To solve this problem, we will use the formula for boiling point elevation:<\/p>\n\n\n\n
[
\\Delta T_b = K_b \\times m
]<\/p>\n\n\n\n
Where:<\/p>\n\n\n\n
- \n
- (\\Delta T_b) is the change in boiling point (in \u00b0C),<\/li>\n\n\n\n
- (K_b) is the boiling point elevation constant of the solvent (in \u00b0C\u00b7kg\/mol),<\/li>\n\n\n\n
- (m) is the molality of the solution (in mol\/kg).<\/li>\n<\/ul>\n\n\n\n
Step 1: Calculate the change in boiling point ((\\Delta T_b))<\/h3>\n\n\n\n
The boiling point elevation is the difference between the boiling point of the solution and the boiling point of the pure solvent:<\/p>\n\n\n\n
[
\\Delta T_b = T_b(\\text{solution}) – T_b(\\text{pure solvent})
]<\/p>\n\n\n\nGiven:<\/p>\n\n\n\n
- \n
- (T_b(\\text{solution}) = 82.3 \\, ^\\circ \\text{C}),<\/li>\n\n\n\n
- (T_b(\\text{pure solvent}) = 79.1 \\, ^\\circ \\text{C}).<\/li>\n<\/ul>\n\n\n\n
[
\\Delta T_b = 82.3 \\, ^\\circ \\text{C} – 79.1 \\, ^\\circ \\text{C} = 3.2 \\, ^\\circ \\text{C}
]<\/p>\n\n\n\nStep 2: Calculate the molality of the solution ((m))<\/h3>\n\n\n\n
Molality is defined as the number of moles of solute per kilogram of solvent:<\/p>\n\n\n\n
[
m = \\frac{\\text{moles of solute}}{\\text{mass of solvent in kg}}
]<\/p>\n\n\n\nTo find the moles of acetaminophen (solute), we use its molar mass. Given:<\/p>\n\n\n\n
- \n
- Mass of acetaminophen = 2.68 g,<\/li>\n\n\n\n
- Molar mass of acetaminophen = 151.163 g\/mol.<\/li>\n<\/ul>\n\n\n\n
[
\\text{moles of acetaminophen} = \\frac{2.68 \\, \\text{g}}{151.163 \\, \\text{g\/mol}} = 0.0177 \\, \\text{mol}
]<\/p>\n\n\n\nNow, we calculate the molality:<\/p>\n\n\n\n
- \n
- Mass of solvent = 45.3 g = 0.0453 kg.<\/li>\n<\/ul>\n\n\n\n
[
m = \\frac{0.0177 \\, \\text{mol}}{0.0453 \\, \\text{kg}} = 0.391 \\, \\text{mol\/kg}
]<\/p>\n\n\n\nStep 3: Solve for the boiling point elevation constant ((K_b))<\/h3>\n\n\n\n
Now we can solve for (K_b) using the equation for boiling point elevation:<\/p>\n\n\n\n
[
\\Delta T_b = K_b \\times m
]<\/p>\n\n\n\nRearranging:<\/p>\n\n\n\n
[
K_b = \\frac{\\Delta T_b}{m}
]<\/p>\n\n\n\nSubstitute the known values:<\/p>\n\n\n\n
[
K_b = \\frac{3.2 \\, ^\\circ \\text{C}}{0.391 \\, \\text{mol\/kg}} = 8.18 \\, ^\\circ \\text{C} \\cdot \\text{kg\/mol}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
The boiling point elevation constant ((K_b)) for solvent XYZ is 8.18 \u00b0C\u00b7kg\/mol<\/strong> (rounded to 3 significant figures).<\/p>\n\n\n\n
Now I will generate the image to show this process step by step.<\/p>\n\n\n\n
Here is the image showing the step-by-step explanation of how to solve the boiling point elevation problem. Let me know if you need further clarification!<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1028.png\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Acetaminophen (C8H9NO2; MOLAR MASS 151.163 G\/MOL) is the main ingredient of Tylenol. When 2.68 g acetaminophen dissolves in 45.3 g of solvent XYZ, the solution boils at 82.3 degrees celsius. If the boiling point of pure solvent XYZ (without acetaminophen) is 79.1 degrees Celcius, determine the boiling point elevation constant (in m\/\u00c3\u00a2\u00e2\u20ac\u017e\u00c6\u2019) of solvent XYZ. […]<\/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-193419","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193419","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=193419"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193419\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Mass of solvent = 45.3 g = 0.0453 kg.<\/li>\n<\/ul>\n\n\n\n