{"id":200,"date":"2021-07-23T09:19:14","date_gmt":"2021-07-23T13:19:14","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/reaction-stoichiometry\/"},"modified":"2022-06-22T09:44:18","modified_gmt":"2022-06-22T13:44:18","slug":"reaction-stoichiometry","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/reaction-stoichiometry\/","title":{"raw":"4.3 Reaction Stoichiometry","rendered":"4.3 Reaction Stoichiometry"},"content":{"raw":"<strong>\u00a0<\/strong>\r\n<div class=\"textbox textbox--learning-objectives\">\r\n<h3><strong>Learning Objectives<\/strong><\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Explain the concept of stoichiometry as it pertains to chemical reactions<\/li>\r\n \t<li>Use balanced chemical equations to derive stoichiometric factors relating amounts of reactants and products<\/li>\r\n \t<li>Perform stoichiometric calculations involving mass, moles, and solution molarity<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"fs-idp65325120\">A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and products involved in the chemical change, allowing classification of the reaction. Coefficients provide the relative numbers of these chemical species, allowing a quantitative assessment of the relationships between the amounts of substances consumed and produced by the reaction. These quantitative relationships are known as the reaction\u2019s <strong>stoichiometry<\/strong>, a term derived from the Greek words <em data-effect=\"italics\">stoicheion<\/em> (meaning \u201celement\u201d) and <em data-effect=\"italics\">metron<\/em> (meaning \u201cmeasure\u201d). In this module, the use of balanced chemical equations for various stoichiometric applications is explored.<\/p>\r\n<p id=\"fs-idp92593072\">The general approach to using stoichiometric relationships is similar in concept to the way people go about many common activities. Food preparation, for example, offers an appropriate comparison. A recipe for making eight pancakes calls for 1 cup pancake mix, 3\/4 cup milk, and one egg. The \u201cequation\u201d representing the preparation of pancakes per this recipe is<\/p>\r\n\r\n<div id=\"fs-idp116126928\" data-type=\"equation\"><img class=\"wp-image-1175 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-300x39.png\" alt=\"\" width=\"331\" height=\"43\" \/><\/div>\r\n<p id=\"fs-idp78338704\">If two dozen pancakes are needed for a big family breakfast, the ingredient amounts must be increased proportionally according to the amounts given in the recipe. For example, the number of eggs required to make 24 pancakes is<\/p>\r\n\r\n<div id=\"fs-idp58586688\" data-type=\"equation\"><img class=\"size-medium wp-image-1176 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-300x62.png\" alt=\"\" width=\"300\" height=\"62\" \/><\/div>\r\n<p id=\"fs-idp98270672\">Balanced chemical equations are used in much the same fashion to determine the amount of one reactant required to react with a given amount of another reactant, or to yield a given amount of product, and so forth. The coefficients in the balanced equation are used to derive <span data-type=\"term\">stoichiometric factors<\/span> that permit computation of the desired quantity. To illustrate this idea, consider the production of ammonia by reaction of hydrogen and nitrogen:<\/p>\r\n\r\n<div id=\"fs-idp124603552\" style=\"text-align: center\" data-type=\"equation\">N<sub>2<\/sub>(<em>g<\/em>) + 3H<sub>2<\/sub>(<em>g<\/em>) \u27f6 2NH<sub>3<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idp124955072\">This equation shows ammonia molecules are produced from hydrogen molecules in a 2:3 ratio, and stoichiometric factors may be derived using any amount (number) unit:<\/p>\r\n\r\n<div id=\"fs-idp64965808\" data-type=\"equation\"><img class=\"wp-image-1178 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-300x31.png\" alt=\"\" width=\"397\" height=\"41\" \/><\/div>\r\n<p id=\"fs-idp56404080\">These stoichiometric factors can be used to compute the number of ammonia molecules produced from a given number of hydrogen molecules, or the number of hydrogen molecules required to produce a given number of ammonia molecules. Similar factors may be derived for any pair of substances in any chemical equation.<\/p>\r\n\r\n<div id=\"fs-idp48900096\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp77269456\"><strong>Moles of Reactant Required in a Reaction:<\/strong><\/p>\r\nHow many moles of I<sub>2<\/sub> are required to react with 0.429 mol of Al according to the following equation (see <a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_iodine\">(Figure)<\/a>)?\r\n<div id=\"fs-idp147980704\" style=\"text-align: center\" data-type=\"equation\">2Al + 3I<sub>2<\/sub> \u27f6 2AlI<sub>3<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"CNX_Chem_04_03_iodine\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Aluminum and iodine react to produce aluminum iodide. The heat of the reaction vaporizes some of the solid iodine as a purple vapor. (credit: modification of work by Mark Ott)<\/div>\r\n<span id=\"fs-idp52310320\" data-type=\"media\" data-alt=\"This figure shows three photos with an arrow leading from one to the next. The first photo shows a small pile of iodine and aluminum on a white surface. The second photo shows a small amount of purple smoke coming from the pile. The third photo shows a large amount of purple and gray smoke coming from the pile.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_iodine-1.jpg\" alt=\"This figure shows three photos with an arrow leading from one to the next. The first photo shows a small pile of iodine and aluminum on a white surface. The second photo shows a small amount of purple smoke coming from the pile. The third photo shows a large amount of purple and gray smoke coming from the pile.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm34598272\"><strong>Solution:<\/strong><\/p>\r\nReferring to the balanced chemical equation, the stoichiometric factor relating the two substances of interest is <img class=\"alignnone size-full wp-image-1179\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3d.png\" alt=\"\" width=\"76\" height=\"48\" \/>. The molar amount of iodine is derived by multiplying the provided molar amount of aluminum by this factor:\r\n\r\n<span id=\"fs-idp136092800\" data-type=\"media\" data-alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of A l.