{"id":197033,"date":"2025-03-06T13:05:57","date_gmt":"2025-03-06T13:05:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=197033"},"modified":"2025-03-06T13:06:00","modified_gmt":"2025-03-06T13:06:00","slug":"the-density-of-gold-metal-is-19-3-g-cm-3-while-that-for-silver-is-10-5-g-cm-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/06\/the-density-of-gold-metal-is-19-3-g-cm-3-while-that-for-silver-is-10-5-g-cm-3\/","title":{"rendered":"The density of gold metal is 19.3 g\/cm 3 , while that for silver is 10.5 g\/cm 3"},"content":{"rendered":"\n<p>The density of gold metal is 19.3 g\/cm 3 , while that for silver is 10.5 g\/cm 3 . Suppose you had the same size bar of each metal, with the dimensions 2.00 in x 10.0 cm x 760 mm. Volume of a cube is height x length x width.<\/p>\n\n\n\n<p>Which bar would have the greatest mass?<br>Which bar contains the greater number of atoms?<br>If the two bars were melted and mixed together to form an alloy (or mixture) what would be the total mass?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-363.png\" alt=\"\" class=\"wp-image-197034\"\/><\/figure>\n\n\n\n<p>To determine which metal bar\u2014gold or silver\u2014has the greatest mass, contains the greater number of atoms, and the total mass if both were melted together, we can follow these steps:<\/p>\n\n\n\n<p><strong>1. Calculate the Volume of Each Bar:<\/strong><\/p>\n\n\n\n<p>Given the dimensions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Length: 2.00 inches<\/li>\n\n\n\n<li>Width: 10.0 cm<\/li>\n\n\n\n<li>Height: 760 mm<\/li>\n<\/ul>\n\n\n\n<p>First, convert all measurements to centimeters:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Length: 2.00 inches \u00d7 2.54 cm\/inch = 5.08 cm<\/li>\n\n\n\n<li>Width: 10.0 cm (already in cm)<\/li>\n\n\n\n<li>Height: 760 mm \u00f7 10 = 76.0 cm<\/li>\n<\/ul>\n\n\n\n<p>Volume = Length \u00d7 Width \u00d7 Height<br>= 5.08 cm \u00d7 10.0 cm \u00d7 76.0 cm<br>= 3860.8 cm\u00b3<\/p>\n\n\n\n<p><strong>2. Determine the Mass of Each Bar:<\/strong><\/p>\n\n\n\n<p>Using the densities provided:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Density of gold (Au): 19.3 g\/cm\u00b3<\/li>\n\n\n\n<li>Density of silver (Ag): 10.5 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n<p>Mass = Density \u00d7 Volume<\/p>\n\n\n\n<p>For gold:<br>Mass_Au = 19.3 g\/cm\u00b3 \u00d7 3860.8 cm\u00b3<br>= 74513.44 g<\/p>\n\n\n\n<p>For silver:<br>Mass_Ag = 10.5 g\/cm\u00b3 \u00d7 3860.8 cm\u00b3<br>= 40538.4 g<\/p>\n\n\n\n<p><strong>3. Identify Which Bar Has the Greatest Mass:<\/strong><\/p>\n\n\n\n<p>The gold bar has a mass of 74,513.44 grams, while the silver bar has a mass of 40,538.4 grams. Therefore, the gold bar has the greater mass.<\/p>\n\n\n\n<p><strong>4. Calculate the Number of Atoms in Each Bar:<\/strong><\/p>\n\n\n\n<p>To find the number of atoms, we use the formula:<\/p>\n\n\n\n<p>Number of atoms = (Mass of the sample \/ Molar mass) \u00d7 Avogadro&#8217;s number<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Molar mass of gold (Au): approximately 196.97 g\/mol<\/li>\n\n\n\n<li>Molar mass of silver (Ag): approximately 107.87 g\/mol<\/li>\n\n\n\n<li>Avogadro&#8217;s number: 6.022 \u00d7 10\u00b2\u00b3 atoms\/mol<\/li>\n<\/ul>\n\n\n\n<p>For gold:<br>Number of atoms_Au = (74513.44 g \/ 196.97 g\/mol) \u00d7 6.022 \u00d7 10\u00b2\u00b3 atoms\/mol<br>\u2248 2.278 \u00d7 10\u00b2\u2076 atoms<\/p>\n\n\n\n<p>For silver:<br>Number of atoms_Ag = (40538.4 g \/ 107.87 g\/mol) \u00d7 6.022 \u00d7 10\u00b2\u00b3 atoms\/mol<br>\u2248 2.263 \u00d7 10\u00b2\u2076 atoms<\/p>\n\n\n\n<p><strong>5. Determine Which Bar Contains the Greater Number of Atoms:<\/strong><\/p>\n\n\n\n<p>The gold bar contains approximately 2.278 \u00d7 10\u00b2\u2076 atoms, while the silver bar contains approximately 2.263 \u00d7 10\u00b2\u2076 atoms. Thus, the gold bar contains a slightly greater number of atoms.<\/p>\n\n\n\n<p><strong>6. Calculate the Total Mass if Both Bars Were Melted Together:<\/strong><\/p>\n\n\n\n<p>Total mass = Mass_Au + Mass_Ag<br>= 74,513.44 g + 40,538.4 g<br>= 115,051.84 g<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>The mass of an object is determined by its volume and density. Given that both bars have the same volume, the metal with the higher density will have a greater mass. Gold&#8217;s density is 19.3 g\/cm\u00b3, significantly higher than silver&#8217;s 10.5 g\/cm\u00b3, resulting in the gold bar having a greater mass.<\/p>\n\n\n\n<p>The number of atoms in a given mass depends on the molar mass of the element. Gold has a higher molar mass (196.97 g\/mol) compared to silver (107.87 g\/mol). However, due to the higher mass of the gold bar, the total number of atoms in the gold bar is slightly greater than in the silver bar.<\/p>\n\n\n\n<p>When combining both bars into an alloy, the total mass is simply the sum of the individual masses, resulting in 115,051.84 grams.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The density of gold metal is 19.3 g\/cm 3 , while that for silver is 10.5 g\/cm 3 . Suppose you had the same size bar of each metal, with the dimensions 2.00 in x 10.0 cm x 760 mm. Volume of a cube is height x length x width. Which bar would have the [&hellip;]<\/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-197033","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197033","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=197033"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197033\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=197033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=197033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=197033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}