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		<title>Atomic Mass by Dulong Petit&#8217;s Law</title>
		<link>https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/dulong-petits-law-atomic-mass/12628/</link>
					<comments>https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/dulong-petits-law-atomic-mass/12628/#respond</comments>
		
		<dc:creator><![CDATA[Hemant More]]></dc:creator>
		<pubDate>Sat, 23 May 2020 15:10:52 +0000</pubDate>
				<category><![CDATA[Physical Chemistry]]></category>
		<category><![CDATA[Atomic mass]]></category>
		<category><![CDATA[Average of atomic mass]]></category>
		<category><![CDATA[Chemistry]]></category>
		<category><![CDATA[Determination of atomic mass]]></category>
		<category><![CDATA[Dulong Petit's law]]></category>
		<category><![CDATA[GAM]]></category>
		<category><![CDATA[GAW]]></category>
		<category><![CDATA[Gram atomic mass]]></category>
		<category><![CDATA[Specific heat]]></category>
		<category><![CDATA[Valency]]></category>
		<guid isPermaLink="false">https://thefactfactor.com/?p=12628</guid>

					<description><![CDATA[<p>Science &#62; Chemistry &#62; Concept of Atomic Mass and Equivalent Mass &#62; Atomic Mass by Dulong Petit&#8217;s Law In previous articles, we have studied Cannizzaro&#8217;s method and law of isomorphism method to determine atomic mass. In this article, we shall study to calculate atomic mass by Dulong Petit&#8217;s law. Specific Heat: The amount of heat [&#8230;]</p>
<p>The post <a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/dulong-petits-law-atomic-mass/12628/">Atomic Mass by Dulong Petit&#8217;s Law</a> appeared first on <a href="https://thefactfactor.com">The Fact Factor</a>.</p>
]]></description>
										<content:encoded><![CDATA[
<h4 class="wp-block-heading"><strong>Science &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/" target="_blank">Chemistry</a> &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/concept-atomic-mass-and-equivalent-mass/" target="_blank">Concept of Atomic Mass and Equivalent Mass</a> &gt; Atomic Mass by Dulong Petit&#8217;s Law</strong></h4>



<p>In previous articles, we have studied Cannizzaro&#8217;s method and law of isomorphism method to determine atomic mass. In this article, we shall study to calculate atomic mass by Dulong Petit&#8217;s law.</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/06/Dulong-Petit-1.png" alt="" class="wp-image-13107" width="263" height="173"/></figure></div>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Specific Heat:</strong></p>



<p>The amount of heat required to raise the temperature of one mole of an element from 287.5 K to 288.5 K is called specific heat of&nbsp;the element. Its S.I. unit is J/mol/ K.</p>



<p>The product of atomic mass and specific heat of the element is called atomic heat of the element.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Dulong-Petit’s Law:</strong></p>



<p>The product of specific heat and the atomic mass of an element in the solid-state is approximately equal to 6.4. OR&nbsp;&nbsp; Atomic heat of a solid element is nearly equal to 6.4.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Limitations of Dulong-Petit’s Law:</strong></p>



<ul class="wp-block-list"><li>This law is applicable to elements which are in solid state.</li><li>This law Is applicable to the heavier element.&nbsp; It is not applicable to lighter elements having high melting points.</li><li>This law gives approximate atomic mass.</li></ul>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Steps Involved:</strong></p>



<ul class="wp-block-list"><li>Find the equivalent mass of the element by any method mentioned in topic equivalent mass.</li><li>Find approximate atomic mass using relation,&nbsp;Approx. atomic mass × Specific heat = 6.4</li><li>Find the valency of the element using relation,&nbsp;Approx. atomic mass = equivalent mass × valency</li><li>Find the nearest whole number for the calculated valency and use this whole number as valency of that element.</li><li>Use following formula to calculate the corrected atomic mass of the element,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency</li></ul>



<p class="has-text-color has-background has-medium-font-size has-luminous-vivid-orange-color has-very-light-gray-background-color"><strong>Numerical Methods:</strong></p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 01:</strong></p>



<p><strong>The specific heat of a metal A is found to be 0.03;&nbsp;its equivalent mass is 69.66. Calculate the valency and exact atomic mass of an element.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">By Dulong-Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.03 = 213.33</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 213.33 / 69.66 = 3.06</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp; =&nbsp;&nbsp;69.66 × 3 = 208.98 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> Hence the valency is 3 and its atomic mass is 208.98 u.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 02:</strong></p>



<p><strong>A solid element of equivalent mass 9 has specific heat 1 J/g/K. calculate its atomic mass.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Specific heat = 1 J/g/K = 1 / 4.188 = 0.2388</p>