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of I subscript 2.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_moleratio1_img-1.jpg\" alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of A l.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of I subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-idp102857120\" data-type=\"equation\"><img class=\"wp-image-1180 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3e.png\" alt=\"\" width=\"267\" height=\"46\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp30742160\"><strong>Check Your Learning:<\/strong><\/p>\r\nHow many moles of Ca(OH)<sub>2<\/sub> are required to react with 1.36 mol of H<sub>3<\/sub>PO<sub>4<\/sub> to produce Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub> according to this equation?\r\n<p style=\"text-align: center\">3Ca(OH)<sub>2<\/sub> + 2H<sub>3<\/sub>PO<sub>4<\/sub> \u27f6 Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub> + 6H<sub>2<\/sub>O<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp5038208\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp115249152\">2.04 mol<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp9124448\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n\r\n<strong>Number of Product Molecules Generated by a Reaction:<\/strong>\r\n\r\nHow many carbon dioxide molecules are produced when 0.75 mol of propane is combusted according to this equation?\r\n<div id=\"fs-idp116053696\" style=\"text-align: center\" data-type=\"equation\">C<sub>3<\/sub>H<sub>8<\/sub> + 5O<sub>2<\/sub> \u27f6 3CO<sub>2<\/sub> + 4H<sub>2<\/sub>O<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp121952928\"><strong>Solution:<\/strong><\/p>\r\nThe approach here is the same as for <a class=\"autogenerated-content\" href=\"#fs-idp48900096\">(Figure)<\/a>, though the absolute number of molecules is requested, not the number of moles of molecules. This will simply require use of the moles-to-numbers conversion factor, Avogadro\u2019s number.\r\n<p id=\"fs-idp229756528\">The balanced equation shows that carbon dioxide is produced from propane in a 3:1 ratio:<\/p>\r\n\r\n<div id=\"fs-idp114307520\" data-type=\"equation\"><img class=\"wp-image-1181 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3f.png\" alt=\"\" width=\"89\" height=\"48\" \/><\/div>\r\n<p id=\"fs-idp83056800\">Using this stoichiometric factor, the provided molar amount of propane, and Avogadro\u2019s number,<\/p>\r\n<span id=\"fs-idp94375456\" data-type=\"media\" data-alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of C subscript 3 H subscript 8.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of C O subscript 2.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_moleratio2_img-1.jpg\" alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of C subscript 3 H subscript 8.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of C O subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-idp52373104\" data-type=\"equation\"><img class=\"wp-image-1182 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-300x25.png\" alt=\"\" width=\"528\" height=\"44\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm14771264\"><strong>Check Your Learning:<\/strong><\/p>\r\nHow many NH<sub>3<\/sub> molecules are produced by the reaction of 4.0 mol of Ca(OH)<sub>2<\/sub> according to the following equation:\r\n<div id=\"fs-idp166213360\" style=\"text-align: center\" data-type=\"equation\">(NH<sub>4<\/sub>)<sub>2<\/sub>SO<sub>4<\/sub> + Ca(OH)<sub>2<\/sub> \u27f6 2NH<sub>3<\/sub> + CaSO<sub>4<\/sub> + 2H<sub>2<\/sub>O<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idp15879648\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp160971824\">4.8 \u00d7 10<sup>24<\/sup> NH<sub>3<\/sub> molecules<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idp222914448\">These examples illustrate the ease with which the amounts of substances involved in a chemical reaction of known stoichiometry may be related. Directly measuring numbers of atoms and molecules is, however, not an easy task, and the practical application of stoichiometry requires that we use the more readily measured property of mass.<\/p>\r\n\r\n<div id=\"fs-idp113495744\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp56844080\"><strong>Relating Masses of Reactants and Products:<\/strong><\/p>\r\nWhat mass of sodium hydroxide, NaOH, would be required to produce 16 g of the antacid milk of magnesia [magnesium hydroxide, Mg(OH)<sub>2<\/sub>] by the following reaction?\r\n<div id=\"fs-idp158099664\" style=\"text-align: center\" data-type=\"equation\">MgCl<sub>2<\/sub>(<em>aq<\/em>) + 2NaOH(<em>aq<\/em>) \u27f6 Mg(OH)<sub>2<\/sub>(<em>s<\/em>) + 2NaCl(<em>aq<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm3520480\"><strong>Solution:<\/strong><\/p>\r\nThe approach used previously in <a class=\"autogenerated-content\" href=\"#fs-idp48900096\">(Figure)<\/a> and <a class=\"autogenerated-content\" href=\"#fs-idp9124448\">(Figure)<\/a> is likewise used here; that is, we must derive an appropriate stoichiometric factor from the balanced chemical equation and use it to relate the amounts of the two substances of interest. In this case, however, masses (not molar amounts) are provided and requested, so additional steps of the sort learned in the previous chapter are required. The calculations required are outlined in this flowchart:\r\n\r\n<span id=\"fs-idp38697232\" data-type=\"media\" data-alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of N a O H.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of N a O H.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_map2_img-1.jpg\" alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of N a O H.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of N a O H.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-idp122145840\" data-type=\"equation\"><img class=\"alignnone wp-image-1183 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-300x26.png\" alt=\"\" width=\"531\" height=\"46\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp52759328\"><strong>Check Your Learning:<\/strong><\/p>\r\nWhat mass of gallium oxide, Ga<sub>2<\/sub>O<sub>3<\/sub>, can be prepared from 29.0 g of gallium metal? The equation for the reaction is 4Ga + 3O<sub>2<\/sub> \u27f6 2Ga<sub>2<\/sub>O<sub>3<\/sub>.