{"id":702,"date":"2021-07-23T09:20:29","date_gmt":"2021-07-23T13:20:29","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/chemical-reaction-rates\/"},"modified":"2022-06-23T09:15:59","modified_gmt":"2022-06-23T13:15:59","slug":"chemical-reaction-rates","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/chemical-reaction-rates\/","title":{"raw":"12.1 Chemical Reaction Rates","rendered":"12.1 Chemical Reaction Rates"},"content":{"raw":"<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>Define chemical reaction rate<\/li>\r\n \t<li>Derive rate expressions from the balanced equation for a given chemical reaction<\/li>\r\n \t<li>Calculate reaction rates from experimental data<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"fs-idp37629504\">A <em data-effect=\"italics\">rate<\/em> is a measure of how some property varies with time. Speed is a familiar rate that expresses the distance travelled by an object in a given amount of time. Wage is a rate that represents the amount of money earned by a person working for a given amount of time. Likewise, the rate of a chemical reaction is a measure of how much reactant is consumed, or how much product is produced, by the reaction in a given amount of time.<\/p>\r\n<p id=\"fs-idp11492384\">The <strong>rate of reaction<\/strong> is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure. For reactions involving one or more coloured substances, rates may be monitored via measurements of light absorption. For reactions involving aqueous electrolytes, rates may be measured via changes in a solution\u2019s conductivity.<\/p>\r\n<p id=\"fs-idm49411904\">For reactants and products in solution, their relative amounts (concentrations) are conveniently used for purposes of expressing reaction rates. For example, the concentration of hydrogen peroxide, H<sub>2<\/sub>O<sub>2<\/sub>, in an aqueous solution changes slowly over time as it decomposes according to the equation:<\/p>\r\n\r\n<div id=\"fs-idp26890848\" style=\"text-align: center\" data-type=\"equation\">2H<sub>2<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) \u27f6 2H<sub>2<\/sub>O(<em>l<\/em>) + O<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idp202399680\">The rate at which the hydrogen peroxide decomposes can be expressed in terms of the rate of change of its concentration, as shown here:<\/p>\r\n\r\n<div id=\"fs-idm23827472\" data-type=\"equation\"><img class=\"wp-image-1686 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-300x69.png\" alt=\"\" width=\"530\" height=\"122\" \/><\/div>\r\n<p id=\"fs-idp37715584\">This mathematical representation of the change in species concentration over time is the<strong> rate expression<\/strong> for the reaction. The brackets indicate molar concentrations, and the symbol delta (\u0394) indicates \u201cchange in.\u201d Thus, [H<sub>2<\/sub>O<sub>2<\/sub>]<sub>t1<\/sub> represents the molar concentration of hydrogen peroxide at some time <em data-effect=\"italics\">t<\/em><sub>1<\/sub>; likewise,[H<sub>2<\/sub>O<sub>2<\/sub>]<sub>t2<\/sub> represents the molar concentration of hydrogen peroxide at a later time <em data-effect=\"italics\">t<\/em><sub>2<\/sub>; and \u0394[H<sub>2<\/sub>O<sub>2<\/sub>] represents the change in molar concentration of hydrogen peroxide during the time interval \u0394<em data-effect=\"italics\">t<\/em> (that is, <em data-effect=\"italics\">t<\/em><sub>2<\/sub> \u2212 <em data-effect=\"italics\">t<\/em><sub>1<\/sub>). Since the reactant concentration decreases as the reaction proceeds, \u0394[H<sub>2<\/sub>O<sub>2<\/sub>] is a negative quantity. Reaction rates are, by convention, positive quantities, and so this negative change in concentration is multiplied by \u22121. <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_KDataH2O2\">(Figure)<\/a> provides an example of data collected during the decomposition of H<sub>2<\/sub>O<sub>2<\/sub>.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_12_01_KDataH2O2\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">The rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> in an aqueous solution decreases as the concentration of H<sub>2<\/sub>O<sub>2<\/sub> decreases.<\/div>\r\n<span id=\"fs-idp13735104\" data-type=\"media\" data-alt=\"A table with five columns is shown. The first column is labeled, \u201cTime, h.\u201d Beneath it the numbers 0.00, 6.00, 12.00, 18.00, and 24.00 are listed. The second column is labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers 1.000, 0.500, 0.250, 0.125, and 0.0625 are double spaced. To the right, a third column is labeled, \u201ccapital delta [ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers negative 0.500, negative 0.250, negative 0.125, and negative 0.062 are listed such that they are double spaced and offset, beginning one line below the first number listed in the column labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d The first two numbers in the second column have line segments extending from their right side to the left side of the first number in the third row. The second and third numbers in the second column have line segments extending from their right side to the left side of the second number in the third row. The third and fourth numbers in the second column have line segments extending from their right side to the left side of the third number in the third row. The fourth and fifth numbers in the second column have line segments extending from their right side to the left side of the fourth number in the third row. The fourth column in labeled, \u201ccapital delta t, h.\u201d Below the title, the value 6.00 is listed four times, each single-spaced. The fifth and final column is labeled \u201cRate of Decomposition, mol \/ L superscript negative 1 \/ h superscript negative 1.\u201d Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.010.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_KDataH2O2-2.jpg\" alt=\"A table with five columns is shown. The first column is labeled, \u201cTime, h.\u201d Beneath it the numbers 0.00, 6.00, 12.00, 18.00, and 24.00 are listed. The second column is labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers 1.000, 0.500, 0.250, 0.125, and 0.0625 are double spaced. To the right, a third column is labeled, \u201ccapital delta [ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers negative 0.500, negative 0.250, negative 0.125, and negative 0.062 are listed such that they are double spaced and offset, beginning one line below the first number listed in the column labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d The first two numbers in the second column have line segments extending from their right side to the left side of the first number in the third row. The second and third numbers in the second column have line segments extending from their right side to the left side of the second number in the third row. The third and fourth numbers in the second column have line segments extending from their right side to the left side of the third number in the third row. The fourth and fifth numbers in the second column have line segments extending from their right side to the left side of the fourth number in the third row. The fourth column in labeled, \u201ccapital delta t, h.\u201d Below the title, the value 6.00 is listed four times, each single-spaced. The fifth and final column is labeled \u201cRate of Decomposition, mol \/ L superscript negative 1 \/ h superscript negative 1.\u201d Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.010.