Carbon disulfide (CS2) boils at 46.30 \u00b0C and has a density of 1.261 g\/mL.(a)When 0.250 mol of a nondissociating solute is dissolved in 400.0 mL of CS2, the solution boils at 47.46 \u00b0C . What is the molal boiling-point-elevation constant for CS2? (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS2, the solution boils at 47.08 \u00b0C. What is the molecular weight of the unknown?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve this, we will use the boiling-point elevation equation:<\/p>\n\n\n\n [ where:<\/p>\n\n\n\n The boiling-point elevation method is based on colligative properties, which depend only on the number of solute particles and not their identity. In (a), (K_b) is found using the known solute and solvent properties. In (b), the molecular weight is determined using the solute mass, boiling-point elevation, and solvent properties. These calculations demonstrate the interplay between boiling-point elevation, solute concentration, and molar mass.<\/p>\n","protected":false},"excerpt":{"rendered":" Carbon disulfide (CS2) boils at 46.30 \u00b0C and has a density of 1.261 g\/mL.(a)When 0.250 mol of a nondissociating solute is dissolved in 400.0 mL of CS2, the solution boils at 47.46 \u00b0C . What is the molal boiling-point-elevation constant for CS2? (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL […]<\/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-183786","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183786","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=183786"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183786\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\Delta T_b = K_b \\cdot m
]<\/p>\n\n\n\n\n
(a) Determining (K_b) for CS(_2):<\/h3>\n\n\n\n
\n
[
\\Delta T_b = 47.46^\\circ \\text{C} – 46.30^\\circ \\text{C} = 1.16^\\circ \\text{C}
]<\/li>\n\n\n\n
The solute is nondissociating, and its moles are given as (0.250). The mass of CS(_2) can be calculated using its density and volume:
[
\\text{Mass of CS}_2 = 400.0 \\, \\text{mL} \\times 1.261 \\, \\text{g\/mL} = 504.4 \\, \\text{g}
]
Convert this to kilograms:
[
\\text{Mass in kg} = \\frac{504.4 \\, \\text{g}}{1000} = 0.5044 \\, \\text{kg}
]
Molality:
[
m = \\frac{\\text{moles of solute}}{\\text{kg of solvent}} = \\frac{0.250}{0.5044} = 0.4957 \\, \\text{mol\/kg}
]<\/li>\n\n\n\n
[
K_b = \\frac{\\Delta T_b}{m} = \\frac{1.16}{0.4957} = 2.34 \\, ^\\circ \\text{C\u00b7kg\/mol}
]<\/li>\n<\/ol>\n\n\n\n(b) Determining the molecular weight of the unknown:<\/h3>\n\n\n\n
\n
[
\\Delta T_b = 47.08^\\circ \\text{C} – 46.30^\\circ \\text{C} = 0.78^\\circ \\text{C}
]<\/li>\n\n\n\n
Rearrange the boiling-point elevation equation:
[
m = \\frac{\\Delta T_b}{K_b} = \\frac{0.78}{2.34} = 0.3333 \\, \\text{mol\/kg}
]<\/li>\n\n\n\n
[
\\text{Mass of CS}_2 = 50.0 \\, \\text{mL} \\times 1.261 \\, \\text{g\/mL} = 63.05 \\, \\text{g}
]
Convert to kilograms:
[
\\text{Mass in kg} = \\frac{63.05 \\, \\text{g}}{1000} = 0.06305 \\, \\text{kg}
]<\/li>\n\n\n\n
[
\\text{Moles of solute} = m \\times \\text{kg of solvent} = 0.3333 \\times 0.06305 = 0.02101 \\, \\text{mol}
]<\/li>\n\n\n\n
The mass of the solute is (5.39 \\, \\text{g}), and its molar mass is:
[
\\text{Molar mass} = \\frac{\\text{mass}}{\\text{moles}} = \\frac{5.39}{0.02101} = 256.5 \\, \\text{g\/mol}
]<\/li>\n<\/ol>\n\n\n\nFinal Answers:<\/h3>\n\n\n\n
\n
Explanation:<\/h3>\n\n\n\n