\r\n\r\n&nbsp;\r\n<div id=\"fs-idp214975456\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp3589264\">39.0 g<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp274853984\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp64260528\"><strong>Relating Masses of Reactants:<\/strong><\/p>\r\nWhat mass of oxygen gas, O<sub>2<\/sub>, from the air is consumed in the combustion of 702 g of octane, C<sub>8<\/sub>H<sub>18<\/sub>, one of the principal components of gasoline?\r\n<div id=\"fs-idp87206624\" style=\"text-align: center\" data-type=\"equation\">2C<sub>8<\/sub>H<sub>18<\/sub> + 25O<sub>2<\/sub> \u27f6 16CO<sub>2<\/sub> + 18H<sub>2<\/sub>O<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp35508016\"><strong>Solution:<\/strong><\/p>\r\nThe approach required here is the same as for the <a class=\"autogenerated-content\" href=\"#fs-idp113495744\">(Figure)<\/a>, differing only in that the provided and requested masses are both for reactant species.\r\n\r\n<span id=\"fs-idp56087040\" data-type=\"media\" data-alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of O subscript 2.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of O subscript 2.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_map3_img-1.jpg\" alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of O subscript 2.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of O subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-idm56417376\" data-type=\"equation\"><img class=\" wp-image-1184 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-300x26.png\" alt=\"\" width=\"485\" height=\"42\" \/><\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp24638432\"><strong>Check Your Learning:<\/strong><\/p>\r\nWhat mass of CO is required to react with 25.13 g of Fe<sub>2<\/sub>O<sub>3<\/sub> according to the equation Fe<sub>2<\/sub>O<sub>3<\/sub> + 3CO \u27f6 2Fe + 3CO<sub>2<\/sub>?\r\n\r\n&nbsp;\r\n<div id=\"fs-idp58164000\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp38243856\">13.22 g<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idp90689472\">These examples illustrate just a few instances of reaction stoichiometry calculations. Numerous variations on the beginning and ending computational steps are possible depending upon what particular quantities are provided and sought (volumes, solution concentrations, and so forth). Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. <a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_flowchart\">(Figure)<\/a> provides a general outline of the various computational steps associated with many reaction stoichiometry calculations.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_04_03_flowchart\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">The flowchart depicts the various computational steps involved in most reaction stoichiometry calculations.<\/div>\r\n<span id=\"fs-idp53443040\" data-type=\"media\" data-alt=\"This flowchart shows 10 rectangles connected by double headed arrows. To the upper left, a rectangle is shaded lavender and is labeled, \u201cVolume of pure substance A.\u201d This rectangle is followed by a horizontal double headed arrow labeled, \u201cDensity.\u201d It connects to a second rectangle which is shaded yellow and is labeled, \u201cMass of A.\u201d This rectangle is followed by a double headed arrow which is labeled, \u201cMolar Mass,\u201d that connects to a third rectangle which is shaded pink and is labeled, \u201cMoles of A.\u201d To the left of this rectangle is a horizontal double headed arrow labeled, \u201cMolarity,\u201d which connects to a lavender rectangle which is labeled, \u201cVolume of solution A.\u201d The pink, \u201cMoles of A,\u201d rectangle is also connected with a double headed arrow below and to the left. This arrow is labeled \u201cAvogadro\u2019s number.\u201d It connects to a green shaded rectangle that is labeled, \u201cNumber of particles of A.\u201d To the right of the pink \u201cMoles of A,\u201d rectangle is a horizontal double headed arrow which is labeled, \u201cStoichiometric factor.\u201d It connects to a second pink rectangle which is labeled, \u201cMoles of B.\u201d A double headed arrow which is labeled, \u201cMolar mass,\u201d extends from the top of this rectangle above and to the right to a yellow shaded rectangle labeled, \u201cMass of B.\u201d A horizontal double headed arrow which is labeled, \u201cDensity\u201d links to a lavender rectangle labeled, \u201cVolume of substance B,\u201d to the right. A horizontal double headed arrow labeled, \u201cMolarity,\u201d extends right to the of the pink \u201cMoles of B\u201d rectangle. This arrow connects to a lavender rectangle that is labeled, \u201cVolume of substance B.\u201d Another double headed arrow extends below and to the right of the pink \u201cMoles of B\u201d rectangle. This arrow is labeled \u201cAvogadro\u2019s number,\u201d and it extends to a green rectangle which is labeled, \u201cNumber of particles of B.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_flowchart-1.jpg\" alt=\"This flowchart shows 10 rectangles connected by double headed arrows. To the upper left, a rectangle is shaded lavender and is labeled, \u201cVolume of pure substance A.\u201d This rectangle is followed by a horizontal double headed arrow labeled, \u201cDensity.\u201d It connects to a second rectangle which is shaded yellow and is labeled, \u201cMass of A.\u201d This rectangle is followed by a double headed arrow which is labeled, \u201cMolar Mass,\u201d that connects to a third rectangle which is shaded pink and is labeled, \u201cMoles of A.\u201d To the left of this rectangle is a horizontal double headed arrow labeled, \u201cMolarity,\u201d which connects to a lavender rectangle which is labeled, \u201cVolume of solution A.\u201d The pink, \u201cMoles of A,\u201d rectangle is also connected with a double headed arrow below and to the left. This arrow is labeled \u201cAvogadro\u2019s number.\u201d It connects to a green shaded rectangle that is labeled, \u201cNumber of particles of A.\u201d To the right of the pink \u201cMoles of A,\u201d rectangle is a horizontal double headed arrow which is labeled, \u201cStoichiometric factor.