Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as Nutra-Sweet. The molecular formula of aspartame is C14H18N2O5. a) Calculate the molar mass of aspartame. b) What amount (moles) of molecules are present in 10.0 g aspartame? c) Calculate the mass in grams of 1.56 mol aspartame.
Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as Nutra-Sweet. The molecular formula of aspartame is C14H18N2O5.
a) Calculate the molar mass of aspartame.
b) What amount (moles) of molecules are present in 10.0 g aspartame?
c) Calculate the mass in grams of 1.56 mol aspartame.
d) What number of molecules are in 5.0 mg aspartame?
e) What number of atoms of nitrogen are in 1.2 g aspartame?
f) What is the mass in grams of 1.0 \u00c3\u0192\u00e2\u20ac\u201d109 molecules of aspartame?
g) What is the mass in grams of one molecule of aspartame??<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n Let’s go step by step to answer each part of the question, using the given molecular formula for aspartame (C14H18N2O5).<\/p>\n\n\n\n The molar mass is calculated by adding up the atomic masses of each element in the molecular formula. Here is the breakdown:<\/p>\n\n\n\n Now, sum these values:<\/p>\n\n\n\n [ So, the molar mass of aspartame is 294.30 g\/mol<\/strong>.<\/p>\n\n\n\n To find the number of moles, use the formula:<\/p>\n\n\n\n [ Substituting the given values:<\/p>\n\n\n\n [ So, the amount of aspartame in 10.0 g is 0.0339 mol<\/strong>.<\/p>\n\n\n\n To find the mass, use the formula:<\/p>\n\n\n\n [ Substituting the given values:<\/p>\n\n\n\n [ So, the mass of 1.56 mol of aspartame is 459.51 g<\/strong>.<\/p>\n\n\n\n First, convert 5.0 mg to grams:<\/p>\n\n\n\n [ Next, calculate the moles of aspartame:<\/p>\n\n\n\n [ Now, calculate the number of molecules using Avogadro\u2019s number ((6.022 \\times 10^{23}) molecules\/mol):<\/p>\n\n\n\n [ So, there are 1.02 \u00d7 10\u00b9\u2079 molecules<\/strong> in 5.0 mg of aspartame.<\/p>\n\n\n\n First, calculate the moles of aspartame in 1.2 g:<\/p>\n\n\n\n [ Each molecule of aspartame has 2 nitrogen atoms, so the number of nitrogen atoms is:<\/p>\n\n\n\n [ So, there are 4.92 \u00d7 10\u00b2\u00b9 atoms of nitrogen<\/strong> in 1.2 g of aspartame.<\/p>\n\n\n\n To find the mass of (1.0 \\times 10^9) molecules, first calculate the moles:<\/p>\n\n\n\n [ Now, calculate the mass:<\/p>\n\n\n\n [ So, the mass of (1.0 \\times 10^9) molecules of aspartame is 4.89 \u00d7 10\u207b\u00b9\u00b3 g<\/strong>.<\/p>\n\n\n\n The mass of one molecule is:<\/p>\n\n\n\n [ So, the mass of one molecule of aspartame is 4.89 \u00d7 10\u207b\u00b2\u00b2 g<\/strong>.<\/p>\n\n\n\n Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as Nutra-Sweet. The molecular formula of aspartame is C14H18N2O5. a) Calculate the molar mass of aspartame. b) What amount (moles) of molecules are present in 10.0 g aspartame? c) Calculate the mass in grams […]<\/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-182937","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182937","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=182937"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182937\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182937"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182937"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}a) Molar Mass of Aspartame<\/h3>\n\n\n\n
\n
\\text{Molar mass of aspartame} = 168.14 \\, \\text{g\/mol} + 18.144 \\, \\text{g\/mol} + 28.02 \\, \\text{g\/mol} + 80.00 \\, \\text{g\/mol} = 294.30 \\, \\text{g\/mol}
]<\/p>\n\n\n\nb) Moles of Molecules in 10.0 g Aspartame<\/h3>\n\n\n\n
\\text{moles} = \\frac{\\text{mass (g)}}{\\text{molar mass (g\/mol)}}
]<\/p>\n\n\n\n
\\text{moles} = \\frac{10.0 \\, \\text{g}}{294.30 \\, \\text{g\/mol}} = 0.0339 \\, \\text{mol}
]<\/p>\n\n\n\nc) Mass in Grams of 1.56 mol Aspartame<\/h3>\n\n\n\n
\\text{mass} = \\text{moles} \\times \\text{molar mass}
]<\/p>\n\n\n\n
\\text{mass} = 1.56 \\, \\text{mol} \\times 294.30 \\, \\text{g\/mol} = 459.51 \\, \\text{g}
]<\/p>\n\n\n\nd) Number of Molecules in 5.0 mg Aspartame<\/h3>\n\n\n\n
5.0 \\, \\text{mg} = 0.0050 \\, \\text{g}
]<\/p>\n\n\n\n
\\text{moles} = \\frac{0.0050 \\, \\text{g}}{294.30 \\, \\text{g\/mol}} = 1.70 \\times 10^{-5} \\, \\text{mol}
]<\/p>\n\n\n\n
\\text{molecules} = 1.70 \\times 10^{-5} \\, \\text{mol} \\times 6.022 \\times 10^{23} \\, \\text{molecules\/mol} = 1.02 \\times 10^{19} \\, \\text{molecules}
]<\/p>\n\n\n\ne) Number of Nitrogen Atoms in 1.2 g Aspartame<\/h3>\n\n\n\n
\\text{moles} = \\frac{1.2 \\, \\text{g}}{294.30 \\, \\text{g\/mol}} = 0.00408 \\, \\text{mol}
]<\/p>\n\n\n\n
\\text{atoms of nitrogen} = 0.00408 \\, \\text{mol} \\times 2 \\, \\text{atoms\/molecule} \\times 6.022 \\times 10^{23} \\, \\text{atoms\/mol} = 4.92 \\times 10^{21} \\, \\text{atoms}
]<\/p>\n\n\n\nf) Mass in Grams of (1.0 \\times 10^9) Molecules of Aspartame<\/h3>\n\n\n\n
\\text{moles} = \\frac{1.0 \\times 10^9 \\, \\text{molecules}}{6.022 \\times 10^{23} \\, \\text{molecules\/mol}} = 1.66 \\times 10^{-15} \\, \\text{mol}
]<\/p>\n\n\n\n
\\text{mass} = 1.66 \\times 10^{-15} \\, \\text{mol} \\times 294.30 \\, \\text{g\/mol} = 4.89 \\times 10^{-13} \\, \\text{g}
]<\/p>\n\n\n\ng) Mass of One Molecule of Aspartame<\/h3>\n\n\n\n
\\text{mass of one molecule} = \\frac{\\text{molar mass}}{\\text{Avogadro’s number}} = \\frac{294.30 \\, \\text{g\/mol}}{6.022 \\times 10^{23} \\, \\text{mol}^{-1}} = 4.89 \\times 10^{-22} \\, \\text{g}
]<\/p>\n\n\n\nSummary:<\/h3>\n\n\n\n
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