{"id":266894,"date":"2025-07-23T08:04:33","date_gmt":"2025-07-23T08:04:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266894"},"modified":"2025-07-23T08:04:35","modified_gmt":"2025-07-23T08:04:35","slug":"the-number-average-molecular-weight-of-polystyrene-is-500000-g-mol","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/the-number-average-molecular-weight-of-polystyrene-is-500000-g-mol\/","title":{"rendered":"The number-average molecular weight of polystyrene is 500,000 g\/mol."},"content":{"rendered":"\n<p>The number-average molecular weight of polystyrene is 500,000 g\/mol. Compute the number-degree of polymerization (molecular structure of polystyrene is C8 H8).<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the number-degree of polymerization (DPn) for polystyrene, we can use the following relationship:DPn=MnM0\\text{DPn} = \\frac{M_n}{M_0}DPn=M0\u200bMn\u200b\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>MnM_nMn\u200b is the number-average molecular weight of the polymer.<\/li>\n\n\n\n<li>M0M_0M0\u200b is the molecular weight of a single monomer unit.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the molecular weight of the monomer (C\u2088H\u2088)<\/h3>\n\n\n\n<p>The molecular weight of the monomer is calculated by adding up the atomic weights of carbon (C) and hydrogen (H) atoms in the monomer structure (C\u2088H\u2088).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Carbon (C) has an atomic weight of approximately 12 g\/mol.<\/li>\n\n\n\n<li>Hydrogen (H) has an atomic weight of approximately 1 g\/mol.<\/li>\n<\/ul>\n\n\n\n<p>The molecular weight of the monomer (C\u2088H\u2088) is:M0=(8\u00d712)+(8\u00d71)=96+8=104\u2009g\/molM_0 = (8 \\times 12) + (8 \\times 1) = 96 + 8 = 104 \\, \\text{g\/mol}M0\u200b=(8\u00d712)+(8\u00d71)=96+8=104g\/mol<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the number-average molecular weight (M\u2099) of polystyrene<\/h3>\n\n\n\n<p>The number-average molecular weight (MnM_nMn\u200b) of the polystyrene is given as 500,000 g\/mol.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the number-degree of polymerization (DPn)<\/h3>\n\n\n\n<p>Now that we have both values, we can substitute them into the formula:DPn=MnM0=500,000\u2009g\/mol104\u2009g\/mol=4807.69\\text{DPn} = \\frac{M_n}{M_0} = \\frac{500,000 \\, \\text{g\/mol}}{104 \\, \\text{g\/mol}} = 4807.69DPn=M0\u200bMn\u200b\u200b=104g\/mol500,000g\/mol\u200b=4807.69<\/p>\n\n\n\n<p>Thus, the number-degree of polymerization (DPn) of polystyrene is approximately <strong>4808<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The number-degree of polymerization represents the average number of monomer units in a polymer chain. In this case, for polystyrene with a molecular weight of 500,000 g\/mol and a monomer molecular weight of 104 g\/mol, the average polymer chain contains about 4808 monomer units. This gives us an understanding of the polymer&#8217;s size and how many repeating units are in the structure.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1631.jpeg\" alt=\"\" class=\"wp-image-266897\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The number-average molecular weight of polystyrene is 500,000 g\/mol. Compute the number-degree of polymerization (molecular structure of polystyrene is C8 H8). The Correct Answer and Explanation is: To calculate the number-degree of polymerization (DPn) for polystyrene, we can use the following relationship:DPn=MnM0\\text{DPn} = \\frac{M_n}{M_0}DPn=M0\u200bMn\u200b\u200b Where: Step 1: Find the molecular weight of the monomer (C\u2088H\u2088) [&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-266894","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266894","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=266894"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266894\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}