<p class="has-text-align-center">By Dulong-Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.2388 = 26.80</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 26.80 / 9 = 2.98</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp; =&nbsp;&nbsp;9 × 3 = 27 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> Hence the valency is 3 and its atomic mass is 27 u.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 03:</strong></p>



<p><strong>Equivalent mass of barium is 68.68 and its valency is 2. Find its atomic mass.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Equivalent mass of barium = 68.68,&nbsp;valency of barium = 2</p>



<p class="has-text-align-center">Atomic mass = Equivalent mass x valency&nbsp;= 68.68 x 2 = 137.6</p>



<p class="has-text-align-center">Thus atomic mass of barium is 137.6.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 04:</strong></p>



<p><strong>The specific heat of a metal was found to be 0.03 and its equivalent mass is 103.5. Find the atomic mass of the metal.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">By Dulong-Petit’s Law,&nbsp;&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.03 = 213.33</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 213.33 / 103.5 = 2.05</p>



<p class="has-text-align-center">∴&nbsp;Valency = 2 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;&nbsp;103.5 × 2 = 207 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> atomic mass is 207 u.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 05:</strong></p>



<p><strong>The specific heat of metal M that forms sulphide MS is 0.032 cal g<sup>-1</sup> deg<sup>-1</sup>. What is the equivalent mass of the metal?</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">By Dulong-Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.032 = 200</p>



<p class="has-text-align-center">Now metal sulphide has formula MS</p>



<p class="has-text-align-center">Hence valency of metal is 2</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Equivalent mass = approx. atomic mass / valency&nbsp; = 200 / 2 = 100</p>



<p class="has-text-align-center"><strong>Ans:</strong> equivalent mass is 100 u.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 06:</strong></p>



<p><strong>The chloride of a metal was found to contain 26.2 % of chlorine. The specific heat of the metal is 0.033. Calculate the atomic mass and equivalent mass of the metal. Also write the molecular formula of metal chloride.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Consider 100 g of metal chloride</p>



<p class="has-text-align-center">% of chlorine = 26.2</p>



<p class="has-text-align-center">% of metal = 100 &#8211; 26.2 = 73.8</p>



<p class="has-text-align-center">Mass of chlorine = 26.2 g,&nbsp;Mass of metal = 73.8 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img decoding="async" width="371" height="84" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-01-1.png" alt="Dulong Petits Law" class="wp-image-12646" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-01-1.png 371w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-01-1-300x68.png 300w" sizes="(max-width: 371px) 100vw, 371px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.033 = 194</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 194 / 100 = 1.94</p>



<p class="has-text-align-center">∴&nbsp;Valency = 2 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp; =&nbsp;&nbsp;100 × 2 = 200 u</p>



<p class="has-text-align-center">Valency of metal (M) is 2 and that of chlorine is 1. Hence the formula of metal chloride is MCl<sub>2</sub>.</p>



<p class="has-text-align-center"><strong>Ans:</strong> the&nbsp;atomic mass of the metal is 200 and its equivalent mass is 100. The formula of metal chloride is MCl<sub>2</sub>.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 07:</strong></p>



<p><strong>1 g of metal having specific heat 0.060205 combines with oxygen to form 1.08 g of oxide. Find atomic mass and valency of the metal. Also, write the molecular formula of the metal oxide.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Mass of metal = 1 g, Mass of oxide = 1.08 g</p>



<p class="has-text-align-center">Mass of oxygen = 1.08 g &#8211; 1 g = 0.08 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img decoding="async" width="343" height="79" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-02-1.png" alt="Dulong Petits Law" class="wp-image-12648" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-02-1.png 343w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-02-1-300x69.png 300w" sizes="(max-width: 343px) 100vw, 343px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.060205 = 103.1</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 103.1 / 100 = 1.03</p>



<p class="has-text-align-center">∴&nbsp; Valency = 1 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;&nbsp;100 × 1 = 200 u</p>



<p class="has-text-align-center">Valency of metal (M) is 1 and that of oxygen is 2. Hence the formula of metal chloride is M<sub>2</sub>O.</p>



<p class="has-text-align-center"><strong>Ans:</strong> the&nbsp;atomic mass of the metal is 100 and its valency is 1, the formula of metal chloride is M<sub>2</sub>O.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 08:</strong></p>



<p><strong>A metallic oxide contains 47.06 % of oxygen. The specific heat of metal is 0.25. Calculate the atomic mass of the metal. Write molecular formula of metal oxide.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Consider 100 g of metal oxide</p>