\u201d It connects to a second pink rectangle which is labeled, \u201cMoles of B.\u201d A double headed arrow which is labeled, \u201cMolar mass,\u201d extends from the top of this rectangle above and to the right to a yellow shaded rectangle labeled, \u201cMass of B.\u201d A horizontal double headed arrow which is labeled, \u201cDensity\u201d links to a lavender rectangle labeled, \u201cVolume of substance B,\u201d to the right. A horizontal double headed arrow labeled, \u201cMolarity,\u201d extends right to the of the pink \u201cMoles of B\u201d rectangle. This arrow connects to a lavender rectangle that is labeled, \u201cVolume of substance B.\u201d Another double headed arrow extends below and to the right of the pink \u201cMoles of B\u201d rectangle. This arrow is labeled \u201cAvogadro\u2019s number,\u201d and it extends to a green rectangle which is labeled, \u201cNumber of particles of B.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idp84121360\" class=\"chemistry everyday-life\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Airbags<\/strong><\/div>\r\n<p id=\"fs-idp124943600\">Airbags (<a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_airbag\">(Figure)<\/a>) are a safety feature provided in most automobiles since the 1990s. The effective operation of an airbag requires that it be rapidly inflated with an appropriate amount (volume) of gas when the vehicle is involved in a collision. This requirement is satisfied in many automotive airbag systems through use of explosive chemical reactions, one common choice being the decomposition of sodium azide, NaN<sub>3<\/sub>. When sensors in the vehicle detect a collision, an electrical current is passed through a carefully measured amount of NaN<sub>3<\/sub> to initiate its decomposition:<\/p>\r\n\r\n<div id=\"fs-idp113504400\" style=\"text-align: center\" data-type=\"equation\">2NaN<sub>3<\/sub>(<em>s<\/em>) \u27f6 3N<sub>2<\/sub>(<em>g<\/em>) + 2Na(<em>s<\/em>)<\/div>\r\n<p id=\"fs-idp9645888\">This reaction is very rapid, generating gaseous nitrogen that can deploy and fully inflate a typical airbag in a fraction of a second (~0.03\u20130.1 s). Among many engineering considerations, the amount of sodium azide used must be appropriate for generating enough nitrogen gas to fully inflate the air bag and ensure its proper function. For example, a small mass (~100 g) of NaN<sub>3<\/sub> will generate approximately 50 L of N<sub>2<\/sub>.<\/p>\r\n\r\n<div id=\"CNX_Chem_04_03_airbag\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Airbags deploy upon impact to minimize serious injuries to passengers. (credit: Jon Seidman)<\/div>\r\n<span id=\"fs-idp103197840\" data-type=\"media\" data-alt=\"This photograph shows the inside of an automobile from the driver\u2019s side area. The image shows inflated airbags positioned just in front of the driver\u2019s and passenger\u2019s seats and along the length of the passenger side over the windows. A large, round airbag covers the steering wheel.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_airbag-1.jpg\" alt=\"This photograph shows the inside of an automobile from the driver\u2019s side area. The image shows inflated airbags positioned just in front of the driver\u2019s and passenger\u2019s seats and along the length of the passenger side over the windows. A large, round airbag covers the steering wheel.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp102563712\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idm3728016\">A balanced chemical equation may be used to describe a reaction\u2019s stoichiometry (the relationships between amounts of reactants and products). Coefficients from the equation are used to derive stoichiometric factors that subsequently may be used for computations relating reactant and product masses, molar amounts, and other quantitative properties.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm1445952\" class=\"exercises\" data-depth=\"1\">\r\n<div id=\"fs-idp149769296\" data-type=\"exercise\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\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-idp127461392\">\r\n \t<dt>stoichiometric factor<\/dt>\r\n \t<dd id=\"fs-idp127462032\">ratio of coefficients in a balanced chemical equation, used in computations relating amounts of reactants and products<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp127462672\">\r\n \t<dt>stoichiometry<\/dt>\r\n \t<dd id=\"fs-idp117365328\">relationships between the amounts of reactants and products of a chemical reaction<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<p><strong>\u00a0<\/strong><\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<h3><strong>Learning Objectives<\/strong><\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Explain the concept of stoichiometry as it pertains to chemical reactions<\/li>\n<li>Use balanced chemical equations to derive stoichiometric factors relating amounts of reactants and products<\/li>\n<li>Perform stoichiometric calculations involving mass, moles, and solution molarity<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-idp65325120\">A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and products involved in the chemical change, allowing classification of the reaction. Coefficients provide the relative numbers of these chemical species, allowing a quantitative assessment of the relationships between the amounts of substances consumed and produced by the reaction. These quantitative relationships are known as the reaction\u2019s <strong>stoichiometry<\/strong>, a term derived from the Greek words <em data-effect=\"italics\">stoicheion<\/em> (meaning \u201celement\u201d) and <em data-effect=\"italics\">metron<\/em> (meaning \u201cmeasure\u201d). In this module, the use of balanced chemical equations for various stoichiometric applications is explored.<\/p>\n<p id=\"fs-idp92593072\">The general approach to using stoichiometric relationships is similar in concept to the way people go about many common activities. Food preparation, for example, offers an appropriate comparison. A recipe for making eight pancakes calls for 1 cup pancake mix, 3\/4 cup milk, and one egg. The \u201cequation\u201d representing the preparation of pancakes per this recipe is<\/p>\n<div id=\"fs-idp116126928\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1175 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-300x39.png\" alt=\"\" width=\"331\" height=\"43\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-300x39.