{"id":24947,"date":"2025-06-18T19:35:04","date_gmt":"2025-06-18T19:35:04","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=24947"},"modified":"2025-06-18T19:35:06","modified_gmt":"2025-06-18T19:35:06","slug":"calculate-the-theoretical-density-of-iron-and-aluminum-using-the-structure-edge-length-and-atomic-weight","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/calculate-the-theoretical-density-of-iron-and-aluminum-using-the-structure-edge-length-and-atomic-weight\/","title":{"rendered":"Calculate the theoretical density of Iron and Aluminum using the structure, edge length, and atomic weight"},"content":{"rendered":"\n<p>Calculate the theoretical density of Iron and Aluminum using the structure, edge length, and atomic weight. 1b) Compare the theoretical density of each metal with the experimental density that you calculated from the mass and volume (Iron: 7.9 g\/cm\u00c2\u00b3 and Aluminum: 2.7 g\/cm\u00c2\u00b3). Remember that when comparing numbers, it is best to use percent difference. Provide a sentence to explain why these densities differ.<br>Show more\u2026<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>) Theoretical Density Calculation<\/strong><\/h3>\n\n\n\n<p>The theoretical density (\u03c1\\rho\u03c1) of a metal is calculated using the formula:\u03c1=n\u22c5AVc\u22c5NA\\rho = \\frac{n \\cdot A}{V_c \\cdot N_A}\u03c1=Vc\u200b\u22c5NA\u200bn\u22c5A\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>nnn = number of atoms per unit cell<\/li>\n\n\n\n<li>AAA = atomic weight (g\/mol)<\/li>\n\n\n\n<li>VcV_cVc\u200b = volume of the unit cell (cm\u00b3)<\/li>\n\n\n\n<li>NAN_ANA\u200b = Avogadro\u2019s number (6.022\u00d71023\u2009atoms\/mol)(6.022 \\times 10^{23} \\, \\text{atoms\/mol})(6.022\u00d71023atoms\/mol)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>For Iron (Fe)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Structure: Body-Centered Cubic (BCC)<\/li>\n\n\n\n<li>Edge length (a): 2.866 \u00c5 = 2.866\u00d710\u221282.866 \\times 10^{-8}2.866\u00d710\u22128 cm<\/li>\n\n\n\n<li>nnn = 2 atoms per unit cell<\/li>\n\n\n\n<li>Atomic weight = 55.85 g\/mol<\/li>\n<\/ul>\n\n\n\n<p>Vc=a3=(2.866\u00d710\u22128)3=2.35\u00d710\u221223\u2009cm3V_c = a^3 = (2.866 \\times 10^{-8})^3 = 2.35 \\times 10^{-23} \\, \\text{cm}^3Vc\u200b=a3=(2.866\u00d710\u22128)3=2.35\u00d710\u221223cm3\u03c1=2\u22c555.852.35\u00d710\u221223\u22c56.022\u00d71023=111.71.415\u00d7101\u22487.89\u2009g\/cm3\\rho = \\frac{2 \\cdot 55.85}{2.35 \\times 10^{-23} \\cdot 6.022 \\times 10^{23}} = \\frac{111.7}{1.415 \\times 10^1} \\approx 7.89 \\, \\text{g\/cm}^3\u03c1=2.35\u00d710\u221223\u22c56.022\u00d710232\u22c555.85\u200b=1.415\u00d7101111.7\u200b\u22487.89g\/cm3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>For Aluminum (Al)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Structure: Face-Centered Cubic (FCC)<\/li>\n\n\n\n<li>Edge length (a): 4.049 \u00c5 = 4.049\u00d710\u221284.049 \\times 10^{-8}4.049\u00d710\u22128 cm<\/li>\n\n\n\n<li>nnn = 4 atoms per unit cell<\/li>\n\n\n\n<li>Atomic weight = 26.98 g\/mol<\/li>\n<\/ul>\n\n\n\n<p>Vc=a3=(4.049\u00d710\u22128)3=6.64\u00d710\u221223\u2009cm3V_c = a^3 = (4.049 \\times 10^{-8})^3 = 6.64 \\times 10^{-23} \\, \\text{cm}^3Vc\u200b=a3=(4.049\u00d710\u22128)3=6.64\u00d710\u221223cm3\u03c1=4\u22c526.986.64\u00d710\u221223\u22c56.022\u00d71023=107.923.996\u22482.70\u2009g\/cm3\\rho = \\frac{4 \\cdot 26.98}{6.64 \\times 10^{-23} \\cdot 6.022 \\times 10^{23}} = \\frac{107.92}{3.996} \\approx 2.70 \\, \\text{g\/cm}^3\u03c1=6.64\u00d710\u221223\u22c56.022\u00d710234\u22c526.98\u200b=3.996107.92\u200b\u22482.70g\/cm3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1b) Comparison with Experimental Densities<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Iron:<\/strong><br>Theoretical = 7.89 g\/cm\u00b3<br>Experimental = 7.9 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n<p>Percent&nbsp;difference=\u22237.89\u22127.9\u22237.9\u00d7100%\u22480.13%\\text{Percent difference} = \\frac{|7.89 &#8211; 7.9|}{7.9} \\times 100\\% \\approx 0.13\\%Percent&nbsp;difference=7.9\u22237.89\u22127.9\u2223\u200b\u00d7100%\u22480.13%<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Aluminum:<\/strong><br>Theoretical = 2.70 g\/cm\u00b3<br>Experimental = 2.7 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n<p>Percent&nbsp;difference=\u22232.70\u22122.7\u22232.7\u00d7100%=0%\\text{Percent difference} = \\frac{|2.70 &#8211; 2.7|}{2.7} \\times 100\\% = 0\\%Percent&nbsp;difference=2.7\u22232.70\u22122.7\u2223\u200b\u00d7100%=0%<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>The theoretical and experimental densities are nearly identical. Slight differences may result from defects in the metal crystal, impurities, or rounding in measured values. Real materials may contain vacancies or dislocations that lower the actual density compared to the ideal crystal used in theoretical calculations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-32.jpeg\" alt=\"\" class=\"wp-image-24954\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-32.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-32-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-32-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the theoretical density of Iron and Aluminum using the structure, edge length, and atomic weight. 1b) Compare the theoretical density of each metal with the experimental density that you calculated from the mass and volume (Iron: 7.9 g\/cm\u00c2\u00b3 and Aluminum: 2.7 g\/cm\u00c2\u00b3). Remember that when comparing numbers, it is best to use percent difference. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24947","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24947","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=24947"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24947\/revisions"}],"predecessor-version":[{"id":24955,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24947\/revisions\/24955"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=24947"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=24947"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=24947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}