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm29280704\">To obtain the tabulated results for this decomposition, the concentration of hydrogen peroxide was measured every 6 hours over the course of a day at a constant temperature of 40 \u00b0C. Reaction rates were computed for each time interval by dividing the change in concentration by the corresponding time increment, as shown here for the first 6-hour period:<\/p>\r\n\r\n<div id=\"fs-idm14828496\" data-type=\"equation\"><img class=\" wp-image-1687 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-300x29.png\" alt=\"\" width=\"434\" height=\"42\" \/><\/div>\r\n<p id=\"fs-idp40709888\">Notice that the reaction rates vary with time, decreasing as the reaction proceeds. Results for the last 6-hour period yield a reaction rate of:<\/p>\r\n\r\n<div id=\"fs-idp151295040\" data-type=\"equation\"><img class=\"alignnone wp-image-1688 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-300x29.png\" alt=\"\" width=\"424\" height=\"41\" \/><\/div>\r\n<p id=\"fs-idp101513872\">This behaviour indicates the reaction continually slows with time. Using the concentrations at the beginning and end of a time period over which the reaction rate is changing results in the calculation of an<strong> average rate<\/strong> for the reaction over this time interval. At any specific time, the rate at which a reaction is proceeding is known as its <strong>instantaneous rate<\/strong>. The instantaneous rate of a reaction at \u201ctime zero,\u201d when the reaction commences, is its <strong>initial rate<\/strong>. Consider the analogy of a car slowing down as it approaches a stop sign. The vehicle\u2019s initial rate\u2014analogous to the beginning of a chemical reaction\u2014would be the speedometer reading at the moment the driver begins pressing the brakes (<em data-effect=\"italics\">t<\/em><sub>0<\/sub>). A few moments later, the instantaneous rate at a specific moment\u2014call it <em data-effect=\"italics\">t<\/em><sub>1<\/sub>\u2014would be somewhat slower, as indicated by the speedometer reading at that point in time. As time passes, the instantaneous rate will continue to fall until it reaches zero, when the car (or reaction) stops. Unlike instantaneous speed, the car\u2019s average speed is not indicated by the speedometer; but it can be calculated as the ratio of the distance travelled to the time required to bring the vehicle to a complete stop (\u0394<em data-effect=\"italics\">t<\/em>). Like the decelerating car, the average rate of a chemical reaction will fall somewhere between its initial and final rates.<\/p>\r\n<p id=\"fs-idm65553280\">The instantaneous rate of a reaction may be determined one of two ways. If experimental conditions permit the measurement of concentration changes over very short time intervals, then average rates computed as described earlier provide reasonably good approximations of instantaneous rates. Alternatively, a graphical procedure may be used that, in effect, yields the results that would be obtained if short time interval measurements were possible. In a plot of the concentration of hydrogen peroxide against time, the instantaneous rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> at any time <em data-effect=\"italics\">t<\/em> is given by the slope of a straight line that is tangent to the curve at that time (<a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_RRateIll\">(Figure)<\/a>). These tangent line slopes may be evaluated using calculus, but the procedure for doing so is beyond the scope of this chapter.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_12_01_RRateIll\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">This graph shows a plot of concentration versus time for a 1.000 <em data-effect=\"italics\">M<\/em> solution of H<sub>2<\/sub>O<sub>2<\/sub>. The rate at any time is equal to the negative of the slope of a line tangent to the curve at that time. Tangents are shown at <em data-effect=\"italics\">t<\/em> = 0 h (\u201cinitial rate\u201d) and at <em data-effect=\"italics\">t<\/em> = 12 h (\u201cinstantaneous rate\u201d at 12 h).<\/div>\r\n<span id=\"fs-idp329500576\" data-type=\"media\" data-alt=\"A graph is shown with the label, \u201cTime ( h ),\u201d appearing on the x-axis and \u201c[ H subscript 2 O subscript 2 ] ( mol per L)\u201d on the y-axis. The x-axis markings begin at 0.00 and end at 24.00. The markings are labeled at intervals of 6.00. The y-axis begins at 0.000 and includes markings every 0.200, up to 1.000. A decreasing, concave up, non-linear curve is shown, which begins at 1.000 on the y-axis and nearly reaches a value of 0 at the far right of the graph around 24.00 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis at 1.000. The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 0 equals initial rate\u201d. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 12 equals instantaneous rate at 12 h.\u201d A second red tangent line segment is drawn near the middle of the curve at 12.00 on the x-axis. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_RRateIll-2.jpg\" alt=\"A graph is shown with the label, \u201cTime ( h ),\u201d appearing on the x-axis and \u201c[ H subscript 2 O subscript 2 ] ( mol per L)\u201d on the y-axis. The x-axis markings begin at 0.00 and end at 24.00. The markings are labeled at intervals of 6.00. The y-axis begins at 0.000 and includes markings every 0.200, up to 1.000. A decreasing, concave up, non-linear curve is shown, which begins at 1.000 on the y-axis and nearly reaches a value of 0 at the far right of the graph around 24.00 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis at 1.000. The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 0 equals initial rate\u201d. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 12 equals instantaneous rate at 12 h.\u201d A second red tangent line segment is drawn near the middle of the curve at 12.00 on the x-axis. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idm69729856\" class=\"chemistry everyday-life\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Reaction Rates in Analysis: Test Strips for Urinalysis<\/strong><\/div>\r\n<p id=\"fs-idp8375264\">Physicians often use disposable test strips to measure the amounts of various substances in a patient\u2019s urine (<a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_Urinestrip\">(Figure)<\/a>). These test strips contain various chemical reagents, embedded in small pads at various locations along the strip, which undergo changes in colour upon exposure to sufficient concentrations of specific substances. The usage instructions for test strips often stress that proper read time is critical for optimal results. This emphasis on read time suggests that kinetic aspects of the chemical reactions occurring on the test strip are important considerations.<\/p>\r\n<p id=\"fs-idp37368560\">The test for urinary glucose relies on a two-step process represented by the chemical equations shown here:<\/p>\r\n<img class=\"size-medium wp-image-1689 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-300x101.png\" alt=\"\" width=\"300\" height=\"101\" \/>\r\n<p id=\"fs-idp79309424\">The first equation depicts the oxidation of glucose in the urine to yield glucolactone and hydrogen peroxide. The hydrogen peroxide produced subsequently oxidizes colourless iodide ion to yield brown iodine, which may be visually detected. Some strips include an additional substance that reacts with iodine to produce a more distinct colour change.<\/p>\r\n<p id=\"fs-idm13608336\">The two test reactions shown above are inherently very slow, but their rates are increased by special enzymes embedded in the test strip pad. This is an example of <em data-effect=\"italics\">catalysis<\/em>, a topic discussed later in this chapter. A typical glucose test strip for use with urine requires approximately 30 seconds for completion of the colour-forming reactions. Reading the result too soon might lead one to conclude that the glucose concentration of the urine sample is lower than it actually is (a <em data-effect=\"italics\">false-negative<\/em> result). Waiting too long to assess the colour change can lead to a <em data-effect=\"italics\">false positive<\/em> due to the slower (not catalyzed) oxidation of iodide ion by other substances found in urine.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_12_01_Urinestrip\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Test strips are commonly used to detect the presence of specific substances in a person\u2019s urine. Many test strips have several pads containing various reagents to permit the detection of multiple substances on a single strip. (credit: Iqbal Osman)<\/div>\r\n<span id=\"fs-idp35718480\" data-type=\"media\" data-alt=\"A photograph shows 8 test strips laid on paper toweling. Each strip contains 11 small sections of various colors, including yellow, tan, black, red, orange, blue, white, and green.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_Urinestrip-2.jpg\" alt=\"A photograph shows 8 test strips laid on paper toweling. Each strip contains 11 small sections of various colors, including yellow, tan, black, red, orange, blue, white, and green.