm56342080\"><strong>Solution:<\/strong><\/p>\n<p>Assuming perfect heat transfer, <em data-effect=\"italics\">heat given off by metal = \u2212heat taken in by water<\/em>, or:<\/p>\n<div id=\"fs-idm199710176\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>metal <\/sub>= &#8211;<em>q<\/em><sub>water<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<p>In expanded form, this is:<\/p>\n<p style=\"text-align: center\"><em>c<\/em><sub>metal<\/sub> \u00d7 <em>m<sub>metal<\/sub><\/em>\u00a0<span style=\"font-size: 1em\">\u00d7 (<em>T<\/em><sub>f,metal<\/sub>\u00a0&#8211; <em>T<\/em><sub>i,metal<\/sub>) = &#8211;<em>c<sub>water<\/sub><\/em> \u00d7 <em>m<sub>water<\/sub><\/em>\u00d7 (<em>T<\/em><sub>f,water<\/sub> &#8211; <em>T<\/em><sub>i,water<\/sub>)<\/span><\/p>\n<p id=\"fs-idm9602288\">Noting that since the metal was submerged in boiling water, its initial temperature was 100.0 \u00b0C; and that for water, 60.0 mL = 60.0 g; we have:<\/p>\n<div id=\"fs-idm127022128\" style=\"text-align: center\" data-type=\"equation\">(<em>c<\/em><sub>metal<\/sub>)(59.7 g)(28.5\u00b0C &#8211; 100.0\u00b0C)=-(4.184 J\/g \u00b0C)(60.0 g)(28.5\u00b0C -22.0\u00b0C)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm4520800\">Solving this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1269 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-300x38.png\" alt=\"\" width=\"332\" height=\"42\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-300x38.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-768x97.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-225x28.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b-350x44.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/5.2b.png 872w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/p>\n<p id=\"fs-idm61018208\">Comparing this with values in the table of specific heat capacities, our experimental specific heat is closest to the value for copper (0.39 J\/g \u00b0C), so we identify the metal as copper.<\/p>\n<p id=\"fs-idm42342688\"><strong>Check Your Learning:<\/strong><\/p>\n<p>A 92.9-g piece of a silver\/gray metal is heated to 178.0 \u00b0C, and then quickly transferred into 75.0 mL of water initially at 24.0 \u00b0C. After 5 minutes, both the metal and the water have reached the same temperature: 29.7 \u00b0C. Determine the specific heat and the identity of the metal. (Note: You should find that the specific heat is close to that of two different metals. Explain how you can confidently determine the identity of the metal).<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm64160064\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm19048032\"><em data-effect=\"italics\">c<\/em><sub>metal<\/sub>= 0.13 J\/g \u00b0C<\/p>\n<p id=\"fs-idm40554112\">This specific heat is close to that of either gold or lead. It would be difficult to determine which metal this was based solely on the numerical values. However, the observation that the metal is silver\/gray in addition to the value for the specific heat indicates that the metal is lead.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idp8565200\">When we use calorimetry to determine the heat involved in a chemical reaction, the same principles we have been discussing apply. The amount of heat absorbed by the calorimeter is often small enough that we can neglect it (though not for highly accurate measurements, as discussed later), and the calorimeter minimizes energy exchange with the outside environment. Because energy is neither created nor destroyed during a chemical reaction, the heat produced or consumed in the reaction (the \u201csystem\u201d), <em data-effect=\"italics\">q<\/em><sub>reaction<\/sub>, plus the heat absorbed or lost by the solution (the \u201csurroundings\u201d), <em data-effect=\"italics\">q<\/em><sub>solution<\/sub>, must add up to zero:<\/p>\n<div id=\"fs-idm289467200\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> + <em>q<\/em><sub>solution<\/sub> = 0<\/div>\n<p id=\"fs-idm98090832\">This means that the amount of heat produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution:<\/p>\n<div id=\"fs-idm208991056\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = &#8211;<em>q<\/em><sub>solution<\/sub><\/div>\n<p id=\"fs-idm68084048\">This concept lies at the heart of all calorimetry problems and calculations.