{"id":209679,"date":"2025-04-29T09:57:39","date_gmt":"2025-04-29T09:57:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=209679"},"modified":"2025-04-29T09:57:41","modified_gmt":"2025-04-29T09:57:41","slug":"a-nugget-of-gold-with-a-mass-of-521-g-is-added-to-50-0-ml-of-water","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/29\/a-nugget-of-gold-with-a-mass-of-521-g-is-added-to-50-0-ml-of-water\/","title":{"rendered":"A nugget of gold with a mass of 521 g is added to 50.0 mL of water"},"content":{"rendered":"\n

A nugget of gold with a mass of 521 g is added to 50.0 mL of water. The water level rises to a volume of 77.0 mL. What is the density of the gold?<\/p>\n\n\n\n

A) 10.4 g\/mL
B) 6.77 g\/mL
C) 1.00 g\/mL
D) 0.0518 g\/mL
E) 19.3 g\/mL<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the density of the gold nugget<\/strong>, we use the density formula<\/strong>:<\/p>\n\n\n\n

[
\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}}
]<\/p>\n\n\n\n

Step 1: Determine the mass<\/strong> of the gold<\/h3>\n\n\n\n

From the question:<\/p>\n\n\n\n

    \n
  • Mass of the gold = 521 g<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step 2: Determine the volume<\/strong> of the gold<\/h3>\n\n\n\n

    Since the nugget is placed into water and causes the water level to rise, we can find the volume of the gold<\/strong> using water displacement:<\/p>\n\n\n\n

      \n
    • Initial volume of water = 50.0 mL<\/strong><\/li>\n\n\n\n
    • Final volume after adding gold = 77.0 mL<\/strong><\/li>\n<\/ul>\n\n\n\n

      [
      \\text{Volume of gold} = 77.0\\, \\text{mL} – 50.0\\, \\text{mL} = 27.0\\, \\text{mL}
      ]<\/p>\n\n\n\n

      Step 3: Calculate the density<\/strong><\/h3>\n\n\n\n

      [
      \\text{Density} = \\frac{521\\, \\text{g}}{27.0\\, \\text{mL}} \\approx 19.3\\, \\text{g\/mL}
      ]<\/p>\n\n\n\n

      \u2705 Correct Answer: E) 19.3 g\/mL<\/strong><\/h3>\n\n\n\n
      \n\n\n\n

      \ud83d\udd0d Explanation (300+ words):<\/h3>\n\n\n\n

      Density is a physical property of matter that relates an object\u2019s mass to its volume<\/strong>. It tells us how compact or concentrated the material in an object is. The formula for density is:<\/p>\n\n\n\n

      [
      \\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}}
      ]<\/p>\n\n\n\n

      In this problem, the mass of the gold is given as 521 grams<\/strong>. However, we are not directly given the volume of the gold nugget. Instead, the displacement method<\/strong> is used. This method is based on Archimedes\u2019 principle<\/strong>, which states that when an object is submerged in a fluid, it displaces a volume of fluid equal to its own volume.<\/p>\n\n\n\n

      By placing the gold nugget in water, the volume rises from 50.0 mL to 77.0 mL, meaning the gold has displaced 27.0 mL<\/strong> of water. This displacement tells us that the volume of the gold is 27.0 mL<\/strong>.<\/p>\n\n\n\n

      Now using the formula:<\/p>\n\n\n\n

      [
      \\text{Density} = \\frac{521\\, \\text{g}}{27.0\\, \\text{mL}} \\approx 19.3\\, \\text{g\/mL}
      ]<\/p>\n\n\n\n

      This result is very close to the known density of pure gold<\/strong>, which is 19.3 g\/mL<\/strong>, confirming the accuracy of the calculation and supporting that the object is indeed gold.<\/p>\n\n\n\n

      The other answer choices:<\/p>\n\n\n\n

        \n
      • A (10.4)<\/strong>, B (6.77)<\/strong>, and C (1.00)<\/strong> are typical of other materials like metals, water, or organic substances.<\/li>\n\n\n\n
      • D (0.0518)<\/strong> is far too low and likely results from misplacing the decimal.<\/li>\n<\/ul>\n\n\n\n

        Thus, Option E<\/strong> is the correct and most reasonable answer based on both calculation and real-world reference.<\/p>\n","protected":false},"excerpt":{"rendered":"

        A nugget of gold with a mass of 521 g is added to 50.0 mL of water. The water level rises to a volume of 77.0 mL. What is the density of the gold? A) 10.4 g\/mLB) 6.77 g\/mLC) 1.00 g\/mLD) 0.0518 g\/mLE) 19.3 g\/mL The correct answer and explanation is : To determine 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-209679","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209679","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=209679"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209679\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=209679"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=209679"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=209679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}