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm24537456\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Relative Rates of Reaction<\/strong><\/h3>\r\n<p id=\"fs-idm26303136\">The rate of a reaction may be expressed as the change in concentration of any reactant or product. For any given reaction, these rate expressions are all related simply to one another according to the reaction stoichiometry. The rate of the general reaction<\/p>\r\n\r\n<div id=\"fs-idm246244416\" style=\"text-align: center\" data-type=\"equation\">aA \u27f6bB<\/div>\r\n<p id=\"fs-idm219494144\">can be expressed in terms of the decrease in the concentration of A or the increase in the concentration of B. These two rate expressions are related by the stoichiometry of the reaction:<\/p>\r\n\r\n<div id=\"fs-idm243742160\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1690 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-300x53.png\" alt=\"\" width=\"300\" height=\"53\" \/><\/div>\r\n<p id=\"fs-idm641684800\">the reaction represented by the following equation:<\/p>\r\n\r\n<div id=\"fs-idp46974560\" style=\"text-align: center\" data-type=\"equation\">2NH<sub>3<\/sub>(<em>g<\/em>) \u27f6 N<sub>2<\/sub>(<em>g<\/em>) + 3H<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idm52700320\">The relation between the reaction rates expressed in terms of nitrogen production and ammonia consumption, for example, is:<\/p>\r\n\r\n<div id=\"fs-idm85736576\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1691 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-300x47.png\" alt=\"\" width=\"300\" height=\"47\" \/><\/div>\r\n<p id=\"fs-idp170662352\">This may be represented in an abbreviated format by omitting the units of the stoichiometric factor:<\/p>\r\n\r\n<div id=\"fs-idp45966480\" data-type=\"equation\"><img class=\"alignnone wp-image-1692 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g-300x63.png\" alt=\"\" width=\"234\" height=\"49\" \/><\/div>\r\n<p id=\"fs-idm93957280\">Note that a negative sign has been included as a factor to account for the opposite signs of the two amount changes (the reactant amount is decreasing while the product amount is increasing). For homogeneous reactions, both the reactants and products are present in the same solution and thus occupy the same volume, so the molar amounts may be replaced with molar concentrations:<\/p>\r\n\r\n<div id=\"fs-idm13902288\" data-type=\"equation\"><img class=\" wp-image-1693 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1h.png\" alt=\"\" width=\"172\" height=\"48\" \/><\/div>\r\n<p id=\"fs-idm70320608\">Similarly, the rate of formation of H<sub>2<\/sub> is three times the rate of formation of N<sub>2<\/sub> because three moles of H<sub>2<\/sub> are produced for each mole of N<sub>2<\/sub> produced.<\/p>\r\n\r\n<div id=\"fs-idm22894544\" data-type=\"equation\"><img class=\"alignnone wp-image-1694 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1i.png\" alt=\"\" width=\"143\" height=\"52\" \/><\/div>\r\n<p id=\"fs-idp24387584\"><a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_NH3Decomp\">(Figure)<\/a> illustrates the change in concentrations over time for the decomposition of ammonia into nitrogen and hydrogen at 1100 \u00b0C. Slopes of the tangent lines at <em data-effect=\"italics\">t<\/em> = 500 s show that the instantaneous rates derived from all three species involved in the reaction are related by their stoichiometric factors. The rate of hydrogen production, for example, is observed to be three times greater than that for nitrogen production:<\/p>\r\n\r\n<div id=\"fs-idp160610960\" data-type=\"equation\"><img class=\"wp-image-1695 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1j.png\" alt=\"\" width=\"182\" height=\"51\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"CNX_Chem_12_01_NH3Decomp\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Changes in concentrations of the reactant and products for the reaction 2NH<sub>3<\/sub> \u27f6 N<sub>2<\/sub> + 3H<sub>2<\/sub>. The rates of change of the three concentrations are related by the reaction stoichiometry, as shown by the different slopes of the tangents at <em data-effect=\"italics\">t<\/em> = 500 s.<\/div>\r\n<span id=\"fs-idm83425632\" data-type=\"media\" data-alt=\"A graph is shown with the label, \u201cTime ( s ),\u201d appearing on the x-axis and, \u201cConcentration ( M ),\u201d on the y-axis. The x-axis markings begin at 0 and end at 2000. The markings are labeled at intervals of 500. The y-axis begins at 0 and includes markings every 1.0 times 10 superscript negative 3, up to 4.0 times 10 superscript negative 3. A decreasing, concave up, non-linear curve is shown, which begins at about 2.8 times 10 superscript negative 3 on the y-axis and nearly reaches a value of 0 at the far right of the graph at the 2000 marking on the x-axis. This curve is labeled, \u201c[ N H subscript 3].\u201d Two additional curves that are increasing and concave down are shown, both beginning at the origin. The lower of these two curves is labeled, \u201c[ N subscript 2 ].\u201d It reaches a value of approximately 1.25 times 10 superscript negative 3 at 2000 seconds. The final curve is labeled, \u201c[ H subscript 2 ].\u201d It reaches a value of about 3.9 times 10 superscript negative 3 at 2000 seconds. A red tangent line segment is drawn to each of the curves on the graph at 500 seconds. At 500 seconds on the x-axis, a vertical dashed line is shown. Next to the [ N H subscript 3] graph appears the equation \u201cnegative capital delta [ N H subscript 3 ] over capital delta t = negative slope = 1.94 times 10 superscript negative 6 M \/ s.\u201d Next to the [ N subscript 2] graph appears the equation \u201cnegative capital delta [ N subscript 2 ] over capital delta t = negative slope = 9.70 times 10 superscript negative 7 M \/ s.\u201d Next to the [ H subscript 2 ] graph appears the equation \u201cnegative capital delta [ H subscript 2 ] over capital delta t = negative slope = 2.91 times 10 superscript negative 6 M \/ s.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_NH3Decomp-2.jpg\" alt=\"A graph is shown with the label, \u201cTime ( s ),\u201d appearing on the x-axis and, \u201cConcentration ( M ),\u201d on the y-axis. The x-axis markings begin at 0 and end at 2000. The markings are labeled at intervals of 500. The y-axis begins at 0 and includes markings every 1.0 times 10 superscript negative 3, up to 4.0 times 10 superscript negative 3. A decreasing, concave up, non-linear curve is shown, which begins at about 2.8 times 10 superscript negative 3 on the y-axis and nearly reaches a value of 0 at the far right of the graph at the 2000 marking on the x-axis. This curve is labeled, \u201c[ N H subscript 3].\u201d Two additional curves that are increasing and concave down are shown, both beginning at the origin. The lower of these two curves is labeled, \u201c[ N subscript 2 ].\u201d It reaches a value of approximately 1.25 times 10 superscript negative 3 at 2000 seconds. The final curve is labeled, \u201c[ H subscript 2 ].\u201d It reaches a value of about 3.9 times 10 superscript negative 3 at 2000 seconds. A red tangent line segment is drawn to each of the curves on the graph at 500 seconds. At 500 seconds on the x-axis, a vertical dashed line is shown. Next to the [ N H subscript 3] graph appears the equation \u201cnegative capital delta [ N H subscript 3 ] over capital delta t = negative slope = 1.94 times 10 superscript negative 6 M \/ s.\u201d Next to the [ N subscript 2] graph appears the equation \u201cnegative capital delta [ N subscript 2 ] over capital delta t = negative slope = 9.70 times 10 superscript negative 7 M \/ s.\u201d Next to the [ H subscript 2 ] graph appears the equation \u201cnegative capital delta [ H subscript 2 ] over capital delta t = negative slope = 2.91 times 10 superscript negative 6 M \/ s.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idp40614224\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp68873968\"><strong>Expressions for Relative Reaction Rates:<\/strong><\/p>\r\nThe first step in the production of nitric acid is the combustion of ammonia:\r\n<div id=\"fs-idm14028784\" style=\"text-align: center\" data-type=\"equation\">4NH<sub>3<\/sub>(<em>g<\/em>) + 5O<sub>2<\/sub>(<em>g<\/em>) \u27f64NO(<em>g<\/em>) + 6H<sub>2<\/sub>O(<em>g<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp12553696\">Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.