{"id":190983,"date":"2025-02-14T04:41:32","date_gmt":"2025-02-14T04:41:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190983"},"modified":"2025-02-14T04:41:34","modified_gmt":"2025-02-14T04:41:34","slug":"calculate-the-number-of-atoms-in-each-sample","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/calculate-the-number-of-atoms-in-each-sample\/","title":{"rendered":"Calculate The Number Of Atoms In Each Sample"},"content":{"rendered":"\n

Calculate The Number Of Atoms In Each Sample: 1.59 G <\/p>\n\n\n\n

A. 14.955 G Cr<\/p>\n\n\n\n

B. 39.733 G S<\/p>\n\n\n\n

C. 12.899 G Pt<\/p>\n\n\n\n

D. 97.552 G Sn <\/p>\n\n\n\n

E. 163.215g Oz (Think About This One Before You Start)<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To calculate the number of atoms in each sample, we use the mole concept<\/strong> and Avogadro\u2019s number<\/strong>.<\/p>\n\n\n\n

Steps to Calculate:<\/strong><\/h3>\n\n\n\n
    \n
  1. Find the atomic mass<\/strong> of the element from the periodic table.<\/li>\n\n\n\n
  2. Convert grams to moles<\/strong> using the formula:
    [
    \\text{Moles} = \\frac{\\text{Mass (g)}}{\\text{Molar Mass (g\/mol)}}
    ]<\/li>\n\n\n\n
  3. Convert moles to atoms<\/strong> using Avogadro\u2019s number<\/strong>:
    [
    \\text{Atoms} = \\text{Moles} \\times (6.022 \\times 10^{23} \\text{ atoms\/mol})
    ]<\/li>\n<\/ol>\n\n\n\n

    Now, let\u2019s compute each:<\/p>\n\n\n\n

    A. Chromium (Cr)<\/strong><\/h3>\n\n\n\n
      \n
    • Atomic Mass<\/strong> = 51.996 g\/mol<\/li>\n\n\n\n
    • Moles<\/strong> = ( \\frac{14.955}{51.996} = 0.2876 ) mol<\/li>\n\n\n\n
    • Atoms<\/strong> = ( 0.2876 \\times 6.022 \\times 10^{23} )<\/li>\n\n\n\n
    • = 1.73 \u00d7 10\u00b2\u00b3 atoms<\/strong><\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      B. Sulfur (S)<\/strong><\/h3>\n\n\n\n
        \n
      • Atomic Mass<\/strong> = 32.065 g\/mol<\/li>\n\n\n\n
      • Moles<\/strong> = ( \\frac{39.733}{32.065} = 1.24 ) mol<\/li>\n\n\n\n
      • Atoms<\/strong> = ( 1.24 \\times 6.022 \\times 10^{23} )<\/li>\n\n\n\n
      • = 7.47 \u00d7 10\u00b2\u00b3 atoms<\/strong><\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        C. Platinum (Pt)<\/strong><\/h3>\n\n\n\n
          \n
        • Atomic Mass<\/strong> = 195.084 g\/mol<\/li>\n\n\n\n
        • Moles<\/strong> = ( \\frac{12.899}{195.084} = 0.0662 ) mol<\/li>\n\n\n\n
        • Atoms<\/strong> = ( 0.0662 \\times 6.022 \\times 10^{23} )<\/li>\n\n\n\n
        • = 3.98 \u00d7 10\u00b2\u00b2 atoms<\/strong><\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          D. Tin (Sn)<\/strong><\/h3>\n\n\n\n
            \n
          • Atomic Mass<\/strong> = 118.710 g\/mol<\/li>\n\n\n\n
          • Moles<\/strong> = ( \\frac{97.552}{118.710} = 0.8218 ) mol<\/li>\n\n\n\n
          • Atoms<\/strong> = ( 0.8218 \\times 6.022 \\times 10^{23} )<\/li>\n\n\n\n
          • = 4.95 \u00d7 10\u00b2\u00b3 atoms<\/strong><\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            E. Oz (Think First!)<\/strong><\/h3>\n\n\n\n
              \n
            • “Oz” commonly refers to ounces (not an element)<\/strong>.<\/li>\n\n\n\n
            • If it meant Oxygen (O), we need to clarify if it’s O (atom)<\/strong> or O\u2082 (molecule)<\/strong>.<\/li>\n\n\n\n
            • Assuming O (atomic oxygen)<\/strong>:<\/li>\n\n\n\n
            • Atomic Mass<\/strong> = 16.00 g\/mol<\/li>\n\n\n\n
            • Moles<\/strong> = ( \\frac{163.215}{16.00} = 10.20 ) mol<\/li>\n\n\n\n
            • Atoms<\/strong> = ( 10.20 \\times 6.022 \\times 10^{23} )<\/li>\n\n\n\n
            • = 6.14 \u00d7 10\u00b2\u2074 atoms<\/strong><\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              Explanation (300 words)<\/strong><\/h3>\n\n\n\n

              The calculation of the number of atoms in a sample involves converting mass to moles and then using Avogadro\u2019s number. The molar mass (or atomic mass) is taken from the periodic table in grams per mole (g\/mol)<\/strong>. This helps determine how many moles are present in the given mass.<\/p>\n\n\n\n

              Moles represent the quantity of a substance that contains 6.022 \u00d7 10\u00b2\u00b3<\/strong> particles (atoms, molecules, or ions). This is known as Avogadro\u2019s constant<\/strong>. By multiplying the number of moles by Avogadro\u2019s number, we obtain the total number of atoms.<\/p>\n\n\n\n

              For example, in the case of Sulfur (S)<\/strong>, with a given mass of 39.733 g<\/strong> and an atomic mass of 32.065 g\/mol<\/strong>, we first convert the mass to moles:<\/p>\n\n\n\n

              [
              Moles = \\frac{39.733}{32.065} = 1.24 \\text{ moles}
              ]<\/p>\n\n\n\n

              Multiplying this by Avogadro\u2019s number<\/strong> gives:<\/p>\n\n\n\n

              [
              1.24 \\times 6.022 \\times 10^{23} = 7.47 \\times 10^{23} \\text{ atoms}
              ]<\/p>\n\n\n\n

              A tricky part in this question is “Oz”<\/strong> in part E. If it refers to ounces (not an element)<\/strong>, then the problem is misleading. However, if it means oxygen (O)<\/strong>, we must clarify whether it refers to atomic oxygen (O) or molecular oxygen (O\u2082)<\/strong>. If we assume atomic oxygen<\/strong>, we follow the same process using 16.00 g\/mol<\/strong> as the atomic mass.<\/p>\n\n\n\n

              Understanding these conversions is essential in chemistry as it allows scientists to calculate substance amounts in chemical reactions and everyday applications like pharmaceuticals and materials science.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Calculate The Number Of Atoms In Each Sample: 1.59 G A. 14.955 G Cr B. 39.733 G S C. 12.899 G Pt D. 97.552 G Sn E. 163.215g Oz (Think About This One Before You Start) The Correct Answer and Explanation is : To calculate the number of atoms in each sample, we use the […]<\/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-190983","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190983","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=190983"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190983\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}