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-225x29.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a-350x45.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3a.png 551w\" sizes=\"auto, (max-width: 331px) 100vw, 331px\" \/><\/div>\n<p id=\"fs-idp78338704\">If two dozen pancakes are needed for a big family breakfast, the ingredient amounts must be increased proportionally according to the amounts given in the recipe. For example, the number of eggs required to make 24 pancakes is<\/p>\n<div id=\"fs-idp58586688\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1176 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-300x62.png\" alt=\"\" width=\"300\" height=\"62\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-300x62.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-65x13.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-225x46.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b-350x72.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3b.png 455w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idp98270672\">Balanced chemical equations are used in much the same fashion to determine the amount of one reactant required to react with a given amount of another reactant, or to yield a given amount of product, and so forth. The coefficients in the balanced equation are used to derive <span data-type=\"term\">stoichiometric factors<\/span> that permit computation of the desired quantity. To illustrate this idea, consider the production of ammonia by reaction of hydrogen and nitrogen:<\/p>\n<div id=\"fs-idp124603552\" style=\"text-align: center\" data-type=\"equation\">N<sub>2<\/sub>(<em>g<\/em>) + 3H<sub>2<\/sub>(<em>g<\/em>) \u27f6 2NH<sub>3<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idp124955072\">This equation shows ammonia molecules are produced from hydrogen molecules in a 2:3 ratio, and stoichiometric factors may be derived using any amount (number) unit:<\/p>\n<div id=\"fs-idp64965808\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1178 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-300x31.png\" alt=\"\" width=\"397\" height=\"41\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-300x31.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-225x23.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c-350x36.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3c.png 738w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/div>\n<p id=\"fs-idp56404080\">These stoichiometric factors can be used to compute the number of ammonia molecules produced from a given number of hydrogen molecules, or the number of hydrogen molecules required to produce a given number of ammonia molecules. Similar factors may be derived for any pair of substances in any chemical equation.<\/p>\n<div id=\"fs-idp48900096\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp77269456\"><strong>Moles of Reactant Required in a Reaction:<\/strong><\/p>\n<p>How many moles of I<sub>2<\/sub> are required to react with 0.429 mol of Al according to the following equation (see <a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_iodine\">(Figure)<\/a>)?<\/p>\n<div id=\"fs-idp147980704\" style=\"text-align: center\" data-type=\"equation\">2Al + 3I<sub>2<\/sub> \u27f6 2AlI<sub>3<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"CNX_Chem_04_03_iodine\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Aluminum and iodine react to produce aluminum iodide. The heat of the reaction vaporizes some of the solid iodine as a purple vapor. (credit: modification of work by Mark Ott)<\/div>\n<p><span id=\"fs-idp52310320\" data-type=\"media\" data-alt=\"This figure shows three photos with an arrow leading from one to the next. The first photo shows a small pile of iodine and aluminum on a white surface. The second photo shows a small amount of purple smoke coming from the pile. The third photo shows a large amount of purple and gray smoke coming from the pile.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_iodine-1.jpg\" alt=\"This figure shows three photos with an arrow leading from one to the next. The first photo shows a small pile of iodine and aluminum on a white surface. The second photo shows a small amount of purple smoke coming from the pile. The third photo shows a large amount of purple and gray smoke coming from the pile.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm34598272\"><strong>Solution:<\/strong><\/p>\n<p>Referring to the balanced chemical equation, the stoichiometric factor relating the two substances of interest is <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1179\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3d.png\" alt=\"\" width=\"76\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3d.png 76w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3d-65x41.png 65w\" sizes=\"auto, (max-width: 76px) 100vw, 76px\" \/>. The molar amount of iodine is derived by multiplying the provided molar amount of aluminum by this factor:<\/p>\n<p><span id=\"fs-idp136092800\" data-type=\"media\" data-alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of A l.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of I subscript 2.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_moleratio1_img-1.jpg\" alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of A l.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of I subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-idp102857120\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1180 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3e.png\" alt=\"\" width=\"267\" height=\"46\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3e.png 255w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3e-65x11.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3e-225x39.png 225w\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp30742160\"><strong>Check Your Learning:<\/strong><\/p>\n<p>How many moles of Ca(OH)<sub>2<\/sub> are required to react with 1.36 mol of H<sub>3<\/sub>PO<sub>4<\/sub> to produce Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub> according to this equation?