<\/p>\r\n<p id=\"fs-idm42014656\"><strong>Solution:<\/strong><\/p>\r\nConsidering the stoichiometry of this homogeneous reaction, the rates for the consumption of reactants and formation of products are:\r\n<div id=\"fs-idp78515888\" data-type=\"equation\"><img class=\"alignnone wp-image-1696 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-300x29.png\" alt=\"\" width=\"393\" height=\"38\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp160458048\"><strong>Check Your Learning:<\/strong><\/p>\r\nThe rate of formation of Br<sub>2<\/sub> is 6.0 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup> in a reaction described by the following net ionic equation:\r\n<div id=\"fs-idp202434352\" style=\"text-align: center\" data-type=\"equation\">5Br<sup>-<\/sup> + BrO<sub>3<\/sub><sup>-<\/sup> + 6H<sup>+ <\/sup>\u27f6 3Br<sub>2<\/sub> + 3H<sub>2<\/sub>O<\/div>\r\n<p id=\"fs-idm61531952\">Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.<\/p>\r\n\r\n<div id=\"fs-idp88636608\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm25685056\"><img class=\" wp-image-1697 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-300x26.png\" alt=\"\" width=\"497\" height=\"43\" \/><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm24260800\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm62578304\"><strong>Reaction Rate Expressions for Decomposition of H<sub>2<\/sub>O<sub>2<\/sub>:<\/strong><\/p>\r\nThe graph in <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_RRateIll\">(Figure)<\/a> shows the rate of the decomposition of H<sub>2<\/sub>O<sub>2<\/sub> over time:\r\n<div id=\"fs-idm25186720\" style=\"text-align: center\" data-type=\"equation\">2H<sub>2<\/sub>O<sub>2<\/sub> \u27f6 2H<sub>2<\/sub>O + O<sub>2<\/sub><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm78350032\">Based on these data, the instantaneous rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> at <em data-effect=\"italics\">t<\/em> = 11.1 h is determined to be 3.20 \u00d7 10<sup>\u22122<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>h<sup>-1<\/sup>, that is:<\/p>\r\n\r\n<div id=\"fs-idm63360896\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1698 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-300x48.png\" alt=\"\" width=\"300\" height=\"48\" \/><\/div>\r\n<p id=\"fs-idp76303472\">What is the instantaneous rate of production of H<sub>2<\/sub>O and O<sub>2<\/sub>?<\/p>\r\n<p id=\"fs-idm41764016\"><strong>Solution:<\/strong><\/p>\r\nThe reaction stoichiometry shows that\r\n<div id=\"fs-idp3043456\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1699 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-300x45.png\" alt=\"\" width=\"300\" height=\"45\" \/><\/div>\r\n<p id=\"fs-idm80784128\">Therefore:<\/p>\r\n\r\n<div id=\"fs-idm48629376\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1700 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-300x48.png\" alt=\"\" width=\"300\" height=\"48\" \/><\/div>\r\n<p id=\"fs-idm45164304\">and<\/p>\r\n\r\n<div id=\"fs-idp160741648\" data-type=\"equation\"><img class=\"alignnone size-medium wp-image-1701 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-300x59.png\" alt=\"\" width=\"300\" height=\"59\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp25364864\"><strong>Check Your Learning:<\/strong><\/p>\r\nIf the rate of decomposition of ammonia, NH<sub>3<\/sub>, at 1150 K is 2.10 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, what is the rate of production of nitrogen and hydrogen?\r\n<div id=\"fs-idp8646208\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm12525296\">1.05 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, N<sub>2<\/sub> and 3.15 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, H<sub>2<\/sub>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp13680896\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idp145842032\">The rate of a reaction can be expressed either in terms of the decrease in the amount of a reactant or the increase in the amount of a product per unit time. Relations between different rate expressions for a given reaction are derived directly from the stoichiometric coefficients of the equation representing the reaction.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp13917664\" class=\"key-equations\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Equations<\/strong><\/h3>\r\n<img class=\"alignnone wp-image-1702\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-300x26.png\" alt=\"\" width=\"519\" height=\"45\" \/>\r\n\r\n<\/div>\r\n<div id=\"fs-idm87178096\" class=\"exercises\" data-depth=\"1\">\r\n<div id=\"fs-idm40595504\" data-type=\"exercise\">\r\n<div id=\"fs-idm26000224\" data-type=\"problem\">\r\n<p id=\"fs-idp2868784\"><\/p>\r\n\r\n<\/div>\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-idp11569888\">\r\n \t<dt>average rate<\/dt>\r\n \t<dd id=\"fs-idm53764208\">rate of a chemical reaction computed as the ratio of a measured change in amount or concentration of substance to the time interval over which the change occurred<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp24984224\">\r\n \t<dt>initial rate<\/dt>\r\n \t<dd id=\"fs-idp15016160\">instantaneous rate of a chemical reaction at <em data-effect=\"italics\">t<\/em> = 0 s (immediately after the reaction has begun)<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp70925872\">\r\n \t<dt>instantaneous rate<\/dt>\r\n \t<dd id=\"fs-idp166671184\">rate of a chemical reaction at any instant in time, determined by the slope of the line tangential to a graph of concentration as a function of time<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp172602144\">\r\n \t<dt>rate of reaction<\/dt>\r\n \t<dd id=\"fs-idm82485008\">measure of the speed at which a chemical reaction takes place<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp193131840\">\r\n \t<dt>rate expression<\/dt>\r\n \t<dd id=\"fs-idm43290528\">mathematical representation defining reaction rate as change in amount, concentration, or pressure of reactant or product species per unit time<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<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>Define chemical reaction rate<\/li>\n<li>Derive rate expressions from the balanced equation for a given chemical reaction<\/li>\n<li>Calculate reaction rates from experimental data<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-idp37629504\">A <em data-effect=\"italics\">rate<\/em> is a measure of how some property varies with time. Speed is a familiar rate that expresses the distance travelled by an object in a given amount of time. Wage is a rate that represents the amount of money earned by a person working for a given amount of time. Likewise, the rate of a chemical reaction is a measure of how much reactant is consumed, or how much product is produced, by the reaction in a given amount of time.<\/p>\n<p id=\"fs-idp11492384\">The <strong>rate of reaction<\/strong> is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure. For reactions involving one or more coloured substances, rates may be monitored via measurements of light absorption. For reactions involving aqueous electrolytes, rates may be measured via changes in a solution\u2019s conductivity.<\/p>\n<p id=\"fs-idm49411904\">For reactants and products in solution, their relative amounts (concentrations) are conveniently used for purposes of expressing reaction rates. For example, the concentration of hydrogen peroxide, H<sub>2<\/sub>O<sub>2<\/sub>, in an aqueous solution changes slowly over time as it decomposes according to the equation:<\/p>\n<div id=\"fs-idp26890848\" style=\"text-align: center\" data-type=\"equation\">2H<sub>2<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) \u27f6 2H<sub>2<\/sub>O(<em>l<\/em>) + O<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idp202399680\">The rate at which the hydrogen peroxide decomposes can be expressed in terms of the rate of change of its concentration, as shown here:<\/p>\n<div id=\"fs-idm23827472\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1686 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-300x69.png\" alt=\"\" width=\"530\" height=\"122\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-300x69.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-65x15.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-225x52.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a-350x81.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1a.png 683w\" sizes=\"auto, (max-width: 530px) 100vw, 530px\" \/><\/div>\n<p id=\"fs-idp37715584\">This mathematical representation of the change in species concentration over time is the<strong> rate expression<\/strong> for the reaction. The brackets indicate molar concentrations, and the symbol delta (\u0394) indicates \u201cchange in.