{"id":183842,"date":"2025-01-17T06:59:37","date_gmt":"2025-01-17T06:59:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183842"},"modified":"2025-01-17T06:59:39","modified_gmt":"2025-01-17T06:59:39","slug":"hydrogen-gas-at-a-temperature-of-22-00c-that-is-confined-is-a-5-00-l-cylinder-exerts-a-pressure-of-4-20-atm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/17\/hydrogen-gas-at-a-temperature-of-22-00c-that-is-confined-is-a-5-00-l-cylinder-exerts-a-pressure-of-4-20-atm\/","title":{"rendered":"Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm"},"content":{"rendered":"\n<p>Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm. If the gas is released into a 10.0-L reaction vessel at a temperature of 33.60C, what will be the pressure inside the reaction vessel? Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm. If the gas is released into a 10.0-L reaction vessel at a temperature of 33.60C, what will be the pressure inside the reaction vessel?<\/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<h3 class=\"wp-block-heading\">Solution:<\/h3>\n\n\n\n<p>We will use the <strong>combined gas law<\/strong>:<\/p>\n\n\n\n<p>[<br>\\frac{P_1 V_1}{T_1} = \\frac{P_2 V_2}{T_2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(P_1, V_1, T_1) are the initial pressure, volume, and temperature.<\/li>\n\n\n\n<li>(P_2, V_2, T_2) are the final pressure, volume, and temperature.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(P_1 = 4.20 \\, \\text{atm})<\/li>\n\n\n\n<li>(V_1 = 5.00 \\, \\text{L})<\/li>\n\n\n\n<li>(T_1 = 22.00 \\, ^\\circ \\text{C} = 22.00 + 273.15 = 295.15 \\, \\text{K})<\/li>\n\n\n\n<li>(V_2 = 10.0 \\, \\text{L})<\/li>\n\n\n\n<li>(T_2 = 33.60 \\, ^\\circ \\text{C} = 33.60 + 273.15 = 306.75 \\, \\text{K})<\/li>\n\n\n\n<li>(P_2 = ?)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Rearrange the equation to solve for (P_2):<\/h3>\n\n\n\n<p>[<br>P_2 = P_1 \\times \\frac{V_1}{V_2} \\times \\frac{T_2}{T_1}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute the values:<\/h3>\n\n\n\n<p>[<br>P_2 = 4.20 \\, \\text{atm} \\times \\frac{5.00 \\, \\text{L}}{10.0 \\, \\text{L}} \\times \\frac{306.75 \\, \\text{K}}{295.15 \\, \\text{K}}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Perform the calculations:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(\\frac{V_1}{V_2} = \\frac{5.00}{10.0} = 0.50)<\/li>\n\n\n\n<li>(\\frac{T_2}{T_1} = \\frac{306.75}{295.15} \\approx 1.0393)<\/li>\n\n\n\n<li>(P_2 = 4.20 \\times 0.50 \\times 1.0393 \\approx 2.18 \\, \\text{atm})<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The pressure in the reaction vessel is approximately <strong>2.18 atm<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The combined gas law relates the pressure, volume, and temperature of a gas system. When hydrogen gas is transferred to the reaction vessel, its volume doubles (from 5.00 L to 10.0 L), reducing the pressure since volume and pressure are inversely proportional. However, the temperature also increases, which increases the pressure as temperature and pressure are directly proportional.<\/p>\n\n\n\n<p>In this problem, the effects of increased volume and temperature oppose each other. The increase in volume (from 5.00 L to 10.0 L) halves the pressure, but the temperature increase (from 22.00\u00b0C to 33.60\u00b0C) slightly raises the pressure. The result is a final pressure of <strong>2.18 atm<\/strong>, which is less than the initial pressure of 4.20 atm due to the dominant effect of the increased volume.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm. If the gas is released into a 10.0-L reaction vessel at a temperature of 33.60C, what will be the pressure inside the reaction vessel? Hydrogen gas at a temperature of 22.00C that is confined is [&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-183842","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183842","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=183842"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183842\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}