Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as NutraSweet. The molecular formula for aspartame is C14H18N2O5. <\/p>\n\n\n\n
a) Calculate the molar mass of for 2 moles of aspartame. <\/p>\n\n\n\n
b) How many moles of molecules are present in 35.0 g of aspartame?<\/p>\n\n\n\n
c) Calculate the mass in grams of 4.56 mol of aspartame. <\/p>\n\n\n\n
d) How many molecules are in 4.0 ng of aspartame? <\/p>\n\n\n\n
e) How many atoms of oxygen are in 2.2 g of aspartame?<\/p>\n\n\n\n
f) What is the mass in grams of 1.0 x 10^32 molecules of aspartame? <\/p>\n\n\n\n
g) What is the mass in grams of three molecules of aspartame?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n Let’s solve each part of this question step by step using the molecular formula of aspartame: C\u2081\u2084H\u2081\u2088N\u2082O\u2085<\/strong><\/p>\n\n\n\n First, calculate the molar mass<\/strong> of aspartame:<\/p>\n\n\n\n Moles = mass \/ molar mass = 35.0 g \/ 294.30 g\/mol \u2248 0.119 mol<\/strong><\/p>\n\n\n\n Mass = moles \u00d7 molar mass = 4.56 mol \u00d7 294.30 g\/mol \u2248 1342.01 g<\/strong><\/p>\n\n\n\n Convert 4.0 ng to grams: 4.0 \u00d7 10\u207b\u2079 g Moles = 2.2 g \/ 294.30 g\/mol \u2248 0.00747 mol Moles = (1.0 \u00d7 10\u00b3\u00b2) \/ (6.022 \u00d7 10\u00b2\u00b3) \u2248 1.661 \u00d7 10\u2078 mol Moles = 3 \/ (6.022 \u00d7 10\u00b2\u00b3) \u2248 4.984 \u00d7 10\u207b\u00b2\u2074 mol Aspartame is a low-calorie artificial sweetener known for being much sweeter than table sugar (sucrose), requiring a much smaller quantity to achieve the same taste. Understanding its chemical makeup and related calculations involves applying concepts from stoichiometry and molecular chemistry. The molecular formula of aspartame is C\u2081\u2084H\u2081\u2088N\u2082O\u2085<\/strong>, which provides us with the number and type of atoms in a single molecule.<\/p>\n\n\n\n The molar mass<\/strong> is a critical value that tells us how much one mole (6.022 \u00d7 10\u00b2\u00b3 molecules) of a substance weighs. By adding the atomic masses of each atom in aspartame, we get approximately 294.30 g\/mol<\/strong>. This value helps in converting between mass and number of molecules or moles, depending on the given problem.<\/p>\n\n\n\n To find out how many moles<\/strong> are in a certain mass (like 35.0 g), we divide by the molar mass. Conversely, if moles are given, we multiply to get the mass. The relationship between molecules and moles<\/strong> involves Avogadro\u2019s number<\/strong> (6.022 \u00d7 10\u00b2\u00b3 molecules\/mol), a fundamental constant in chemistry.<\/p>\n\n\n\n When we’re working with very small amounts like nanograms<\/strong> (ng), the math involves converting to grams, then using the same steps. Determining how many oxygen atoms<\/strong> are present involves multiplying the number of molecules by how many oxygen atoms are in each molecule\u2014five in this case. Even from a few grams of aspartame, the number of individual atoms or molecules can reach into the trillions or more.<\/p>\n\n\n\n Such calculations showcase how chemistry allows us to understand matter at both the molecular and macroscopic levels, providing essential insights into everything from food science to pharmaceuticals.<\/p>\n","protected":false},"excerpt":{"rendered":" Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as NutraSweet. The molecular formula for aspartame is C14H18N2O5. a) Calculate the molar mass of for 2 moles of aspartame. b) How many moles of molecules are present in 35.0 g of aspartame? c) […]<\/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-207692","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207692","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=207692"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207692\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=207692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=207692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=207692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\na) Molar Mass of 2 moles of aspartame<\/strong><\/h3>\n\n\n\n
\n
Total molar mass<\/strong> = 168.14 + 18.144 + 28.02 + 80.00 = 294.30 g\/mol<\/strong>
So, for 2 moles<\/strong>:
2 \u00d7 294.30 = 588.60 g<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nb) Moles in 35.0 g of aspartame<\/strong><\/h3>\n\n\n\n
\n\n\n\nc) Mass of 4.56 mol of aspartame<\/strong><\/h3>\n\n\n\n
\n\n\n\nd) Molecules in 4.0 ng of aspartame<\/strong><\/h3>\n\n\n\n
Moles = (4.0 \u00d7 10\u207b\u2079 g) \/ 294.30 g\/mol \u2248 1.359 \u00d7 10\u207b\u00b9\u00b9 mol<\/strong>
Molecules = moles \u00d7 Avogadro\u2019s number
\u2248 1.359 \u00d7 10\u207b\u00b9\u00b9 \u00d7 6.022 \u00d7 10\u00b2\u00b3 \u2248 8.19 \u00d7 10\u00b9\u00b2 molecules<\/strong><\/p>\n\n\n\n
\n\n\n\ne) Oxygen atoms in 2.2 g of aspartame<\/strong><\/h3>\n\n\n\n
Molecules = 0.00747 \u00d7 6.022 \u00d7 10\u00b2\u00b3 \u2248 4.5 \u00d7 10\u00b2\u00b9 molecules
O atoms = 4.5 \u00d7 10\u00b2\u00b9 \u00d7 5 = 2.25 \u00d7 10\u00b2\u00b2 atoms of O<\/strong><\/p>\n\n\n\n
\n\n\n\nf) Mass of 1.0 \u00d7 10\u00b3\u00b2 molecules<\/strong><\/h3>\n\n\n\n
Mass = 1.661 \u00d7 10\u2078 mol \u00d7 294.30 g\/mol \u2248 4.89 \u00d7 10\u00b9\u2070 g<\/strong><\/p>\n\n\n\n
\n\n\n\ng) Mass of 3 molecules of aspartame<\/strong><\/h3>\n\n\n\n
Mass = 4.984 \u00d7 10\u207b\u00b2\u2074 mol \u00d7 294.30 g\/mol \u2248 1.47 \u00d7 10\u207b\u00b2\u00b9 g<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation (Approx. 300 words):<\/h3>\n\n\n\n