{"id":182620,"date":"2025-01-14T13:16:23","date_gmt":"2025-01-14T13:16:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182620"},"modified":"2025-01-14T13:16:26","modified_gmt":"2025-01-14T13:16:26","slug":"relative-volatility-of-a-binary-system","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/14\/relative-volatility-of-a-binary-system\/","title":{"rendered":"Relative Volatility of a Binary System"},"content":{"rendered":"\n<p>Relative Volatility of a Binary System. Using the equilibrium data for the n-pentane\u2013n-heptane system given in Example 26.3-2, calculate the relative volatility for each concentration and plot \u03b1 versus the liquid composition xA.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the relative volatility (\u03b1\\alpha) of a binary system, such as the n-pentane\u2013n-heptane system, we use the following formula: \u03b1=(yA\/xA)(yB\/xB)\\alpha = \\frac{(y_A \/ x_A)}{(y_B \/ x_B)}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yAy_A and yBy_B are the mole fractions of components A (n-pentane) and B (n-heptane) in the vapor phase.<\/li>\n\n\n\n<li>xAx_A and xBx_B are the mole fractions of components A and B in the liquid phase.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Steps for Calculation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Data Extraction<\/strong>: First, extract equilibrium data for the binary system (typically, mole fractions of the components in both the liquid and vapor phases for a given total pressure and temperature). This data is often presented in tables in the problem.<\/li>\n\n\n\n<li><strong>Apply the Formula<\/strong>: For each concentration, use the mole fractions in the liquid phase xAx_A and the vapor phase yAy_A (similarly for component B). Calculate \u03b1\\alpha for each pair of values.<\/li>\n\n\n\n<li><strong>Plot \u03b1\\alpha vs xAx_A<\/strong>: Once you have calculated \u03b1\\alpha for each concentration, plot the relative volatility (\u03b1\\alpha) on the y-axis and the liquid phase mole fraction of n-pentane (xAx_A) on the x-axis. This plot helps understand the behavior of the system as the composition of the liquid phase changes.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Example Calculation:<\/h3>\n\n\n\n<p>Suppose you have the following data for the n-pentane\u2013n-heptane system:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>xA (liquid)<\/th><th>yA (vapor)<\/th><\/tr><\/thead><tbody><tr><td>0.10<\/td><td>0.15<\/td><\/tr><tr><td>0.20<\/td><td>0.25<\/td><\/tr><tr><td>0.30<\/td><td>0.35<\/td><\/tr><tr><td>0.40<\/td><td>0.45<\/td><\/tr><tr><td>0.50<\/td><td>0.55<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For each concentration, you can calculate \u03b1\\alpha using the formula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At xA=0.10x_A = 0.10, \u03b1=0.15\/0.10(1\u22120.15)\/(1\u22120.10)=1.50.944=1.59\\alpha = \\frac{0.15 \/ 0.10}{(1 &#8211; 0.15) \/ (1 &#8211; 0.10)} = \\frac{1.5}{0.944} = 1.59<\/li>\n\n\n\n<li>Repeat for other concentrations.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of Relative Volatility:<\/h3>\n\n\n\n<p>Relative volatility (\u03b1\\alpha) is a measure of the ease with which two components in a mixture can be separated by distillation. If \u03b1&gt;1\\alpha &gt; 1, component A is more volatile than component B. As \u03b1\\alpha increases, the separation between the components becomes easier. The plot of \u03b1\\alpha versus xAx_A helps determine how relative volatility changes as the liquid composition changes, typically decreasing as the mixture approaches the azeotrope, where \u03b1=1\\alpha = 1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Relative Volatility of a Binary System. Using the equilibrium data for the n-pentane\u2013n-heptane system given in Example 26.3-2, calculate the relative volatility for each concentration and plot \u03b1 versus the liquid composition xA. The Correct Answer and Explanation is : To calculate the relative volatility (\u03b1\\alpha) of a binary system, such as the n-pentane\u2013n-heptane system, [&hellip;]<\/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-182620","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182620","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=182620"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182620\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}