<\/p>\n<div id=\"fs-idm19242032\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm66182640\"><strong>Heat Produced by an Exothermic Reaction:<\/strong><\/p>\n<p>When 50.0 mL of 1.00 M HCl(<em data-effect=\"italics\">aq<\/em>) and 50.0 mL of 1.00 M NaOH(<em data-effect=\"italics\">aq<\/em>), both at 22.0 \u00b0C, are added to a coffee cup calorimeter, the temperature of the mixture reaches a maximum of 28.9 \u00b0C. What is the approximate amount of heat produced by this reaction?<\/p>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idm32936848\" style=\"text-align: center\" data-type=\"equation\">HCl(<em>aq<\/em>) + NaOH(<em>aq<\/em>) \u27f6 NaCl(<em>aq<\/em>)+ H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm73607008\"><strong>Solution:<\/strong><\/p>\n<p>To visualize what is going on, imagine that you could combine the two solutions so quickly that no reaction took place while they mixed; then after mixing, the reaction took place. At the instant of mixing, you have 100.0 mL of a mixture of HCl and NaOH at 22.0 \u00b0C. The HCl and NaOH then react until the solution temperature reaches 28.9 \u00b0C.<\/p>\n<p id=\"fs-idm74180672\">The heat given off by the reaction is equal to that taken in by the solution. Therefore:<\/p>\n<div id=\"fs-idm259063904\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = &#8211;<em>q<\/em><sub>solution<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm11281888\">(It is important to remember that this relationship only holds if the calorimeter does not absorb any heat from the reaction, and there is no heat exchange between the calorimeter and the outside environment.)<\/p>\n<p id=\"fs-idm12358560\">Next, we know that the heat absorbed by the solution depends on its specific heat, mass, and temperature change:<\/p>\n<div id=\"fs-idm174034752\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>solution<\/sub> = (<em>c<\/em> \u00d7 <em>m<\/em> \u00d7 \u0394<em>T<\/em>)<sub>solution<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp12432\">To proceed with this calculation, we need to make a few more reasonable assumptions or approximations. Since the solution is aqueous, we can proceed as if it were water in terms of its specific heat and mass values. The density of water is approximately 1.0 g\/mL, so 100.0 mL has a mass of about 1.0 \u00d7 10<sup>2<\/sup> g (two significant figures). The specific heat of water is 4.184 J\/g \u00b0C, so we use that for the specific heat of the solution. Substituting these values gives:<\/p>\n<div id=\"fs-idm261390032\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>solution<\/sub> = (4.184 J\/g \u00b0C) \u00d7 (1.0 x 10<sup>2<\/sup> g)(28.9\u00b0C -22.0\u00b0C) = 2.9 \u00d7 10<sup>3 <\/sup>J<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm6689328\">Finally, since we are trying to find the heat of the reaction, we have:<\/p>\n<div id=\"fs-idm178566000\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>reaction<\/sub> = &#8211;<em>q<\/em><sub>solution <\/sub>=-2.9 \u00d7 10<sup>3 <\/sup>J<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm66484944\">The negative sign indicates that the reaction is exothermic. It produces 2.9 kJ of heat.<\/p>\n<p id=\"fs-idm55750416\"><strong>Check Your Learning:<\/strong><\/p>\n<p>When 100 mL of 0.200 M NaCl(<em data-effect=\"italics\">aq<\/em>) and 100 mL of 0.200 M AgNO<sub>3<\/sub>(<em data-effect=\"italics\">aq<\/em>), both at 21.9 \u00b0C, are mixed in a coffee cup calorimeter, the temperature increases to 23.5 \u00b0C as solid AgCl forms. How much heat is produced by this precipitation reaction? What assumptions did you make to determine your value?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm9227984\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm94618544\">1.34 \u00d7 10<sup>3<\/sup> J; assume no heat is absorbed by the calorimeter, no heat is exchanged between the calorimeter and its surroundings, and that the specific heat and mass of the solution are the same as those for water<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm9530672\" class=\"chemistry everyday-life\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Thermochemistry of Hand Warmers<\/strong><\/div>\n<p id=\"fs-idm19355440\">When working or playing outdoors on a cold day, you might use a hand warmer to warm your hands (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_HandWarmer\">(Figure)<\/a>). A common reusable hand warmer contains a supersaturated solution of NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> (sodium acetate) and a metal disc. Bending the disk creates nucleation sites around which the metastable NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> quickly crystallizes (a later chapter on solutions will investigate saturation and supersaturation in more detail).