{"id":192599,"date":"2025-02-18T05:06:56","date_gmt":"2025-02-18T05:06:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192599"},"modified":"2025-02-18T05:06:58","modified_gmt":"2025-02-18T05:06:58","slug":"a-piece-of-metal-has-a-measured-mass-of-5-00-g-in-air-3-00-g-in-water-and-3-24-g-in-benzene","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/18\/a-piece-of-metal-has-a-measured-mass-of-5-00-g-in-air-3-00-g-in-water-and-3-24-g-in-benzene\/","title":{"rendered":"A piece of metal has a measured mass of 5.00 g in air, 3.00 g in water, and 3.24 g in benzene"},"content":{"rendered":"\n

A piece of metal has a measured mass of 5.00 g in air, 3.00 g in water, and 3.24 g in benzene. Determine the mass density of the metal and of the benzene.<\/p>\n\n\n\n

A spring whose composition is not completely known might be either bronze (sp gr 8.8) or brass (sp gr 8.4). It has a mass of 1.26 g when measured in air and 1.11 g in water. Which is it made of?<\/p>\n\n\n\n

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

Solution to the Metal Mass Density Problem:<\/h3>\n\n\n\n

To solve for the mass density of the metal and the benzene, we will first use the apparent mass<\/strong> method. The apparent mass<\/strong> is the difference between the weight in air and the weight in a fluid, which allows us to calculate the density of the object<\/strong>.<\/p>\n\n\n\n

Step 1: Mass Density of the Metal<\/h4>\n\n\n\n

Given:<\/p>\n\n\n\n

    \n
  • Mass in air = 5.00 g<\/li>\n\n\n\n
  • Mass in water = 3.00 g<\/li>\n\n\n\n
  • Mass in benzene = 3.24 g<\/li>\n<\/ul>\n\n\n\n

    To find the density of the metal, we use the principle of buoyancy<\/strong>:<\/p>\n\n\n\n

    [
    \\text{Density of the fluid} = \\frac{\\text{Buoyant force}}{\\text{Volume displaced}}
    ]<\/p>\n\n\n\n

    The buoyant force<\/strong> is equal to the weight lost when the metal is submerged in the fluid. The volume of the metal can be determined using the Archimedes\u2019 principle<\/strong>, which states that the volume of the displaced fluid is equal to the volume of the object.<\/p>\n\n\n\n

    For water:
    [
    \\text{Apparent Mass in Water} = \\text{Mass in Air} – \\text{Mass in Water}
    ]
    [
    \\text{Volume of Metal} = \\frac{\\text{Apparent Mass in Water}}{\\text{Density of Water}}
    ]
    Given that the density of water is approximately 1 g\/cm\u00b3:
    [
    \\text{Volume of Metal} = \\frac{5.00 \\, \\text{g} – 3.00 \\, \\text{g}}{1 \\, \\text{g\/cm\u00b3}} = 2.00 \\, \\text{cm\u00b3}
    ]<\/p>\n\n\n\n

    Now, to find the density of the metal:
    [
    \\text{Density of Metal} = \\frac{\\text{Mass in Air}}{\\text{Volume of Metal}} = \\frac{5.00 \\, \\text{g}}{2.00 \\, \\text{cm\u00b3}} = 2.50 \\, \\text{g\/cm\u00b3}
    ]<\/p>\n\n\n\n

    Step 2: Mass Density of Benzene<\/h4>\n\n\n\n

    To calculate the density of the benzene:
    [
    \\text{Apparent Mass in Benzene} = \\text{Mass in Air} – \\text{Mass in Benzene}
    ]
    [
    \\text{Apparent Mass in Benzene} = 5.00 \\, \\text{g} – 3.24 \\, \\text{g} = 1.76 \\, \\text{g}
    ]<\/p>\n\n\n\n

    Since the metal’s volume is 2.00 cm\u00b3 (calculated earlier), the density of benzene can be calculated using the formula:<\/p>\n\n\n\n