\u201d Thus, [H<sub>2<\/sub>O<sub>2<\/sub>]<sub>t1<\/sub> represents the molar concentration of hydrogen peroxide at some time <em data-effect=\"italics\">t<\/em><sub>1<\/sub>; likewise,[H<sub>2<\/sub>O<sub>2<\/sub>]<sub>t2<\/sub> represents the molar concentration of hydrogen peroxide at a later time <em data-effect=\"italics\">t<\/em><sub>2<\/sub>; and \u0394[H<sub>2<\/sub>O<sub>2<\/sub>] represents the change in molar concentration of hydrogen peroxide during the time interval \u0394<em data-effect=\"italics\">t<\/em> (that is, <em data-effect=\"italics\">t<\/em><sub>2<\/sub> \u2212 <em data-effect=\"italics\">t<\/em><sub>1<\/sub>). Since the reactant concentration decreases as the reaction proceeds, \u0394[H<sub>2<\/sub>O<sub>2<\/sub>] is a negative quantity. Reaction rates are, by convention, positive quantities, and so this negative change in concentration is multiplied by \u22121. <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_KDataH2O2\">(Figure)<\/a> provides an example of data collected during the decomposition of H<sub>2<\/sub>O<sub>2<\/sub>.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_12_01_KDataH2O2\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> in an aqueous solution decreases as the concentration of H<sub>2<\/sub>O<sub>2<\/sub> decreases.<\/div>\n<p><span id=\"fs-idp13735104\" data-type=\"media\" data-alt=\"A table with five columns is shown. The first column is labeled, \u201cTime, h.\u201d Beneath it the numbers 0.00, 6.00, 12.00, 18.00, and 24.00 are listed. The second column is labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers 1.000, 0.500, 0.250, 0.125, and 0.0625 are double spaced. To the right, a third column is labeled, \u201ccapital delta [ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers negative 0.500, negative 0.250, negative 0.125, and negative 0.062 are listed such that they are double spaced and offset, beginning one line below the first number listed in the column labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d The first two numbers in the second column have line segments extending from their right side to the left side of the first number in the third row. The second and third numbers in the second column have line segments extending from their right side to the left side of the second number in the third row. The third and fourth numbers in the second column have line segments extending from their right side to the left side of the third number in the third row. The fourth and fifth numbers in the second column have line segments extending from their right side to the left side of the fourth number in the third row. The fourth column in labeled, \u201ccapital delta t, h.\u201d Below the title, the value 6.00 is listed four times, each single-spaced. The fifth and final column is labeled \u201cRate of Decomposition, mol \/ L superscript negative 1 \/ h superscript negative 1.\u201d Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.010.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_KDataH2O2-2.jpg\" alt=\"A table with five columns is shown. The first column is labeled, \u201cTime, h.\u201d Beneath it the numbers 0.00, 6.00, 12.00, 18.00, and 24.00 are listed. The second column is labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers 1.000, 0.500, 0.250, 0.125, and 0.0625 are double spaced. To the right, a third column is labeled, \u201ccapital delta [ H subscript 2 O subscript 2 ], mol \/ L.\u201d Below, the numbers negative 0.500, negative 0.250, negative 0.125, and negative 0.062 are listed such that they are double spaced and offset, beginning one line below the first number listed in the column labeled, \u201c[ H subscript 2 O subscript 2 ], mol \/ L.\u201d The first two numbers in the second column have line segments extending from their right side to the left side of the first number in the third row. The second and third numbers in the second column have line segments extending from their right side to the left side of the second number in the third row. The third and fourth numbers in the second column have line segments extending from their right side to the left side of the third number in the third row. The fourth and fifth numbers in the second column have line segments extending from their right side to the left side of the fourth number in the third row. The fourth column in labeled, \u201ccapital delta t, h.\u201d Below the title, the value 6.00 is listed four times, each single-spaced. The fifth and final column is labeled \u201cRate of Decomposition, mol \/ L superscript negative 1 \/ h superscript negative 1.\u201d Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.010.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm29280704\">To obtain the tabulated results for this decomposition, the concentration of hydrogen peroxide was measured every 6 hours over the course of a day at a constant temperature of 40 \u00b0C. Reaction rates were computed for each time interval by dividing the change in concentration by the corresponding time increment, as shown here for the first 6-hour period:<\/p>\n<div id=\"fs-idm14828496\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1687 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-300x29.png\" alt=\"\" width=\"434\" height=\"42\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-300x29.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-225x21.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b-350x33.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1b.png 747w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/div>\n<p id=\"fs-idp40709888\">Notice that the reaction rates vary with time, decreasing as the reaction proceeds. Results for the last 6-hour period yield a reaction rate of:<\/p>\n<div id=\"fs-idp151295040\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1688 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-300x29.png\" alt=\"\" width=\"424\" height=\"41\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-300x29.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-225x22.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c-350x34.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1c.png 739w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/div>\n<p id=\"fs-idp101513872\">This behaviour indicates the reaction continually slows with time. Using the concentrations at the beginning and end of a time period over which the reaction rate is changing results in the calculation of an<strong> average rate<\/strong> for the reaction over this time interval. At any specific time, the rate at which a reaction is proceeding is known as its <strong>instantaneous rate<\/strong>. The instantaneous rate of a reaction at \u201ctime zero,\u201d when the reaction commences, is its <strong>initial rate<\/strong>. Consider the analogy of a car slowing down as it approaches a stop sign. The vehicle\u2019s initial rate\u2014analogous to the beginning of a chemical reaction\u2014would be the speedometer reading at the moment the driver begins pressing the brakes (<em data-effect=\"italics\">t<\/em><sub>0<\/sub>). A few moments later, the instantaneous rate at a specific moment\u2014call it <em data-effect=\"italics\">t<\/em><sub>1<\/sub>\u2014would be somewhat slower, as indicated by the speedometer reading at that point in time. As time passes, the instantaneous rate will continue to fall until it reaches zero, when the car (or reaction) stops. Unlike instantaneous speed, the car\u2019s average speed is not indicated by the speedometer; but it can be calculated as the ratio of the distance travelled to the time required to bring the vehicle to a complete stop (\u0394<em data-effect=\"italics\">t<\/em>). Like the decelerating car, the average rate of a chemical reaction will fall somewhere between its initial and final rates.