<p class="has-text-align-center">% of oxygen = 47.06</p>



<p class="has-text-align-center">% of metal = 100 &#8211; 47.06 = 52.94</p>



<p class="has-text-align-center">Mass of oxygen&nbsp;= 47.06 g,&nbsp;Mass of metal = 52.94 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1.png" alt="Dulong Petits Law" class="wp-image-12650" width="390" height="47" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1.png 333w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1-300x36.png 300w" sizes="auto, (max-width: 390px) 100vw, 390px" /></figure></div>



<p class="has-text-align-center">Equivalent mass = (52.94&nbsp;× 8) / 47.06 = 9</p>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.25 = 25.6</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 25.6 / 9&nbsp; = 2.8</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp; =&nbsp;&nbsp;9 × 3 = 27 u</p>



<p class="has-text-align-center">Valency of metal (M) is 3 and that of oxygen is 2. Hence the formula of metal chloride is M<sub>2</sub>O<sub>3</sub>.</p>



<p class="has-text-align-center"><strong>Ans:</strong> the&nbsp;atomic mass of the metal is 27 and&nbsp;the formula of metal oxide is M<sub>2</sub>O<sub>3</sub>.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 09:</strong></p>



<p><strong>0.54 g of a metal combines with 0.48 g of oxygen to form its oxide. Its specific heat is 0.22 cal per deg. What is the atomic mass of the metal?</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Mass of oxygen&nbsp;= 0.48 g,&nbsp;Mass of metal = 0.54 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1.png" alt="Dulong Petits Law" class="wp-image-12650" width="386" height="46" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1.png 333w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-03-1-300x36.png 300w" sizes="auto, (max-width: 386px) 100vw, 386px" /></figure></div>



<p class="has-text-align-center">Equivalent mass = (0.54 × 8) / 0.48 = 9</p>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.22 = 29.09</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 29.09 / 9&nbsp;= 3.2</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;9 × 3 = 27 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> the&nbsp;atomic mass of the metal is 27.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 10:</strong></p>



<p><strong>0.45 g of metal displaced 560 ml of hydrogen at STP from acid. Specific heat of metal is 0.214. Calculate the equivalent mass and atomic mass of the metal.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Mass of metal = 0.45 g</p>



<p class="has-text-align-center">Volume of hydrogen = 560 ml = 0.560 dm³ at STP</p>



<p class="has-text-align-center">Mass of 0.560 dm³ of hydrogen at STP&nbsp;</p>



<p class="has-text-align-center">= (Molecular mass of gas x volume of gas in dm³)&nbsp; / 22.4</p>



<p class="has-text-align-center">Mass of hydrogen displaced&nbsp;= (2 x 0.560)&nbsp;/ 22.4 = 0.05 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-04.png" alt="Dulong Petits Law" class="wp-image-12653" width="406" height="45" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-04.png 373w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-04-300x33.png 300w" sizes="auto, (max-width: 406px) 100vw, 406px" /></figure></div>



<p class="has-text-align-center">Equivalent mass of metal = 0.45 / 0.05 = 9</p>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.214 = 29.9</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 29.9 / 9&nbsp;= 3.3</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;9 × 3 = 27 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> the atomic mass of the metal is 27 and its equivalent mass is 9.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 11:</strong></p>



<p><strong>0.2160 g of metal,&nbsp;when treated with an excess of dilute sulphuric acid gave 80.4 cc of moist hydrogen measured at 20 °C and 770 mm of pressure. The specific heat of the metal is 0.0955. Calculate the valency and exact atomic mass of the metal. The aqueous tension at 20 °C is 17.5 mm.</strong></p>



<p><strong>Solution:</strong></p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="310" height="366" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-05-1.png" alt="" class="wp-image-12655" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-05-1.png 310w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-05-1-254x300.png 254w" sizes="auto, (max-width: 310px) 100vw, 310px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.0955 = 67.02</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 67.02 / 32.36&nbsp;= 2.07</p>



<p class="has-text-align-center">∴&nbsp; Valency = 2 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;</p>



<p class="has-text-align-center">=&nbsp;32.36 × 2 = 64.72 u</p>



<p><strong>Ans: </strong>the&nbsp;atomic mass of the metal is 64.72 and its valency is 2.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 12:</strong></p>



<p><strong>0.45 g of metal gave 176.6 ml of hydrogen at 23 °C and 743 mm pressure when treated with dilute sulphuric acid. Calculate the equivalent mass of the metal. Aqueous tension at 23 °C is 21 mm. If the specific heat of the metal is 0.091, calculate the exact atomic mass of the metal.</strong></p>



