{"id":130582,"date":"2023-02-13T13:35:23","date_gmt":"2023-02-13T08:05:23","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=130582"},"modified":"2023-02-13T13:35:23","modified_gmt":"2023-02-13T08:05:23","slug":"a-first-order-reaction-takes-69-3-min-for-50-completion-what-is-the-time-needed-for-80-of-the-reaction-to-get-completed","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/a-first-order-reaction-takes-69-3-min-for-50-completion-what-is-the-time-needed-for-80-of-the-reaction-to-get-completed","title":{"rendered":"A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed?"},"content":{"rendered":"<h2>Question 1:.A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed?<\/h2>\n<h3>The correct answer is -The time required for a reaction to reach a certain extent of completion can be determined using the half-life (t1\/2) of the reaction, which is the time taken for half of the reactants to be consumed. The half-life of a first-order reaction is constant and can be calculated using the rate constant (k) of the reaction.<\/h3>\n<div class=\"w-full border-b border-black\/10 dark:border-gray-900\/50 text-gray-800 dark:text-gray-100 group bg-gray-50 dark:bg-[#444654]\">\n<div class=\"text-base gap-4 md:gap-6 m-auto md:max-w-2xl lg:max-w-2xl xl:max-w-3xl p-4 md:py-6 flex lg:px-0\">\n<div class=\"relative flex w-[calc(100%-50px)] flex-col gap-1 md:gap-3 lg:w-[calc(100%-115px)]\">\n<div class=\"flex flex-grow flex-col gap-3\">\n<div class=\"min-h-[20px] flex flex-col items-start gap-4 whitespace-pre-wrap\">\n<div class=\"markdown prose w-full break-words dark:prose-invert dark\">\n<h3>The relationship between half-life and the extent of completion (x) can be expressed as:<\/h3>\n<h3>t1\/2 = 0.693\/k<\/h3>\n<h3>Where k = -ln(1\/2)\/t1\/2<\/h3>\n<h3>We can use this relationship to find the time required for 80% completion as follows:<\/h3>\n<h3>First, we need to find k.<\/h3>\n<h3>k = -ln(1\/2)\/t1\/2 = -ln(1\/2)\/(69.3\/2)<\/h3>\n<h3>Next, we need to find the half-life of the reaction when 80% of the reactants have been consumed.<\/h3>\n<h3>Let&#8217;s call the time required for 80% completion t80. Then, the extent of completion after t80 would be 0.8 * 0.5 = 0.4.<\/h3>\n<h3>Using the relationship between half-life and extent of completion:<\/h3>\n<h3>t80\/2 = 0.693\/k = 0.693\/-ln(0.4)\/k<\/h3>\n<h3>Next, we can solve for t80:<\/h3>\n<h3>t80 = 2 * t80\/2 = 2 * 0.693\/-ln(0.4)\/k<\/h3>\n<h3>We can now use the logarithmic values given in the question to find t80:<\/h3>\n<h3>t80 = 2 * 0.693\/-ln(0.4)\/k = 2 * 0.693\/(0.3010 &#8211; log(0.4)) = 2 * 0.693\/(0.3010 &#8211; 0.5228)<\/h3>\n<h3>t80 = 2 * 0.693\/(-0.2218) = 2 * 0.693\/0.2218<\/h3>\n<h3>t80 = 6.48 min<\/h3>\n<h3>Therefore, it would take 6.48 minutes for 80% of the reaction to get completed.<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"flex justify-between\">\n<div class=\"text-gray-400 flex self-end lg:self-center justify-center mt-2 gap-3 md:gap-4 lg:gap-1 lg:absolute lg:top-0 lg:translate-x-full lg:right-0 lg:mt-0 lg:pl-2 visible\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Question 1:.A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed? The correct answer is -The time required for a reaction to reach a certain extent of completion can be determined using the half-life (t1\/2) of the reaction, which is the time taken [&hellip;]<\/p>\n","protected":false},"author":21830,"featured_media":130487,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-130582","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/130582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=130582"}],"version-history":[{"count":2,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/130582\/revisions"}],"predecessor-version":[{"id":130588,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/130582\/revisions\/130588"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/130487"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=130582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=130582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=130582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}