<\/p>\n<p id=\"fs-idm65553280\">The instantaneous rate of a reaction may be determined one of two ways. If experimental conditions permit the measurement of concentration changes over very short time intervals, then average rates computed as described earlier provide reasonably good approximations of instantaneous rates. Alternatively, a graphical procedure may be used that, in effect, yields the results that would be obtained if short time interval measurements were possible. In a plot of the concentration of hydrogen peroxide against time, the instantaneous rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> at any time <em data-effect=\"italics\">t<\/em> is given by the slope of a straight line that is tangent to the curve at that time (<a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_RRateIll\">(Figure)<\/a>). These tangent line slopes may be evaluated using calculus, but the procedure for doing so is beyond the scope of this chapter.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_12_01_RRateIll\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">This graph shows a plot of concentration versus time for a 1.000 <em data-effect=\"italics\">M<\/em> solution of H<sub>2<\/sub>O<sub>2<\/sub>. The rate at any time is equal to the negative of the slope of a line tangent to the curve at that time. Tangents are shown at <em data-effect=\"italics\">t<\/em> = 0 h (\u201cinitial rate\u201d) and at <em data-effect=\"italics\">t<\/em> = 12 h (\u201cinstantaneous rate\u201d at 12 h).<\/div>\n<p><span id=\"fs-idp329500576\" data-type=\"media\" data-alt=\"A graph is shown with the label, \u201cTime ( h ),\u201d appearing on the x-axis and \u201c[ H subscript 2 O subscript 2 ] ( mol per L)\u201d on the y-axis. The x-axis markings begin at 0.00 and end at 24.00. The markings are labeled at intervals of 6.00. The y-axis begins at 0.000 and includes markings every 0.200, up to 1.000. A decreasing, concave up, non-linear curve is shown, which begins at 1.000 on the y-axis and nearly reaches a value of 0 at the far right of the graph around 24.00 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis at 1.000. The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 0 equals initial rate\u201d. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 12 equals instantaneous rate at 12 h.\u201d A second red tangent line segment is drawn near the middle of the curve at 12.00 on the x-axis. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_RRateIll-2.jpg\" alt=\"A graph is shown with the label, \u201cTime ( h ),\u201d appearing on the x-axis and \u201c[ H subscript 2 O subscript 2 ] ( mol per L)\u201d on the y-axis. The x-axis markings begin at 0.00 and end at 24.00. The markings are labeled at intervals of 6.00. The y-axis begins at 0.000 and includes markings every 0.200, up to 1.000. A decreasing, concave up, non-linear curve is shown, which begins at 1.000 on the y-axis and nearly reaches a value of 0 at the far right of the graph around 24.00 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis at 1.000. The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 0 equals initial rate\u201d. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d The slope is labeled as \u201cslope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 12 equals instantaneous rate at 12 h.\u201d A second red tangent line segment is drawn near the middle of the curve at 12.00 on the x-axis. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled \u201ccapital delta [ H subscript 2 O subscript 2 ]\u201d and the horizontal leg is labeled, \u201ccapital delta t.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idm69729856\" class=\"chemistry everyday-life\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Reaction Rates in Analysis: Test Strips for Urinalysis<\/strong><\/div>\n<p id=\"fs-idp8375264\">Physicians often use disposable test strips to measure the amounts of various substances in a patient\u2019s urine (<a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_Urinestrip\">(Figure)<\/a>). These test strips contain various chemical reagents, embedded in small pads at various locations along the strip, which undergo changes in colour upon exposure to sufficient concentrations of specific substances. The usage instructions for test strips often stress that proper read time is critical for optimal results. This emphasis on read time suggests that kinetic aspects of the chemical reactions occurring on the test strip are important considerations.<\/p>\n<p id=\"fs-idp37368560\">The test for urinary glucose relies on a two-step process represented by the chemical equations shown here:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1689 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-300x101.png\" alt=\"\" width=\"300\" height=\"101\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-300x101.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-65x22.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-225x76.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d-350x118.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1d.png 443w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p id=\"fs-idp79309424\">The first equation depicts the oxidation of glucose in the urine to yield glucolactone and hydrogen peroxide. The hydrogen peroxide produced subsequently oxidizes colourless iodide ion to yield brown iodine, which may be visually detected. Some strips include an additional substance that reacts with iodine to produce a more distinct colour change.<\/p>\n<p id=\"fs-idm13608336\">The two test reactions shown above are inherently very slow, but their rates are increased by special enzymes embedded in the test strip pad. This is an example of <em data-effect=\"italics\">catalysis<\/em>, a topic discussed later in this chapter. A typical glucose test strip for use with urine requires approximately 30 seconds for completion of the colour-forming reactions. Reading the result too soon might lead one to conclude that the glucose concentration of the urine sample is lower than it actually is (a <em data-effect=\"italics\">false-negative<\/em> result). Waiting too long to assess the colour change can lead to a <em data-effect=\"italics\">false positive<\/em> due to the slower (not catalyzed) oxidation of iodide ion by other substances found in urine.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_12_01_Urinestrip\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Test strips are commonly used to detect the presence of specific substances in a person\u2019s urine. Many test strips have several pads containing various reagents to permit the detection of multiple substances on a single strip. (credit: Iqbal Osman)<\/div>\n<p><span id=\"fs-idp35718480\" data-type=\"media\" data-alt=\"A photograph shows 8 test strips laid on paper toweling. Each strip contains 11 small sections of various colors, including yellow, tan, black, red, orange, blue, white, and green.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_Urinestrip-2.jpg\" alt=\"A photograph shows 8 test strips laid on paper toweling. Each strip contains 11 small sections of various colors, including yellow, tan, black, red, orange, blue, white, and green.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm24537456\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Relative Rates of Reaction<\/strong><\/h3>\n<p id=\"fs-idm26303136\">The rate of a reaction may be expressed as the change in concentration of any reactant or product. For any given reaction, these rate expressions are all related simply to one another according to the reaction stoichiometry. The rate of the general reaction<\/p>\n<div id=\"fs-idm246244416\" style=\"text-align: center\" data-type=\"equation\">aA \u27f6bB<\/div>\n<p id=\"fs-idm219494144\">can be expressed in terms of the decrease in the concentration of A or the increase in the concentration of B. These two rate expressions are related by the stoichiometry of the reaction:<\/p>\n<div id=\"fs-idm243742160\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1690 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-300x53.png\" alt=\"\" width=\"300\" height=\"53\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-300x53.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-65x11.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-225x40.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e-350x62.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1e.png 441w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idm641684800\">the reaction represented by the following equation:<\/p>\n<div id=\"fs-idp46974560\" style=\"text-align: center\" data-type=\"equation\">2NH<sub>3<\/sub>(<em>g<\/em>) \u27f6 N<sub>2<\/sub>(<em>g<\/em>) + 3H<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idm52700320\">The relation between the reaction rates expressed in terms of nitrogen production and ammonia consumption, for example, is:<\/p>\n<div id=\"fs-idm85736576\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1691 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-300x47.png\" alt=\"\" width=\"300\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-300x47.