    [
    \\text{Density of Benzene} = \\frac{\\text{Apparent Mass in Benzene}}{\\text{Volume of Metal}} = \\frac{1.76 \\, \\text{g}}{2.00 \\, \\text{cm\u00b3}} = 0.88 \\, \\text{g\/cm\u00b3}
    ]<\/p>\n\n\n\n

    Thus, the density of the metal<\/strong> is 2.50 g\/cm\u00b3<\/strong>, and the density of benzene<\/strong> is 0.88 g\/cm\u00b3<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Solution to the Spring Material Problem:<\/h3>\n\n\n\n

    We are given:<\/p>\n\n\n\n

      \n
    • Mass in air = 1.26 g<\/li>\n\n\n\n
    • Mass in water = 1.11 g<\/li>\n\n\n\n
    • The two possible materials for the spring are bronze<\/strong> (specific gravity = 8.8) and brass<\/strong> (specific gravity = 8.4).<\/li>\n<\/ul>\n\n\n\n

      Step 1: Calculate the Volume of the Spring<\/h4>\n\n\n\n

      Using Archimedes’ principle, the volume of the spring is determined by the loss of weight<\/strong> in water:<\/p>\n\n\n\n

      [
      \\text{Apparent Mass in Water} = \\text{Mass in Air} – \\text{Mass in Water}
      ]
      [
      \\text{Apparent Mass in Water} = 1.26 \\, \\text{g} – 1.11 \\, \\text{g} = 0.15 \\, \\text{g}
      ]<\/p>\n\n\n\n

      This apparent mass represents the weight of the water displaced, and thus the volume of the spring can be found by dividing this by the density of water (1 g\/cm\u00b3):<\/p>\n\n\n\n

      [
      \\text{Volume of Spring} = \\frac{\\text{Apparent Mass in Water}}{\\text{Density of Water}} = \\frac{0.15 \\, \\text{g}}{1 \\, \\text{g\/cm\u00b3}} = 0.15 \\, \\text{cm\u00b3}
      ]<\/p>\n\n\n\n

      Step 2: Determine the Material of the Spring<\/h4>\n\n\n\n

      Now we calculate the density<\/strong> of the spring. The real mass<\/strong> of the spring is given as 1.26 g, so the density is:<\/p>\n\n\n\n

      [
      \\text{Density of Spring} = \\frac{\\text{Mass in Air}}{\\text{Volume of Spring}} = \\frac{1.26 \\, \\text{g}}{0.15 \\, \\text{cm\u00b3}} = 8.4 \\, \\text{g\/cm\u00b3}
      ]<\/p>\n\n\n\n

      Since the density calculated (8.4 g\/cm\u00b3) matches the specific gravity of brass<\/strong>, the spring is made of brass<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Conclusion:<\/h3>\n\n\n\n
        \n
      • The metal’s density<\/strong> is 2.50 g\/cm\u00b3<\/strong>, and the benzene’s density<\/strong> is 0.88 g\/cm\u00b3<\/strong>.<\/li>\n\n\n\n
      • The spring<\/strong> is made of brass<\/strong> based on its density of 8.4 g\/cm\u00b3<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Now, I\u2019ll generate an image based on these calculations.<\/p>\n\n\n\n

        Here is the diagram illustrating the principle of buoyancy and the related calculations. It shows a spring submerged in water, with annotations for the air mass, water mass, and the apparent mass difference. The density calculations and explanations are included to help visualize the process. Let me know if you need any further details or clarifications!<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        A piece of metal has a measured mass of 5.00 g in air, 3.00 g in water, and 3.24 g in benzene. Determine the mass density of the metal and of the benzene. A spring whose composition is not completely known might be either bronze (sp gr 8.8) or brass (sp gr 8.4). It has […]<\/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-192599","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192599","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=192599"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192599\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}