<\/p>\n<p id=\"fs-idm213136\">The process NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) \u27f6NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub>(<em>s<\/em>) is exothermic, and the heat produced by this process is absorbed by your hands, thereby warming them (at least for a while). If the hand warmer is reheated, the NaC<sub>2<\/sub>H<sub>3<\/sub>O<sub>2<\/sub> redissolves and can be reused.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_HandWarmer\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Chemical hand warmers produce heat that warms your hand on a cold day. In this one, you can see the metal disc that initiates the exothermic precipitation reaction. (credit: modification of work by Science Buddies TV\/YouTube)<\/div>\n<p><span id=\"fs-idm20337008\" data-type=\"media\" data-alt=\"A series of three photos is shown. There are two right-facing arrows connecting one photo to the next. The first photo shows a chemical hand warmer. It is a bag that contains a clear, colorless liquid. There is a white disk located to the right inside the bag. The second photo shows the same thing, except the white disc has become a white, cloudy substance. The third photo shows the entire bag filled with this white substance.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_HandWarmer-1.jpg\" alt=\"A series of three photos is shown. There are two right-facing arrows connecting one photo to the next. The first photo shows a chemical hand warmer. It is a bag that contains a clear, colorless liquid. There is a white disk located to the right inside the bag. The second photo shows the same thing, except the white disc has become a white, cloudy substance. The third photo shows the entire bag filled with this white substance.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm15246800\">Another common hand warmer produces heat when it is ripped open, exposing iron and water in the hand warmer to oxygen in the air. One simplified version of this exothermic reaction is 2Fe(<em>s<\/em>) + (3\/2)O<sub>2<\/sub>(<em>g<\/em>) \u27f6 Fe<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>). Salt in the hand warmer catalyzes the reaction, so it produces heat more rapidly; cellulose, vermiculite, and activated carbon help distribute the heat evenly. Other types of hand warmers use lighter fluid (a platinum catalyst helps lighter fluid oxidize exothermically), charcoal (charcoal oxidizes in a special case), or electrical units that produce heat by passing an electrical current from a battery through resistive wires.<\/p>\n<\/div>\n<div id=\"fs-idm79691632\" class=\"chemistry link-to-learning\" data-type=\"note\">\n<p id=\"fs-idm81095744\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16Handwarmer\">link<\/a> shows the precipitation reaction that occurs when the disk in a chemical hand warmer is flexed.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-idp325184\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm52519632\"><strong>Heat Flow in an Instant Ice Pack:<\/strong><\/p>\n<p>When solid ammonium nitrate dissolves in water, the solution becomes cold. This is the basis for an \u201cinstant ice pack\u201d (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_IcePack\">(Figure)<\/a>). When 3.21 g of solid NH<sub>4<\/sub>NO<sub>3<\/sub> dissolves in 50.0 g of water at 24.9 \u00b0C in a calorimeter, the temperature decreases to 20.3 \u00b0C.<\/p>\n<p id=\"fs-idp41329920\">Calculate the value of <em data-effect=\"italics\">q<\/em> for this reaction and explain the meaning of its arithmetic sign. State any assumptions that you made.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_IcePack\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">An instant cold pack consists of a bag containing solid ammonium nitrate and a second bag of water. When the bag of water is broken, the pack becomes cold because the dissolution of ammonium nitrate is an endothermic process that removes thermal energy from the water. The cold pack then removes thermal energy from your body.<\/div>\n<p><span id=\"fs-idm30928704\" data-type=\"media\" data-alt=\"A diagram depicts a rectangular pack containing a white, solid substance and an interior bag full of water. The white solid is labeled \u201cammonium nitrate.\u201d The top of the packet has the words \u201cInstant Cold Pack\u201d written on it. It also has three pictograms, which from right to left, show a hand squeezing the pack, agitating the pack and placing the pack on a person\u2019s body. The bottom of the pack has printed words that read \u201csingle use only.