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-225x35.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f-350x55.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1f.png 476w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idp170662352\">This may be represented in an abbreviated format by omitting the units of the stoichiometric factor:<\/p>\n<div id=\"fs-idp45966480\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1692 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g-300x63.png\" alt=\"\" width=\"234\" height=\"49\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g-300x63.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g-65x14.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g-225x47.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1g.png 332w\" sizes=\"auto, (max-width: 234px) 100vw, 234px\" \/><\/div>\n<p id=\"fs-idm93957280\">Note that a negative sign has been included as a factor to account for the opposite signs of the two amount changes (the reactant amount is decreasing while the product amount is increasing). For homogeneous reactions, both the reactants and products are present in the same solution and thus occupy the same volume, so the molar amounts may be replaced with molar concentrations:<\/p>\n<div id=\"fs-idm13902288\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1693 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1h.png\" alt=\"\" width=\"172\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1h.png 255w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1h-65x18.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1h-225x63.png 225w\" sizes=\"auto, (max-width: 172px) 100vw, 172px\" \/><\/div>\n<p id=\"fs-idm70320608\">Similarly, the rate of formation of H<sub>2<\/sub> is three times the rate of formation of N<sub>2<\/sub> because three moles of H<sub>2<\/sub> are produced for each mole of N<sub>2<\/sub> produced.<\/p>\n<div id=\"fs-idm22894544\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1694 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1i.png\" alt=\"\" width=\"143\" height=\"52\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1i.png 212w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1i-65x24.png 65w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/div>\n<p id=\"fs-idp24387584\"><a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_NH3Decomp\">(Figure)<\/a> illustrates the change in concentrations over time for the decomposition of ammonia into nitrogen and hydrogen at 1100 \u00b0C. Slopes of the tangent lines at <em data-effect=\"italics\">t<\/em> = 500 s show that the instantaneous rates derived from all three species involved in the reaction are related by their stoichiometric factors. The rate of hydrogen production, for example, is observed to be three times greater than that for nitrogen production:<\/p>\n<div id=\"fs-idp160610960\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1695 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1j.png\" alt=\"\" width=\"182\" height=\"51\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1j.png 264w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1j-65x18.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1j-225x63.png 225w\" sizes=\"auto, (max-width: 182px) 100vw, 182px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"CNX_Chem_12_01_NH3Decomp\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Changes in concentrations of the reactant and products for the reaction 2NH<sub>3<\/sub> \u27f6 N<sub>2<\/sub> + 3H<sub>2<\/sub>. The rates of change of the three concentrations are related by the reaction stoichiometry, as shown by the different slopes of the tangents at <em data-effect=\"italics\">t<\/em> = 500 s.<\/div>\n<p><span id=\"fs-idm83425632\" data-type=\"media\" data-alt=\"A graph is shown with the label, \u201cTime ( s ),\u201d appearing on the x-axis and, \u201cConcentration ( M ),\u201d on the y-axis. The x-axis markings begin at 0 and end at 2000. The markings are labeled at intervals of 500. The y-axis begins at 0 and includes markings every 1.0 times 10 superscript negative 3, up to 4.0 times 10 superscript negative 3. A decreasing, concave up, non-linear curve is shown, which begins at about 2.8 times 10 superscript negative 3 on the y-axis and nearly reaches a value of 0 at the far right of the graph at the 2000 marking on the x-axis. This curve is labeled, \u201c[ N H subscript 3].\u201d Two additional curves that are increasing and concave down are shown, both beginning at the origin. The lower of these two curves is labeled, \u201c[ N subscript 2 ].\u201d It reaches a value of approximately 1.25 times 10 superscript negative 3 at 2000 seconds. The final curve is labeled, \u201c[ H subscript 2 ].\u201d It reaches a value of about 3.9 times 10 superscript negative 3 at 2000 seconds. A red tangent line segment is drawn to each of the curves on the graph at 500 seconds. At 500 seconds on the x-axis, a vertical dashed line is shown. Next to the [ N H subscript 3] graph appears the equation \u201cnegative capital delta [ N H subscript 3 ] over capital delta t = negative slope = 1.94 times 10 superscript negative 6 M \/ s.\u201d Next to the [ N subscript 2] graph appears the equation \u201cnegative capital delta [ N subscript 2 ] over capital delta t = negative slope = 9.70 times 10 superscript negative 7 M \/ s.\u201d Next to the [ H subscript 2 ] graph appears the equation \u201cnegative capital delta [ H subscript 2 ] over capital delta t = negative slope = 2.91 times 10 superscript negative 6 M \/ s.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_01_NH3Decomp-2.jpg\" alt=\"A graph is shown with the label, \u201cTime ( s ),\u201d appearing on the x-axis and, \u201cConcentration ( M ),\u201d on the y-axis. The x-axis markings begin at 0 and end at 2000. The markings are labeled at intervals of 500. The y-axis begins at 0 and includes markings every 1.0 times 10 superscript negative 3, up to 4.0 times 10 superscript negative 3. A decreasing, concave up, non-linear curve is shown, which begins at about 2.8 times 10 superscript negative 3 on the y-axis and nearly reaches a value of 0 at the far right of the graph at the 2000 marking on the x-axis. This curve is labeled, \u201c[ N H subscript 3].\u201d Two additional curves that are increasing and concave down are shown, both beginning at the origin. The lower of these two curves is labeled, \u201c[ N subscript 2 ].\u201d It reaches a value of approximately 1.25 times 10 superscript negative 3 at 2000 seconds. The final curve is labeled, \u201c[ H subscript 2 ].\u201d It reaches a value of about 3.9 times 10 superscript negative 3 at 2000 seconds. A red tangent line segment is drawn to each of the curves on the graph at 500 seconds. At 500 seconds on the x-axis, a vertical dashed line is shown. Next to the [ N H subscript 3] graph appears the equation \u201cnegative capital delta [ N H subscript 3 ] over capital delta t = negative slope = 1.94 times 10 superscript negative 6 M \/ s.\u201d Next to the [ N subscript 2] graph appears the equation \u201cnegative capital delta [ N subscript 2 ] over capital delta t = negative slope = 9.70 times 10 superscript negative 7 M \/ s.\u201d Next to the [ H subscript 2 ] graph appears the equation \u201cnegative capital delta [ H subscript 2 ] over capital delta t = negative slope = 2.91 times 10 superscript negative 6 M \/ s.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idp40614224\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp68873968\"><strong>Expressions for Relative Reaction Rates:<\/strong><\/p>\n<p>The first step in the production of nitric acid is the combustion of ammonia:<\/p>\n<div id=\"fs-idm14028784\" style=\"text-align: center\" data-type=\"equation\">4NH<sub>3<\/sub>(<em>g<\/em>) + 5O<sub>2<\/sub>(<em>g<\/em>) \u27f64NO(<em>g<\/em>) + 6H<sub>2<\/sub>O(<em>g<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp12553696\">Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.