{"id":3225,"date":"2016-08-25T19:33:20","date_gmt":"2016-08-25T19:33:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/?post_type=chapter&#038;p=3225"},"modified":"2016-08-26T19:19:34","modified_gmt":"2016-08-26T19:19:34","slug":"rate-law-and-specific-rate-constant","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/rate-law-and-specific-rate-constant\/","title":{"raw":"Rate Law and Specific Rate Constant","rendered":"Rate Law and Specific Rate Constant"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div>\r\n<ul>\r\n \t<li>Define rate law.<\/li>\r\n \t<li>Define specific rate constant.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>ExamplesWhat are the migration patterns of the current population?<\/h3>\r\n[caption id=\"\" align=\"aligncenter\" width=\"600\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212843\/20140811155714994723.png\" alt=\"Map of North Carolina showing the population changes in counties. The rate of change of a quantity is often very important.\" width=\"600\" height=\"189\" \/> State of North Carolina Population Change. Courtesy of the US Census\/<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:North-Carolina-Population-Change-2000-to-2008.png\">Wikimedia<\/a>.[\/caption]\r\n\r\nWhere are people moving from and where are they moving to? How fast is the population changing in different areas? These are important questions for people involved in deciding about where to build schools or hospitals or where to open new businesses. If an area is growing rapidly, action needs to be taken soon to accommodate the growth. How fast the growth is will determine how many schools to build. Rates of change affect a lot of decisions.\r\n\r\n<\/div>\r\n<h2>Rate Law and Specific Rate Constant<\/h2>\r\nConsider a simple chemical reaction in which reactant <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> is converted into product <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> according to the equation below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/881bf241e70aea811728aff9c139726b.png\" alt=\"A rightarrow B\" width=\"56\" height=\"13\" \/>\r\n\r\nThe rate of reaction is given by the change in concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> as a function of time. The rate of disappearance of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> is also proportional to the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> .\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/156a972617935907fef9f2a30a25a891.png\" alt=\"-frac{Delta [A]}{Delta t} alpha [A]\" width=\"99\" height=\"38\" \/>\r\n\r\nSince the rate of a reaction generally depends upon collision frequency, it stands to reason that as the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> increases, the rate of reaction increases. Likewise, as the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> decreases, the rate of reaction decreases. The expression for the rate of the reaction can be shown as follows:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/4ff2fe099ca6ac0e167e6725c33c52b9.png\" alt=\"text{rate}=-frac{Delta [A]}{Delta t} quad text{or} quad text{rate}=k[A]\" width=\"248\" height=\"38\" \/>\r\n\r\nThe proportionality between the rate and <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212846\/9dc83c994c30bd8abf0bc5ad6ea817f0.png\" alt=\"[A]\" width=\"19\" height=\"18\" \/> becomes an equal sign by the insertion of a constant <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/>. A <strong> rate law <\/strong> is an expression showing the relationship of the reaction rate to the concentrations of each reactant. The <strong> specific rate constant <\/strong><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/> is the proportionality constant relating the rate of the reaction to the concentrations of reactants. The rate law and the specific rate constant for any chemical reaction must be determined experimentally. The value of the rate constant is temperature dependent. A large value of the rate constant means that the reaction is relatively fast, while a small value of the rate constant means that the reaction is relatively slow.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul>\r\n \t<li>The rate law and specific rate constant are defined.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\nRead the material at the link below and answer the following questions:\r\n\r\n<a href=\"http:\/\/www.differencebetween.com\/difference-between-reaction-rate-and-vs-specific-rate-constant\/\"> http:\/\/www.differencebetween.com\/difference-between-reaction-rate-and-vs-specific-rate-constant\/ <\/a>\r\n<ol>\r\n \t<li>Why is the sign for reactant concentration negative?<\/li>\r\n \t<li>Why is the sign for product concentration positive?<\/li>\r\n \t<li>What do the lower-case letters in the rate equation represent?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<ol>\r\n \t<li>What is a rate law?<\/li>\r\n \t<li>What is a specific rate constant?<\/li>\r\n \t<li>How are these parameters determined?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h2>\u00a0Glossary<\/h2>\r\n<div>\r\n<ul>\r\n \t<li><strong> rate law: <\/strong> An expression showing the relationship of the reaction rate to the concentrations of each reactant.<\/li>\r\n \t<li><strong> specific rate constant <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/> : <\/strong> The proportionality constant relating the rate of the reaction to the concentrations of reactants.<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div>\n<ul>\n<li>Define rate law.<\/li>\n<li>Define specific rate constant.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>ExamplesWhat are the migration patterns of the current population?<\/h3>\n<div style=\"width: 610px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212843\/20140811155714994723.png\" alt=\"Map of North Carolina showing the population changes in counties. The rate of change of a quantity is often very important.