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_IcePack-1.jpg\" alt=\"A diagram depicts a rectangular pack containing a white, solid substance and an interior bag full of water. The white solid is labeled \u201cammonium nitrate.\u201d The top of the packet has the words \u201cInstant Cold Pack\u201d written on it. It also has three pictograms, which from right to left, show a hand squeezing the pack, agitating the pack and placing the pack on a person\u2019s body. The bottom of the pack has printed words that read \u201csingle use only.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idp364256\"><strong>Solution:<\/strong><\/p>\n<p>We assume that the calorimeter prevents heat transfer between the solution and its external environment (including the calorimeter itself), in which case:<\/p>\n<div id=\"fs-idm127206368\" style=\"text-align: center\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = &#8211;<em>q<\/em><sub>soln<\/sub><\/div>\n<p id=\"fs-idm76420496\">with \u201crxn\u201d and \u201csoln\u201d used as shorthand for \u201creaction\u201d and \u201csolution,\u201d respectively.<\/p>\n<p id=\"fs-idm52847712\">Assuming also that the specific heat of the solution is the same as that for water, we have:<\/p>\n<div id=\"fs-idm183045408\" style=\"text-align: left\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = &#8211;<em>q<\/em><sub>soln <\/sub>= -(<em>c<\/em> \u00d7 <em>m<\/em> \u00d7 \u0394<em>T<\/em>)<sub>soln<\/sub><\/div>\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 = \u2212(4.184 J\/g \u00b0C)(53.2 g)(20.3\u00b0C -24.9\u00b0C)<\/div>\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 =\u2212(4.184 J\/g \u00b0C)(53.2\u00a0 g)(-4.6\u00b0C)<\/div>\n<div style=\"text-align: left\" data-type=\"equation\">\u00a0 \u00a0 \u00a0 \u00a0 =+1.0 \u00d7 <i>10<sup>3 <\/sup><\/i>J<i> = +1.0 <\/i>kJ<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp8566608\">The positive sign for <em data-effect=\"italics\">q<\/em> indicates that the dissolution is an endothermic process.<\/p>\n<p id=\"fs-idm6778640\"><strong>Check Your Learning:<\/strong><\/p>\n<p>When a 3.00-g sample of KCl was added to 3.00 \u00d7 10<sup>2<\/sup> g of water in a coffee cup calorimeter, the temperature decreased by 1.05 \u00b0C. How much heat is involved in the dissolution of the KCl? What assumptions did you make?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm9544544\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm5945296\">1.33 kJ; assume that the calorimeter prevents heat transfer between the solution and its external environment (including the calorimeter itself) and that the specific heat of the solution is the same as that for water<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idm33984192\">If the amount of heat absorbed by a calorimeter is too large to neglect or if we require more accurate results, then we must take into account the heat absorbed both by the solution and by the calorimeter.<\/p>\n<p id=\"fs-idm75111136\">The calorimeters described are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow accompanying processes that occur in solution. A different type of calorimeter that operates at constant volume, colloquially known as a <strong>bomb calorimeter<\/strong>, is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions. (The term \u201cbomb\u201d comes from the observation that these reactions can be vigorous enough to resemble explosions that would damage other calorimeters.) This type of calorimeter consists of a robust steel container (the \u201cbomb\u201d) that contains the reactants and is itself submerged in water (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_BombCalor\">(Figure)<\/a>). The sample is placed in the bomb, which is then filled with oxygen at high pressure. A small electrical spark is used to ignite the sample. The energy produced by the reaction is absorbed by the steel bomb and the surrounding water. The temperature increase is measured and, along with the known heat capacity of the calorimeter, is used to calculate the energy produced by the reaction. Bomb calorimeters require calibration to determine the heat capacity of the calorimeter and ensure accurate results. The calibration is accomplished using a reaction with a known <em data-effect=\"italics\">q<\/em>, such as a measured quantity of benzoic acid ignited by a spark from a nickel fuse wire that is weighed before and after the reaction. The temperature change produced by the known reaction is used to determine the heat capacity of the calorimeter. The calibration is generally performed each time before the calorimeter is used to gather research data.