<\/p>\n<p style=\"text-align: center\">3Ca(OH)<sub>2<\/sub> + 2H<sub>3<\/sub>PO<sub>4<\/sub> \u27f6 Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub> + 6H<sub>2<\/sub>O<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp5038208\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp115249152\">2.04 mol<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp9124448\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p><strong>Number of Product Molecules Generated by a Reaction:<\/strong><\/p>\n<p>How many carbon dioxide molecules are produced when 0.75 mol of propane is combusted according to this equation?<\/p>\n<div id=\"fs-idp116053696\" style=\"text-align: center\" data-type=\"equation\">C<sub>3<\/sub>H<sub>8<\/sub> + 5O<sub>2<\/sub> \u27f6 3CO<sub>2<\/sub> + 4H<sub>2<\/sub>O<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp121952928\"><strong>Solution:<\/strong><\/p>\n<p>The approach here is the same as for <a class=\"autogenerated-content\" href=\"#fs-idp48900096\">(Figure)<\/a>, though the absolute number of molecules is requested, not the number of moles of molecules. This will simply require use of the moles-to-numbers conversion factor, Avogadro\u2019s number.<\/p>\n<p id=\"fs-idp229756528\">The balanced equation shows that carbon dioxide is produced from propane in a 3:1 ratio:<\/p>\n<div id=\"fs-idp114307520\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1181 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3f.png\" alt=\"\" width=\"89\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3f.png 137w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3f-65x35.png 65w\" sizes=\"auto, (max-width: 89px) 100vw, 89px\" \/><\/div>\n<p id=\"fs-idp83056800\">Using this stoichiometric factor, the provided molar amount of propane, and Avogadro\u2019s number,<\/p>\n<p><span id=\"fs-idp94375456\" data-type=\"media\" data-alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of C subscript 3 H subscript 8.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of C O subscript 2.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_moleratio2_img-1.jpg\" alt=\"This figure shows two pink rectangles. The first is labeled, \u201cMoles of C subscript 3 H subscript 8.\u201d This rectangle is followed by an arrow pointing right to a second rectangle labeled, \u201cMoles of C O subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-idp52373104\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1182 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-300x25.png\" alt=\"\" width=\"528\" height=\"44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-300x25.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-1024x86.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-768x64.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-65x5.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-225x19.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g-350x29.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3g.png 1037w\" sizes=\"auto, (max-width: 528px) 100vw, 528px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm14771264\"><strong>Check Your Learning:<\/strong><\/p>\n<p>How many NH<sub>3<\/sub> molecules are produced by the reaction of 4.0 mol of Ca(OH)<sub>2<\/sub> according to the following equation:<\/p>\n<div id=\"fs-idp166213360\" style=\"text-align: center\" data-type=\"equation\">(NH<sub>4<\/sub>)<sub>2<\/sub>SO<sub>4<\/sub> + Ca(OH)<sub>2<\/sub> \u27f6 2NH<sub>3<\/sub> + CaSO<sub>4<\/sub> + 2H<sub>2<\/sub>O<\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idp15879648\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp160971824\">4.8 \u00d7 10<sup>24<\/sup> NH<sub>3<\/sub> molecules<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idp222914448\">These examples illustrate the ease with which the amounts of substances involved in a chemical reaction of known stoichiometry may be related. Directly measuring numbers of atoms and molecules is, however, not an easy task, and the practical application of stoichiometry requires that we use the more readily measured property of mass.<\/p>\n<div id=\"fs-idp113495744\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp56844080\"><strong>Relating Masses of Reactants and Products:<\/strong><\/p>\n<p>What mass of sodium hydroxide, NaOH, would be required to produce 16 g of the antacid milk of magnesia [magnesium hydroxide, Mg(OH)<sub>2<\/sub>] by the following reaction?<\/p>\n<div id=\"fs-idp158099664\" style=\"text-align: center\" data-type=\"equation\">MgCl<sub>2<\/sub>(<em>aq<\/em>) + 2NaOH(<em>aq<\/em>) \u27f6 Mg(OH)<sub>2<\/sub>(<em>s<\/em>) + 2NaCl(<em>aq<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm3520480\"><strong>Solution:<\/strong><\/p>\n<p>The approach used previously in <a class=\"autogenerated-content\" href=\"#fs-idp48900096\">(Figure)<\/a> and <a class=\"autogenerated-content\" href=\"#fs-idp9124448\">(Figure)<\/a> is likewise used here; that is, we must derive an appropriate stoichiometric factor from the balanced chemical equation and use it to relate the amounts of the two substances of interest. In this case, however, masses (not molar amounts) are provided and requested, so additional steps of the sort learned in the previous chapter are required. The calculations required are outlined in this flowchart:<\/p>\n<p><span id=\"fs-idp38697232\" data-type=\"media\" data-alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of N a O H.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of N a O H.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_map2_img-1.jpg\" alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of M g ( O H ) subscript 2.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of N a O H.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of N a O H.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-idp122145840\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1183 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-300x26.png\" alt=\"\" width=\"531\" height=\"46\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-300x26.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-768x67.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-225x20.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h-350x31.