<\/p>\n<p id=\"fs-idm42014656\"><strong>Solution:<\/strong><\/p>\n<p>Considering the stoichiometry of this homogeneous reaction, the rates for the consumption of reactants and formation of products are:<\/p>\n<div id=\"fs-idp78515888\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1696 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-300x29.png\" alt=\"\" width=\"393\" height=\"38\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-300x29.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-225x22.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k-350x34.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1k.png 627w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp160458048\"><strong>Check Your Learning:<\/strong><\/p>\n<p>The rate of formation of Br<sub>2<\/sub> is 6.0 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup> in a reaction described by the following net ionic equation:<\/p>\n<div id=\"fs-idp202434352\" style=\"text-align: center\" data-type=\"equation\">5Br<sup>&#8211;<\/sup> + BrO<sub>3<\/sub><sup>&#8211;<\/sup> + 6H<sup>+ <\/sup>\u27f6 3Br<sub>2<\/sub> + 3H<sub>2<\/sub>O<\/div>\n<p id=\"fs-idm61531952\">Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.<\/p>\n<div id=\"fs-idp88636608\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm25685056\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1697 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-300x26.png\" alt=\"\" width=\"497\" height=\"43\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-300x26.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-225x19.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l-350x30.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1l.png 658w\" sizes=\"auto, (max-width: 497px) 100vw, 497px\" \/><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm24260800\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm62578304\"><strong>Reaction Rate Expressions for Decomposition of H<sub>2<\/sub>O<sub>2<\/sub>:<\/strong><\/p>\n<p>The graph in <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_01_RRateIll\">(Figure)<\/a> shows the rate of the decomposition of H<sub>2<\/sub>O<sub>2<\/sub> over time:<\/p>\n<div id=\"fs-idm25186720\" style=\"text-align: center\" data-type=\"equation\">2H<sub>2<\/sub>O<sub>2<\/sub> \u27f6 2H<sub>2<\/sub>O + O<sub>2<\/sub><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm78350032\">Based on these data, the instantaneous rate of decomposition of H<sub>2<\/sub>O<sub>2<\/sub> at <em data-effect=\"italics\">t<\/em> = 11.1 h is determined to be 3.20 \u00d7 10<sup>\u22122<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>h<sup>-1<\/sup>, that is:<\/p>\n<div id=\"fs-idm63360896\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1698 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-300x48.png\" alt=\"\" width=\"300\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-300x48.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-225x36.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m-350x56.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1m.png 437w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idp76303472\">What is the instantaneous rate of production of H<sub>2<\/sub>O and O<sub>2<\/sub>?<\/p>\n<p id=\"fs-idm41764016\"><strong>Solution:<\/strong><\/p>\n<p>The reaction stoichiometry shows that<\/p>\n<div id=\"fs-idp3043456\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1699 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-300x45.png\" alt=\"\" width=\"300\" height=\"45\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-300x45.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-225x34.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n-350x53.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1n.png 444w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idm80784128\">Therefore:<\/p>\n<div id=\"fs-idm48629376\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1700 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-300x48.png\" alt=\"\" width=\"300\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-300x48.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-225x36.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o-350x56.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1o.png 457w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<p id=\"fs-idm45164304\">and<\/p>\n<div id=\"fs-idp160741648\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1701 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-300x59.png\" alt=\"\" width=\"300\" height=\"59\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-300x59.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-65x13.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-225x44.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p-350x68.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1p.png 384w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp25364864\"><strong>Check Your Learning:<\/strong><\/p>\n<p>If the rate of decomposition of ammonia, NH<sub>3<\/sub>, at 1150 K is 2.10 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, what is the rate of production of nitrogen and hydrogen?<\/p>\n<div id=\"fs-idp8646208\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm12525296\">1.05 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, N<sub>2<\/sub> and 3.15 \u00d7 10<sup>\u22126<\/sup> mol<sup>.<\/sup>L<sup>-1.<\/sup>s<sup>-1<\/sup>, H<sub>2<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp13680896\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idp145842032\">The rate of a reaction can be expressed either in terms of the decrease in the amount of a reactant or the increase in the amount of a product per unit time. Relations between different rate expressions for a given reaction are derived directly from the stoichiometric coefficients of the equation representing the reaction.<\/p>\n<\/div>\n<div id=\"fs-idp13917664\" class=\"key-equations\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Equations<\/strong><\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1702\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-300x26.png\" alt=\"\" width=\"519\" height=\"45\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-300x26.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-225x20.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q-350x31.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.1q.png 649w\" sizes=\"auto, (max-width: 519px) 100vw, 519px\" \/><\/p>\n<\/div>\n<div id=\"fs-idm87178096\" class=\"exercises\" data-depth=\"1\">\n<div id=\"fs-idm40595504\" data-type=\"exercise\">\n<div id=\"fs-idm26000224\" data-type=\"problem\">\n<p id=\"fs-idp2868784\">\n<\/div>\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-idp11569888\">\n<dt>average rate<\/dt>\n<dd id=\"fs-idm53764208\">rate of a chemical reaction computed as the ratio of a measured change in amount or concentration of substance to the time interval over which the change occurred<\/dd>\n<\/dl>\n<dl id=\"fs-idp24984224\">\n<dt>initial rate<\/dt>\n<dd id=\"fs-idp15016160\">instantaneous rate of a chemical reaction at <em data-effect=\"italics\">t<\/em> = 0 s (immediately after the reaction has begun)<\/dd>\n<\/dl>\n<dl id=\"fs-idp70925872\">\n<dt>instantaneous rate<\/dt>\n<dd id=\"fs-idp166671184\">rate of a chemical reaction at any instant in time, determined by the slope of the line tangential to a graph of concentration as a function of time<\/dd>\n<\/dl>\n<dl id=\"fs-idp172602144\">\n<dt>rate of reaction<\/dt>\n<dd id=\"fs-idm82485008\">measure of the speed at which a chemical reaction takes place<\/dd>\n<\/dl>\n<dl id=\"fs-idp193131840\">\n<dt>rate expression<\/dt>\n<dd id=\"fs-idm43290528\">mathematical representation defining reaction rate as change in amount, concentration, or pressure of reactant or product species per unit time<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":1392,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-702","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":695,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/702","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\/702\/revisions"}],"predecessor-version":[{"id":2159,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/702\/revisions\/2159"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/695"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/702\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=702"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=702"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=702"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}