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_BombCalor\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(a) A bomb calorimeter is used to measure heat produced by reactions involving gaseous reactants or products, such as combustion. (b) The reactants are contained in the gas-tight \u201cbomb,\u201d which is submerged in water and surrounded by insulating materials. (credit a: modification of work by \u201cHarbor1\u201d\/Wikimedia commons)<\/div>\n<p><span id=\"fs-idp22458144\" data-type=\"media\" data-alt=\"A picture and a diagram are shown, labeled a and b, respectively. Picture a depicts a bomb calorimeter. It is a cube-shaped machine with a cavity in the top, a metal cylinder that is above the cavity, and a read-out panel attached to the top-right side. Diagram b depicts a cut away figure of a cube with a cylindrical container full of water in the middle of it. Another container, labeled \u201cbomb,\u201d sits inside of a smaller cylinder which holds a sample cup and is nested in the cylindrical container surrounded by the water. A black line extends into the water and is labeled \u201cPrecision thermometer.\u201d Two wires labeled \u201cElectrodes\u201d extend away from a cover that sits on top of the interior container. A read-out panel is located at the top right of the cube.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_BombCalor-1.jpg\" alt=\"A picture and a diagram are shown, labeled a and b, respectively. Picture a depicts a bomb calorimeter. It is a cube-shaped machine with a cavity in the top, a metal cylinder that is above the cavity, and a read-out panel attached to the top-right side. Diagram b depicts a cut away figure of a cube with a cylindrical container full of water in the middle of it. Another container, labeled \u201cbomb,\u201d sits inside of a smaller cylinder which holds a sample cup and is nested in the cylindrical container surrounded by the water. A black line extends into the water and is labeled \u201cPrecision thermometer.\u201d Two wires labeled \u201cElectrodes\u201d extend away from a cover that sits on top of the interior container. A read-out panel is located at the top right of the cube.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idm2366288\" class=\"chemistry link-to-learning\" data-type=\"note\">\n<p id=\"fs-idp41066256\">Click on this <a href=\"http:\/\/openstaxcollege.org\/l\/16BombCal\">link<\/a> to view how a bomb calorimeter is prepared for action.<\/p>\n<p id=\"fs-idm11069408\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16Calorcalcs\">site<\/a> shows calorimetric calculations using sample data.<\/p>\n<\/div>\n<div id=\"fs-idm49773520\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp23917952\"><strong>Bomb Calorimetry:<\/strong><\/p>\n<p>When 3.12 g of glucose, C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>, is burned in a bomb calorimeter, the temperature of the calorimeter increases from 23.8 \u00b0C to 35.6 \u00b0C. The bomb calorimeter assembly, which <em>includes<\/em> the water, has a heat capacity of 4.13 kJ\/\u00b0C. How much heat was produced by the combustion of the glucose sample?<\/p>\n<p id=\"fs-idm103829360\"><strong>Solution:<\/strong><\/p>\n<p>The combustion produces heat that is primarily absorbed by the bomb calorimetry assembly. (The amounts of heat absorbed by the reaction products and the unreacted excess oxygen are relatively small and dealing with them is beyond the scope of this text. We will neglect them in our calculations.)<\/p>\n<p id=\"fs-idm51439440\">The heat produced by the reaction is absorbed by the water and the bomb:<\/p>\n<div id=\"fs-idm137623248\" data-type=\"equation\"><em>q<\/em><sub>rxn<\/sub> = &#8211;<em>q<\/em><sub>calorimeter <\/sub><\/div>\n<div data-type=\"equation\">=-(4.31 kJ\/\u00b0C)(35.6\u00b0C &#8211; 23.8\u00b0C)<\/div>\n<div data-type=\"equation\">=-(4.31 kJ\/\u00b0C)(11.8\u00b0C)<\/div>\n<div data-type=\"equation\">=-50.8 kJ<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm51688848\">This reaction released 50.8 kJ of heat when 3.12 g of glucose was burned.<\/p>\n<p id=\"fs-idm39952704\"><strong>Check Your Learning:<\/strong><\/p>\n<p>When 0.963 g of benzene, C<sub>6<\/sub>H<sub>6<\/sub>, is burned in a bomb calorimeter, the temperature of the calorimeter increases by 8.39 \u00b0C. The bomb calorimetry assembly has a heat capacity of 4.65 kJ\/\u00b0C.. How much heat was produced by the combustion of the glucose sample?