{"id":207101,"date":"2025-04-18T09:59:50","date_gmt":"2025-04-18T09:59:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=207101"},"modified":"2025-04-18T09:59:53","modified_gmt":"2025-04-18T09:59:53","slug":"silicon-nitride-si3n4-is-made-by-combining-si-and-nitrogen-gas-at-a-high-temperature","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/18\/silicon-nitride-si3n4-is-made-by-combining-si-and-nitrogen-gas-at-a-high-temperature\/","title":{"rendered":"Silicon nitride (Si3N4) is made by combining Si and nitrogen gas at a high temperature"},"content":{"rendered":"\n<p>Silicon nitride (Si3N4) is made by combining Si and nitrogen gas at a high temperature. How much (in grams) of Si is needed to react with an excess of nitrogen gas to prepare 125 g of silicon nitride if the percent yield of the reaction is 95.0%?<\/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 find the mass of silicon (Si) needed to prepare 125 g of silicon nitride (Si\u2083N\u2084) with a <strong>95.0% yield<\/strong>, we follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Write the balanced chemical equation<\/strong><\/h3>\n\n\n\n<p>3Si+2N2\u2192Si3N43Si + 2N_2 \\rightarrow Si_3N_4<\/p>\n\n\n\n<p>This tells us that <strong>3 moles of silicon<\/strong> react with <strong>2 moles of nitrogen<\/strong> to form <strong>1 mole of silicon nitride (Si\u2083N\u2084)<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Molar masses<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Si:<\/strong> 28.09 g\/mol<\/li>\n\n\n\n<li><strong>Si\u2083N\u2084:<\/strong> 3\u00d728.09+4\u00d714.01=84.27+56.04=140.31\u00a0g\/mol3 \\times 28.09 + 4 \\times 14.01 = 84.27 + 56.04 = 140.31 \\text{ g\/mol}<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Adjust for percent yield<\/strong><\/h3>\n\n\n\n<p>The actual yield is 125 g, but the reaction was <strong>only 95.0% efficient<\/strong>. So, we calculate the <strong>theoretical yield<\/strong>: Theoretical&nbsp;yield=125&nbsp;g0.950=131.58&nbsp;g\\text{Theoretical yield} = \\frac{125\\text{ g}}{0.950} = 131.58\\text{ g}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Convert theoretical yield to moles of Si\u2083N\u2084<\/strong><\/h3>\n\n\n\n<p>131.58&nbsp;g140.31&nbsp;g\/mol=0.9375&nbsp;mol&nbsp;of&nbsp;Si3N4\\frac{131.58\\text{ g}}{140.31\\text{ g\/mol}} = 0.9375\\text{ mol of } Si_3N_4<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 5: Use stoichiometry to find moles of Si needed<\/strong><\/h3>\n\n\n\n<p>From the balanced equation:<br><strong>3 mol Si : 1 mol Si\u2083N\u2084<\/strong> 0.9375&nbsp;mol&nbsp;Si3N4\u00d73&nbsp;mol&nbsp;Si1&nbsp;mol&nbsp;Si3N4=2.8125&nbsp;mol&nbsp;Si0.9375 \\text{ mol Si}_3\\text{N}_4 \\times \\frac{3 \\text{ mol Si}}{1 \\text{ mol Si}_3\\text{N}_4} = 2.8125 \\text{ mol Si}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 6: Convert moles of Si to grams<\/strong><\/h3>\n\n\n\n<p>2.8125&nbsp;mol&nbsp;Si\u00d728.09&nbsp;g\/mol=79.01&nbsp;g&nbsp;of&nbsp;Si2.8125 \\text{ mol Si} \\times 28.09 \\text{ g\/mol} = \\boxed{79.01 \\text{ g of Si}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer: 79.01 g of Si<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcac <strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>To determine how much silicon is needed to prepare 125 grams of silicon nitride (Si\u2083N\u2084) with a 95.0% reaction yield, we must work backward from the product to the reactant. The reaction between elemental silicon (Si) and nitrogen gas (N\u2082) produces Si\u2083N\u2084, and the balanced chemical equation shows a 3:1 molar ratio of Si to Si\u2083N\u2084.<\/p>\n\n\n\n<p>First, we account for the percent yield. Since the reaction only gives 95.0% of the possible product, the actual yield (125 g) is less than the theoretical maximum. Dividing the actual yield by the percent yield (expressed as a decimal) gives us the theoretical yield, or how much product would form if the reaction went perfectly.<\/p>\n\n\n\n<p>Next, we convert this theoretical mass of Si\u2083N\u2084 into moles using its molar mass (140.31 g\/mol). With the number of moles of Si\u2083N\u2084 known, we use stoichiometry to determine how many moles of silicon are required. The equation shows that 3 moles of Si are needed to make 1 mole of Si\u2083N\u2084, so we multiply the moles of product by 3.<\/p>\n\n\n\n<p>Finally, converting the required moles of silicon into grams using its molar mass (28.09 g\/mol) gives us the final answer: <strong>79.01 grams of silicon<\/strong> must be used when nitrogen is in excess, and the yield is 95.0%. This approach ensures we accurately adjust for both stoichiometry and reaction efficiency.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/04\/image-156.png\" alt=\"\" class=\"wp-image-207102\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Silicon nitride (Si3N4) is made by combining Si and nitrogen gas at a high temperature. How much (in grams) of Si is needed to react with an excess of nitrogen gas to prepare 125 g of silicon nitride if the percent yield of the reaction is 95.0%? The correct answer and explanation is : To [&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-207101","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207101","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=207101"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207101\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=207101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=207101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=207101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}