\" width=\"600\" height=\"189\" \/><\/p>\n<p class=\"wp-caption-text\">State of North Carolina Population Change. Courtesy of the US Census\/<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:North-Carolina-Population-Change-2000-to-2008.png\">Wikimedia<\/a>.<\/p>\n<\/div>\n<p>Where are people moving from and where are they moving to? How fast is the population changing in different areas? These are important questions for people involved in deciding about where to build schools or hospitals or where to open new businesses. If an area is growing rapidly, action needs to be taken soon to accommodate the growth. How fast the growth is will determine how many schools to build. Rates of change affect a lot of decisions.<\/p>\n<\/div>\n<h2>Rate Law and Specific Rate Constant<\/h2>\n<p>Consider a simple chemical reaction in which reactant <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> is converted into product <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> according to the equation below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/881bf241e70aea811728aff9c139726b.png\" alt=\"A rightarrow B\" width=\"56\" height=\"13\" \/><\/p>\n<p>The rate of reaction is given by the change in concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> as a function of time. The rate of disappearance of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> is also proportional to the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> .<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/156a972617935907fef9f2a30a25a891.png\" alt=\"-frac{Delta [A]}{Delta t} alpha [A]\" width=\"99\" height=\"38\" \/><\/p>\n<p>Since the rate of a reaction generally depends upon collision frequency, it stands to reason that as the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> increases, the rate of reaction increases. Likewise, as the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> decreases, the rate of reaction decreases. The expression for the rate of the reaction can be shown as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212845\/4ff2fe099ca6ac0e167e6725c33c52b9.png\" alt=\"text{rate}=-frac{Delta [A]}{Delta t} quad text{or} quad text{rate}=k[A]\" width=\"248\" height=\"38\" \/><\/p>\n<p>The proportionality between the rate and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212846\/9dc83c994c30bd8abf0bc5ad6ea817f0.png\" alt=\"[A]\" width=\"19\" height=\"18\" \/> becomes an equal sign by the insertion of a constant <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/>. A <strong> rate law <\/strong> is an expression showing the relationship of the reaction rate to the concentrations of each reactant. The <strong> specific rate constant <\/strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/> is the proportionality constant relating the rate of the reaction to the concentrations of reactants. The rate law and the specific rate constant for any chemical reaction must be determined experimentally. The value of the rate constant is temperature dependent. A large value of the rate constant means that the reaction is relatively fast, while a small value of the rate constant means that the reaction is relatively slow.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul>\n<li>The rate law and specific rate constant are defined.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p>Read the material at the link below and answer the following questions:<\/p>\n<p><a href=\"http:\/\/www.differencebetween.com\/difference-between-reaction-rate-and-vs-specific-rate-constant\/\"> http:\/\/www.differencebetween.com\/difference-between-reaction-rate-and-vs-specific-rate-constant\/ <\/a><\/p>\n<ol>\n<li>Why is the sign for reactant concentration negative?<\/li>\n<li>Why is the sign for product concentration positive?<\/li>\n<li>What do the lower-case letters in the rate equation represent?<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<ol>\n<li>What is a rate law?<\/li>\n<li>What is a specific rate constant?<\/li>\n<li>How are these parameters determined?<\/li>\n<\/ol>\n<\/div>\n<h2>\u00a0Glossary<\/h2>\n<div>\n<ul>\n<li><strong> rate law: <\/strong> An expression showing the relationship of the reaction rate to the concentrations of each reactant.<\/li>\n<li><strong> specific rate constant <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212122\/8c0cf0a5c7fa06aa679382f3c2076f4d.png\" alt=\"(k)\" width=\"22\" height=\"18\" \/> : <\/strong> The proportionality constant relating the rate of the reaction to the concentrations of reactants.<\/li>\n<\/ul>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-3225\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry Concepts Intermediate. <strong>Authored by<\/strong>: Calbreath, Baxter, et al.. <strong>Provided by<\/strong>: CK12.org. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\">http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/\">CC BY-NC: Attribution-NonCommercial<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":29,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry Concepts Intermediate\",\"author\":\"Calbreath, Baxter, et al.\",\"organization\":\"CK12.org\",\"url\":\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\",\"project\":\"\",\"license\":\"cc-by-nc\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3225","chapter","type-chapter","status-publish","hentry"],"part":2339,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/users\/29"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3225\/revisions"}],"predecessor-version":[{"id":3434,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3225\/revisions\/3434"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/parts\/2339"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3225\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=3225"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=3225"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=3225"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=3225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}