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm11360480\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm88592432\">39.0 kJ<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idm30236928\">Since the first one was constructed in 1899, 35 calorimeters have been built to measure the heat produced by a living person.<sup data-type=\"footnote-number\"><a href=\"#footnote1\" data-type=\"footnote-link\">1<\/a><\/sup> These whole-body calorimeters of various designs are large enough to hold an individual human being. More recently, whole-room calorimeters allow for relatively normal activities to be performed, and these calorimeters generate data that more closely reflect the real world. These calorimeters are used to measure the metabolism of individuals under different environmental conditions, different dietary regimes, and with different health conditions, such as diabetes. In humans, metabolism is typically measured in Calories per day. A <span data-type=\"term\">nutritional calorie (Calorie)<\/span> is the energy unit used to quantify the amount of energy derived from the metabolism of foods; one Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 \u00b0C.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm19033248\" class=\"chemistry everyday-life\" data-type=\"note\">\n<div data-type=\"title\"><strong>Measuring Nutritional Calories<\/strong><\/div>\n<p id=\"fs-idm130611536\">The macronutrients in food are proteins, carbohydrates, and fats or oils. Proteins provide about 4 Calories per gram, carbohydrates also provide about 4 Calories per gram, and fats and oils provide about 9 Calories\/g. Nutritional labels on food packages show the caloric content of one serving of the food, as well as the breakdown into Calories from each of the three macronutrients (<a class=\"autogenerated-content\" href=\"#CNX_Chem_05_02_FoodLabel\">(Figure)<\/a>).<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_05_02_FoodLabel\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(a) Macaroni and cheese contain energy in the form of the macronutrients in the food. (b) The food\u2019s nutritional information is shown on the package label. In the US, the energy content is given in Calories (per serving); the rest of the world usually uses kilojoules. (credit a: modification of work by \u201cRex Roof\u201d\/Flickr)<\/div>\n<p><span id=\"fs-idm70103536\" data-type=\"media\" data-alt=\"Two pictures are shown and labeled a and b. Picture a shows a close-up of a bowl of macaroni and cheese. Picture b is a food label that contains highlighted information in a table format. The top of the label reads \u201cSample label for macaroni and cheese.\u201d Below this are the words \u201cNutrition facts.\u201d Below this are two lines of highlighted text that read \u201cServing size one cup (228 g)\u201d and \u201cServings per container 2.\u201d A label to the left of these lines reads \u201cStart here\u201d and a right-facing arrow is beside these words. Below this are the words \u201ccheck calories\u201d which lie to the left of the phrases \u201cAmount per serving\u201d which is above the words \u201cCalories 250\u201d and \u201cCalories from fat 210.\u201d The next segment of the label is highlighted and contains five phrases \u201cTotal fat 12 g,\u201d \u201cSaturated fat 3 g,\u201d \u201cTrans fat 3 g,\u201d \u201cCholesterol 30 m g,\u201d and \u201cSodium 470 m g.\u201d The phrase \u201cLimit these nutrients\u201d lies to the left of these five phrases. The phrase below these is \u201cTotal carbohydrates 31 g\u201d and is followed by a highlighted phrase, \u201cDietary fiber 0 g.\u201d Below this are the phrases \u201cSugars 5 g\u201d and \u201cProteins 5 g.\u201d Below this is a highlighted portion containing the phrases \u201cVitamin A,\u201d \u201cVitamin C,\u201d \u201cCalcium,\u201d and \u201cIron.\u201d A label to the left of these terms states \u201cGet enough of these nutrients.\u201d The bottom of the label is labeled \u201cFootnote\u201d and reads \u201cPercent daily values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.\u201d Each of the highlighted terms in the table are in line with a percentage value to the right of the table. A note on the outer right of the table states \u201cQuick guide to % DV\u201d, \u201c5% or less is low\u201d and \u201c20% or more is high. The daily value for total fat is 18%, for saturated fat is 15%, for cholesterol is 10%, for sodium is 20%, for total carbohydrates is 10%, for dietary fiber is 0%, for vitamin A is 4%, for vitamin C is 2%, for calcium is 20%, and for iron is 4%.