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3h.png 993w\" sizes=\"auto, (max-width: 531px) 100vw, 531px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp52759328\"><strong>Check Your Learning:<\/strong><\/p>\n<p>What mass of gallium oxide, Ga<sub>2<\/sub>O<sub>3<\/sub>, can be prepared from 29.0 g of gallium metal? The equation for the reaction is 4Ga + 3O<sub>2<\/sub> \u27f6 2Ga<sub>2<\/sub>O<sub>3<\/sub>.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp214975456\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp3589264\">39.0 g<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp274853984\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp64260528\"><strong>Relating Masses of Reactants:<\/strong><\/p>\n<p>What mass of oxygen gas, O<sub>2<\/sub>, from the air is consumed in the combustion of 702 g of octane, C<sub>8<\/sub>H<sub>18<\/sub>, one of the principal components of gasoline?<\/p>\n<div id=\"fs-idp87206624\" style=\"text-align: center\" data-type=\"equation\">2C<sub>8<\/sub>H<sub>18<\/sub> + 25O<sub>2<\/sub> \u27f6 16CO<sub>2<\/sub> + 18H<sub>2<\/sub>O<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp35508016\"><strong>Solution:<\/strong><\/p>\n<p>The approach required here is the same as for the <a class=\"autogenerated-content\" href=\"#fs-idp113495744\">(Figure)<\/a>, differing only in that the provided and requested masses are both for reactant species.<\/p>\n<p><span id=\"fs-idp56087040\" data-type=\"media\" data-alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of O subscript 2.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of O subscript 2.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_map3_img-1.jpg\" alt=\"This figure shows four rectangles. The first is shaded yellow and is labeled, \u201cMass of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a second rectangle which is shaded pink and is labeled, \u201cMoles of C subscript 8 H subscript 18.\u201d This rectangle is followed by an arrow pointing right to a third rectangle which is shaded pink and is labeled, \u201cMoles of O subscript 2.\u201d This rectangle is followed by an arrow pointing right to a fourth rectangle which is shaded yellow and is labeled, \u201cMass of O subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-idm56417376\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1184 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-300x26.png\" alt=\"\" width=\"485\" height=\"42\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-300x26.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-768x67.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-225x20.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i-350x31.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/4.3i.png 950w\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" \/><\/div>\n<div style=\"text-align: center\" data-type=\"equation\"><\/div>\n<p id=\"fs-idp24638432\"><strong>Check Your Learning:<\/strong><\/p>\n<p>What mass of CO is required to react with 25.13 g of Fe<sub>2<\/sub>O<sub>3<\/sub> according to the equation Fe<sub>2<\/sub>O<sub>3<\/sub> + 3CO \u27f6 2Fe + 3CO<sub>2<\/sub>?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp58164000\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp38243856\">13.22 g<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idp90689472\">These examples illustrate just a few instances of reaction stoichiometry calculations. Numerous variations on the beginning and ending computational steps are possible depending upon what particular quantities are provided and sought (volumes, solution concentrations, and so forth). Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. <a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_flowchart\">(Figure)<\/a> provides a general outline of the various computational steps associated with many reaction stoichiometry calculations.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_04_03_flowchart\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The flowchart depicts the various computational steps involved in most reaction stoichiometry calculations.<\/div>\n<p><span id=\"fs-idp53443040\" data-type=\"media\" data-alt=\"This flowchart shows 10 rectangles connected by double headed arrows. To the upper left, a rectangle is shaded lavender and is labeled, \u201cVolume of pure substance A.\u201d This rectangle is followed by a horizontal double headed arrow labeled, \u201cDensity.\u201d It connects to a second rectangle which is shaded yellow and is labeled, \u201cMass of A.\u201d This rectangle is followed by a double headed arrow which is labeled, \u201cMolar Mass,\u201d that connects to a third rectangle which is shaded pink and is labeled, \u201cMoles of A.\u201d To the left of this rectangle is a horizontal double headed arrow labeled, \u201cMolarity,\u201d which connects to a lavender rectangle which is labeled, \u201cVolume of solution A.\u201d The pink, \u201cMoles of A,\u201d rectangle is also connected with a double headed arrow below and to the left. This arrow is labeled \u201cAvogadro\u2019s number.\u201d It connects to a green shaded rectangle that is labeled, \u201cNumber of particles of A.\u201d To the right of the pink \u201cMoles of A,\u201d rectangle is a horizontal double headed arrow which is labeled, \u201cStoichiometric factor.\u201d It connects to a second pink rectangle which is labeled, \u201cMoles of B.\u201d A double headed arrow which is labeled, \u201cMolar mass,\u201d extends from the top of this rectangle above and to the right to a yellow shaded rectangle labeled, \u201cMass of B.\u201d A horizontal double headed arrow which is labeled, \u201cDensity\u201d links to a lavender rectangle labeled, \u201cVolume of substance B,\u201d to the right. A horizontal double headed arrow labeled, \u201cMolarity,\u201d extends right to the of the pink \u201cMoles of B\u201d rectangle. This arrow connects to a lavender rectangle that is labeled, \u201cVolume of substance B.\u201d Another double headed arrow extends below and to the right of the pink \u201cMoles of B\u201d rectangle. This arrow is labeled \u201cAvogadro\u2019s number,\u201d and it extends to a green rectangle which is labeled, \u201cNumber of particles of B.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_flowchart-1.jpg\" alt=\"This flowchart shows 10 rectangles connected by double headed arrows. To the upper left, a rectangle is shaded lavender and is labeled, \u201cVolume of pure substance A.