{"id":257260,"date":"2025-07-16T20:35:12","date_gmt":"2025-07-16T20:35:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257260"},"modified":"2025-07-16T20:35:14","modified_gmt":"2025-07-16T20:35:14","slug":"consider-the-initial-rate-data-at-a-certain-temperature-in-the-table-for-the-reaction-described-by","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/consider-the-initial-rate-data-at-a-certain-temperature-in-the-table-for-the-reaction-described-by\/","title":{"rendered":"Consider the initial-rate data at a certain temperature in the table for the reaction described by"},"content":{"rendered":"\n

Consider the initial-rate data at a certain temperature in the table for the reaction described by: [NO2]o (M) 0.650 1.10 1.76 O3<\/a> 0.800 0.800 1.40 Initial rate (Ms) 3.25 x 10^4 5.50 x 10^4 15.40 x 10^4 2 NO2(g) + O3(g) -> N2O5(g) + O2(g) Determine the value and units of the rate constant, k. Units: 4.9 x 10^4 M^-1 s^-1<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong><\/p>\n\n\n\n

k = 6.25 x 10\u2074<\/strong>
Units: M\u207b\u00b9s\u207b\u00b9<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine the value and units of the rate constant, k, we must first establish the rate law for the reaction. The general form of the rate law is Rate = k[NO\u2082]^m[O\u2083]^n, where m and n are the reaction orders with respect to NO\u2082 and O\u2083, respectively.<\/p>\n\n\n\n

    \n
  1. Determine the reaction order for NO\u2082 (m):<\/strong>
    We use the method of initial rates by comparing two experiments where the concentration of one reactant changes while the other remains constant. Comparing experiments 1 and 2, the concentration of O\u2083 is constant at 0.800 M.\n
      \n
    • Ratio of rates: Rate\u2082 \/ Rate\u2081 = (5.50 \u00d7 10\u2074) \/ (3.25 \u00d7 10\u2074) \u2248 1.69<\/li>\n\n\n\n
    • Ratio of [NO\u2082] concentrations: [NO\u2082]\u2082 \/ [NO\u2082]\u2081 = 1.10 \/ 0.650 \u2248 1.69
      Since (1.69)^m = 1.69, the reaction order m is 1.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Determine the reaction order for O\u2083 (n):<\/strong>
      Now that we know m=1, we can use any two experiments to find n. Let’s use experiments 2 and 3. We set up the ratio of their rate laws:
      Rate\u2083 \/ Rate\u2082 = (k[NO\u2082]\u2083\u00b9[O\u2083]\u2083\u207f) \/ (k[NO\u2082]\u2082\u00b9[O\u2083]\u2082\u207f)
      (15.40 \u00d7 10\u2074) \/ (5.50 \u00d7 10\u2074) = (1.76 \/ 1.10) * ([1.40] \/ [0.800])\u207f
      2.8 = 1.6 * (1.75)\u207f
      Dividing both sides by 1.6 gives 1.75 = (1.75)\u207f, so the reaction order n is 1.<\/li>\n\n\n\n
    • Determine the rate law and units of k:<\/strong>
      With m=1 and n=1, the rate law is: Rate = k[NO\u2082][O\u2083].
      The overall reaction order is m + n = 1 + 1 = 2.
      The units of k can be found by rearranging the rate law: k = Rate \/ ([NO\u2082][O\u2083]).
      Units = (M\/s) \/ (M * M) = M\u207b\u00b9s\u207b\u00b9.<\/li>\n\n\n\n
    • Calculate the value of k:<\/strong>
      We can use the data from any experiment to solve for k. Using experiment 1:
      k = Rate \/ ([NO\u2082][O\u2083])
      k = (3.25 \u00d7 10\u2074 M\/s) \/ (0.650 M * 0.800 M)
      k = (3.25 \u00d7 10\u2074) \/ (0.52) M\u207b\u00b9s\u207b\u00b9
      k = 6.25 \u00d7 10\u2074 M\u207b\u00b9s\u207b\u00b9<\/li>\n<\/ol>\n\n\n\n

      Using data from the other experiments yields the same result, confirming the value.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Consider the initial-rate data at a certain temperature in the table for the reaction described by: [NO2]o (M) 0.650 1.10 1.76 O3 0.800 0.800 1.40 Initial rate (Ms) 3.25 x 10^4 5.50 x 10^4 15.40 x 10^4 2 NO2(g) + O3(g) -> N2O5(g) + O2(g) Determine the value and units of the rate constant, k. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-257260","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257260","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=257260"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257260\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}