\u201d At the very bottom is a table that indicates calories at 2,000 and 2,500. For total fat the table indicates less than 65 g for 2,000 calories and 80 g from 2,500 calories. For saturated fat the table indicates less than 20 g for 2,000 calories and 25 g for 2,500 calories. For cholesterol the table indicates less than 300 m g for 2,000 calories and 300 m g for 2,500 calories. For sodium the table indicates less than 2,400 m g for 2,000 calories and 2,400 m g for 2,500 calories. For total carbohydrate the table indicates 300 g for 2,000 calories and 375 g for 2,500 calories. For dietary fiber the table indicates 25 g for 2,000 calories and 30 g for 2,500 calories.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_05_02_FoodLabel-1.jpg\" alt=\"Two pictures are shown and labeled a and b. Picture a shows a close-up of a bowl of macaroni and cheese. Picture b is a food label that contains highlighted information in a table format. The top of the label reads \u201cSample label for macaroni and cheese.\u201d Below this are the words \u201cNutrition facts.\u201d Below this are two lines of highlighted text that read \u201cServing size one cup (228 g)\u201d and \u201cServings per container 2.\u201d A label to the left of these lines reads \u201cStart here\u201d and a right-facing arrow is beside these words. Below this are the words \u201ccheck calories\u201d which lie to the left of the phrases \u201cAmount per serving\u201d which is above the words \u201cCalories 250\u201d and \u201cCalories from fat 210.\u201d The next segment of the label is highlighted and contains five phrases \u201cTotal fat 12 g,\u201d \u201cSaturated fat 3 g,\u201d \u201cTrans fat 3 g,\u201d \u201cCholesterol 30 m g,\u201d and \u201cSodium 470 m g.\u201d The phrase \u201cLimit these nutrients\u201d lies to the left of these five phrases. The phrase below these is \u201cTotal carbohydrates 31 g\u201d and is followed by a highlighted phrase, \u201cDietary fiber 0 g.\u201d Below this are the phrases \u201cSugars 5 g\u201d and \u201cProteins 5 g.\u201d Below this is a highlighted portion containing the phrases \u201cVitamin A,\u201d \u201cVitamin C,\u201d \u201cCalcium,\u201d and \u201cIron.\u201d A label to the left of these terms states \u201cGet enough of these nutrients.\u201d The bottom of the label is labeled \u201cFootnote\u201d and reads \u201cPercent daily values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.\u201d Each of the highlighted terms in the table are in line with a percentage value to the right of the table. A note on the outer right of the table states \u201cQuick guide to % DV\u201d, \u201c5% or less is low\u201d and \u201c20% or more is high. The daily value for total fat is 18%, for saturated fat is 15%, for cholesterol is 10%, for sodium is 20%, for total carbohydrates is 10%, for dietary fiber is 0%, for vitamin A is 4%, for vitamin C is 2%, for calcium is 20%, and for iron is 4%.\u201d At the very bottom is a table that indicates calories at 2,000 and 2,500. For total fat the table indicates less than 65 g for 2,000 calories and 80 g from 2,500 calories. For saturated fat the table indicates less than 20 g for 2,000 calories and 25 g for 2,500 calories. For cholesterol the table indicates less than 300 m g for 2,000 calories and 300 m g for 2,500 calories. For sodium the table indicates less than 2,400 m g for 2,000 calories and 2,400 m g for 2,500 calories. For total carbohydrate the table indicates 300 g for 2,000 calories and 375 g for 2,500 calories. For dietary fiber the table indicates 25 g for 2,000 calories and 30 g for 2,500 calories.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm42605520\">For the example shown in (b), the total energy per 228-g portion is calculated by:<\/p>\n<div id=\"fs-idm196775520\" style=\"text-align: center\" data-type=\"equation\">(5 g protein \u00d74 Calories\/g) + (31 g carb \u00d7 4 Calories\/g) + (12 g fat \u00d7 9 Calories\/g) = 252 Calories<\/div>\n<p id=\"fs-idm63696\">So, you can use food labels to count your Calories. But where do the values come from? And how accurate are they? The caloric content of foods can be determined by using bomb calorimetry; that is, by burning the food and measuring the energy it contains. A sample of food is weighed, mixed in a blender, freeze-dried, ground into powder, and formed into a pellet. The pellet is burned inside a bomb calorimeter, and the measured temperature change is converted into energy per gram of food.