\u201d This rectangle is followed by a horizontal double headed arrow labeled, \u201cDensity.\u201d It connects to a second rectangle which is shaded yellow and is labeled, \u201cMass of A.\u201d This rectangle is followed by a double headed arrow which is labeled, \u201cMolar Mass,\u201d that connects to a third rectangle which is shaded pink and is labeled, \u201cMoles of A.\u201d To the left of this rectangle is a horizontal double headed arrow labeled, \u201cMolarity,\u201d which connects to a lavender rectangle which is labeled, \u201cVolume of solution A.\u201d The pink, \u201cMoles of A,\u201d rectangle is also connected with a double headed arrow below and to the left. This arrow is labeled \u201cAvogadro\u2019s number.\u201d It connects to a green shaded rectangle that is labeled, \u201cNumber of particles of A.\u201d To the right of the pink \u201cMoles of A,\u201d rectangle is a horizontal double headed arrow which is labeled, \u201cStoichiometric factor.\u201d It connects to a second pink rectangle which is labeled, \u201cMoles of B.\u201d A double headed arrow which is labeled, \u201cMolar mass,\u201d extends from the top of this rectangle above and to the right to a yellow shaded rectangle labeled, \u201cMass of B.\u201d A horizontal double headed arrow which is labeled, \u201cDensity\u201d links to a lavender rectangle labeled, \u201cVolume of substance B,\u201d to the right. A horizontal double headed arrow labeled, \u201cMolarity,\u201d extends right to the of the pink \u201cMoles of B\u201d rectangle. This arrow connects to a lavender rectangle that is labeled, \u201cVolume of substance B.\u201d Another double headed arrow extends below and to the right of the pink \u201cMoles of B\u201d rectangle. This arrow is labeled \u201cAvogadro\u2019s number,\u201d and it extends to a green rectangle which is labeled, \u201cNumber of particles of B.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idp84121360\" class=\"chemistry everyday-life\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Airbags<\/strong><\/div>\n<p id=\"fs-idp124943600\">Airbags (<a class=\"autogenerated-content\" href=\"#CNX_Chem_04_03_airbag\">(Figure)<\/a>) are a safety feature provided in most automobiles since the 1990s. The effective operation of an airbag requires that it be rapidly inflated with an appropriate amount (volume) of gas when the vehicle is involved in a collision. This requirement is satisfied in many automotive airbag systems through use of explosive chemical reactions, one common choice being the decomposition of sodium azide, NaN<sub>3<\/sub>. When sensors in the vehicle detect a collision, an electrical current is passed through a carefully measured amount of NaN<sub>3<\/sub> to initiate its decomposition:<\/p>\n<div id=\"fs-idp113504400\" style=\"text-align: center\" data-type=\"equation\">2NaN<sub>3<\/sub>(<em>s<\/em>) \u27f6 3N<sub>2<\/sub>(<em>g<\/em>) + 2Na(<em>s<\/em>)<\/div>\n<p id=\"fs-idp9645888\">This reaction is very rapid, generating gaseous nitrogen that can deploy and fully inflate a typical airbag in a fraction of a second (~0.03\u20130.1 s). Among many engineering considerations, the amount of sodium azide used must be appropriate for generating enough nitrogen gas to fully inflate the air bag and ensure its proper function. For example, a small mass (~100 g) of NaN<sub>3<\/sub> will generate approximately 50 L of N<sub>2<\/sub>.<\/p>\n<div id=\"CNX_Chem_04_03_airbag\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Airbags deploy upon impact to minimize serious injuries to passengers. (credit: Jon Seidman)<\/div>\n<p><span id=\"fs-idp103197840\" data-type=\"media\" data-alt=\"This photograph shows the inside of an automobile from the driver\u2019s side area. The image shows inflated airbags positioned just in front of the driver\u2019s and passenger\u2019s seats and along the length of the passenger side over the windows. A large, round airbag covers the steering wheel.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_04_03_airbag-1.jpg\" alt=\"This photograph shows the inside of an automobile from the driver\u2019s side area. The image shows inflated airbags positioned just in front of the driver\u2019s and passenger\u2019s seats and along the length of the passenger side over the windows. A large, round airbag covers the steering wheel.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp102563712\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idm3728016\">A balanced chemical equation may be used to describe a reaction\u2019s stoichiometry (the relationships between amounts of reactants and products). Coefficients from the equation are used to derive stoichiometric factors that subsequently may be used for computations relating reactant and product masses, molar amounts, and other quantitative properties.<\/p>\n<\/div>\n<div id=\"fs-idm1445952\" class=\"exercises\" data-depth=\"1\">\n<div id=\"fs-idp149769296\" data-type=\"exercise\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\n<dl id=\"fs-idp127461392\">\n<dt>stoichiometric factor<\/dt>\n<dd id=\"fs-idp127462032\">ratio of coefficients in a balanced chemical equation, used in computations relating amounts of reactants and products<\/dd>\n<\/dl>\n<dl id=\"fs-idp127462672\">\n<dt>stoichiometry<\/dt>\n<dd id=\"fs-idp117365328\">relationships between the amounts of reactants and products of a chemical reaction<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":1392,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-200","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":177,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/200","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":7,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/200\/revisions"}],"predecessor-version":[{"id":2118,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/200\/revisions\/2118"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/177"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/200\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=200"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=200"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=200"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}