![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-729.png\")
<\/figure>\n\n\n\nThe Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n It seems that I cannot access the image directly, but I can still help you solve the problem based on the general understanding of the ideal gas law (PV = nRT).<\/p>\n\n\n\n From the ideal gas law, we can rearrange it to show the relationship between pressure (P) and temperature (T) at constant volume (V) and constant number of moles (n):<\/p>\n\n\n\n [ This shows that pressure (P) is directly proportional to temperature (T), and the slope of the P vs. T graph is given by:<\/p>\n\n\n\n [ Now, let’s find the units of the slope:<\/p>\n\n\n\n Thus, the slope has units of:<\/p>\n\n\n\n [ So, the units of the slope are atm\/mol\u00b7K<\/strong>.<\/p>\n\n\n\n Given:<\/p>\n\n\n\n We need to find the mass of nitrogen gas in the tank.<\/p>\n\n\n\n First, rearrange the ideal gas law to solve for ( n ) (number of moles):<\/p>\n\n\n\n [ Now, plug in the known values (assuming ( P = 1 \\, \\text{atm} ), and ( R = 0.0821 \\, \\text{L\u00b7atm\/(mol\u00b7K)} )):<\/p>\n\n\n\n [ This will give the number of moles of gas. To find the mass, multiply by the molar mass of nitrogen (28 g\/mol):<\/p>\n\n\n\n [ Given:<\/p>\n\n\n\n First, calculate the number of moles of oxygen:<\/p>\n\n\n\n [ Now, use the ideal gas law to find the volume:<\/p>\n\n\n\n [ Plugging in the known values, assuming ( P = 1 \\, \\text{atm} ) and ( T = 300 \\, \\text{K} ):<\/p>\n\n\n\n [ This will give the volume in liters.<\/p>\n\n\n\n Would you like me to solve the exact numerical results for (b) and (c)?<\/p>\n","protected":false},"excerpt":{"rendered":" The graph shows the ideal gas law relationship (PV = nRT) between pressure (P) and temperature (T). (a) What are the units of the slope (0.0087)? (b) If the tank has a volume of 12 liters and is filled with nitrogen (formula, N2; molecular weight, 28 grams per mole), what is the mass of gas […]<\/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-192029","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192029","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=192029"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192029\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}(a) Units of the slope (0.0087)<\/h3>\n\n\n\n
P = \\frac{nR}{V} \\times T
]<\/p>\n\n\n\n
\\text{slope} = \\frac{nR}{V}
]<\/p>\n\n\n\n\n
\\frac{nR}{V} = \\frac{\\text{L\u00b7atm\/mol\u00b7K}}{\\text{L}} = \\frac{\\text{atm}}{\\text{mol\u00b7K}}
]<\/p>\n\n\n\n(b) Mass of gas in the tank (in grams)<\/h3>\n\n\n\n
\n
n = \\frac{PV}{RT}
]<\/p>\n\n\n\n
n = \\frac{(1 \\, \\text{atm})(12 \\, \\text{L})}{(0.0821 \\, \\text{L\u00b7atm\/mol\u00b7K})(300 \\, \\text{K})}
]<\/p>\n\n\n\n
\\text{mass} = n \\times \\text{molar mass}
]<\/p>\n\n\n\n(c) Volume of the tank for 48 grams of oxygen<\/h3>\n\n\n\n
\n
n = \\frac{48 \\, \\text{g}}{32 \\, \\text{g\/mol}} = 1.5 \\, \\text{mol}
]<\/p>\n\n\n\n
V = \\frac{nRT}{P}
]<\/p>\n\n\n\n
V = \\frac{(1.5 \\, \\text{mol})(0.0821 \\, \\text{L\u00b7atm\/mol\u00b7K})(300 \\, \\text{K})}{1 \\, \\text{atm}}
]<\/p>\n\n\n\n