<\/p>\n<p id=\"fs-idm53626320\">Today, the caloric content on food labels is derived using a method called the <span class=\"no-emphasis\" data-type=\"term\">Atwater system<\/span> that uses the average caloric content of the different chemical constituents of food, protein, carbohydrate, and fats. The average amounts are those given in the equation and are derived from the various results given by bomb calorimetry of whole foods. The carbohydrate amount is discounted a certain amount for the fiber content, which is indigestible carbohydrate. To determine the energy content of a food, the quantities of carbohydrate, protein, and fat are each multiplied by the average Calories per gram for each and the products summed to obtain the total energy.<\/p>\n<\/div>\n<div id=\"fs-idm72852528\" class=\"chemistry link-to-learning\" data-type=\"note\">\n<p id=\"fs-idm56857472\">Click on this <a href=\"http:\/\/openstaxcollege.org\/l\/16USDA\">link<\/a> to access the US Department of Agriculture (USDA) National Nutrient Database, containing nutritional information on over 8000 foods.<\/p>\n<\/div>\n<div id=\"fs-idm31992064\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idm25518976\">Calorimetry is used to measure the amount of thermal energy transferred in a chemical or physical process. This requires careful measurement of the temperature change that occurs during the process and the masses of the system and surroundings. These measured quantities are then used to compute the amount of heat produced or consumed in the process using known mathematical relations.<\/p>\n<p id=\"fs-idm11014384\">Calorimeters are designed to minimize energy exchange between their contents and the external environment. They range from simple coffee cup calorimeters used by introductory chemistry students to sophisticated bomb calorimeters used to determine the energy content of food.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-idm18398304\" class=\"exercises\" data-depth=\"1\">\n<div id=\"fs-idp47244464\" data-type=\"exercise\">\n<div id=\"fs-idp47244720\" data-type=\"problem\">\n<p id=\"fs-idp47244976\"><strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em\">Footnotes<\/span><\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"footnote-refs\">\n<ul data-list-type=\"bulleted\" data-bullet-style=\"none\">\n<li data-type=\"footnote-ref\"><a href=\"#footnote-ref1\" data-type=\"footnote-ref-link\">1<\/a><span data-type=\"footnote-ref-content\">Francis D. Reardon et al. \u201cThe Snellen human calorimeter revisited, re-engineered and upgraded: Design and performance characteristics.\u201d <em data-effect=\"italics\">Medical and Biological Engineering and Computing<\/em> 8 (2006)721\u201328, http:\/\/link.springer.com\/article\/10.1007\/s11517-006-0086-5.<\/span><\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\n<dl id=\"fs-idm56360448\">\n<dt>bomb calorimeter<\/dt>\n<dd id=\"fs-idm56360064\">device designed to measure the energy change for processes occurring under conditions of constant volume; commonly used for reactions involving solid and gaseous reactants or products<\/dd>\n<\/dl>\n<dl id=\"fs-idm56359488\">\n<dt>calorimeter<\/dt>\n<dd id=\"fs-idm56359104\">device used to measure the amount of heat absorbed or released in a chemical or physical process<\/dd>\n<\/dl>\n<dl id=\"fs-idm56358720\">\n<dt>calorimetry<\/dt>\n<dd id=\"fs-idm56358336\">process of measuring the amount of heat involved in a chemical or physical process<\/dd>\n<\/dl>\n<dl id=\"fs-idp41853040\">\n<dt>surroundings<\/dt>\n<dd id=\"fs-idp41853424\">all matter other than the system being studied<\/dd>\n<\/dl>\n<dl id=\"fs-idp41853808\">\n<dt>system<\/dt>\n<dd id=\"fs-idp41854192\">portion of matter undergoing a chemical or physical change being studied<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":1392,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-235","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":214,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/235","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/users\/1392"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions"}],"predecessor-version":[{"id":2207,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions\/2207"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/214"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/235\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=235"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=235"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=235"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}