<p><strong>Solution:</strong></p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="313" height="367" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-06.png" alt="" class="wp-image-12656" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-06.png 313w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-06-256x300.png 256w" sizes="auto, (max-width: 313px) 100vw, 313px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.091 = 70.33</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 70.33 / 32.32&nbsp;= 2.1</p>



<p class="has-text-align-center">∴&nbsp;Valency = 2 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;32.32 × 2 = 64.64 u</p>



<p class="has-text-align-center"><strong>Ans: </strong>the&nbsp;atomic mass of the metal is 64.64 and its valency is 2.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 13:</strong></p>



<p><strong>A metal M forms a volatile chloride, containing 80% of chlorine. The vapour density of the chloride is 66.75. Calculate the exact atomic mass of the element.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Molecular mass = 2 x Vapour Density&nbsp;= 2 x 66.75 = 133.5</p>



<p class="has-text-align-center">% of chlorine = 80</p>



<p class="has-text-align-center">% of the element = 100 &#8211; 80 = 20</p>



<p class="has-text-align-center">Mass of element = 20 g,&nbsp;Mass of chlorine = 80 g</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-07-1.png" alt="" class="wp-image-12659" width="401" height="39" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-07-1.png 352w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-07-1-300x29.png 300w" sizes="auto, (max-width: 401px) 100vw, 401px" /></figure></div>



<p class="has-text-align-center">Equivalent mass of metal = (20 x 35.5) / 80 = 8.875</p>



<p class="has-text-align-center">Let valency of the metal be ‘x’, hence the formula&nbsp;of the chloride is MCl<sub>x</sub>.</p>



<p class="has-text-align-center">Atomic mass of metal = Equivalent mass x valency = 8.875 x</p>



<p class="has-text-align-center">Molecular mass of chloride = Atomic mass of metal + Atomic mass of chlorine × x</p>



<p class="has-text-align-center">Molecular mass of chloride = 8.875 x + 35.5 × x = 133.5</p>



<p class="has-text-align-center">∴&nbsp; &nbsp;8.875 x + 35.5 × x = 133.5</p>



<p class="has-text-align-center">∴&nbsp; &nbsp;44.375 x = 133.5</p>



<p class="has-text-align-center">∴&nbsp; &nbsp;x = 133.5 /44.375 = 3.01</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Actual atomic mass = Equivalent mass x valency&nbsp;= 8.875 x 3 = 26.625</p>



<p class="has-text-align-center"><strong>Ans:</strong> The exact atomic mass of the element is 26.635</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 14:</strong></p>



<p><strong>The specific heat of a metal A is found to be 0.03. 10 g of metal on evaporation of nitric acid gave 18.9 g of pure dry nitrate. Calculate the equivalent mass and exact atomic mass of the metal.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Mass of metal = 10 g</p>



<p class="has-text-align-center">By double decomposition method</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="321" height="255" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-08-1.png" alt="" class="wp-image-12661" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-08-1.png 321w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-08-1-300x238.png 300w" sizes="auto, (max-width: 321px) 100vw, 321px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.03 = 213.33</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 213.33 / 69.66&nbsp; = 3.06</p>



<p class="has-text-align-center">∴&nbsp;Valency = 3 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp; =&nbsp;&nbsp;69.66 × 3 = 208.98 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> the&nbsp;atomic mass of the metal is 208.98 and its equivalent mass is 69.66.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 15:</strong></p>



<p><strong>1 g of metallic bromide dissolved in water gave with the excess of silver nitrate, 1.88 g of silver bromide. Calculate the accurate atomic mass of the element, if its specific heat is 0.15 cal (atomic mass of Ag is 108 and that of bromine is 80).</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Molecular mass of silver bromide&nbsp;= 108 + 80 = 188 g</p>



<p class="has-text-align-center">Mass of bromine in 1.88 g of silver bromide = (80/180) x 1.8 = 0.8 g</p>



<p class="has-text-align-center">Mass of metallic bromide = 1g,&nbsp;Mass of bromine&nbsp; = 0.8 g</p>



<p class="has-text-align-center">Mass of metal = 1 &#8211; 0.8 = 0.2 g</p>



<p class="has-text-align-center">By double decomposition method</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="361" height="161" src="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-09-1.png" alt="" class="wp-image-12663" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-09-1.png 361w, https://thefactfactor.com/wp-content/uploads/2020/05/Dulong-Petits-Law-09-1-300x134.png 300w" sizes="auto, (max-width: 361px) 100vw, 361px" /></figure></div>



<p class="has-text-align-center">By Dulong Petit’s Law,&nbsp;Atomic mass × Specific heat = 6.4 (Approx.)</p>



<p class="has-text-align-center">∴&nbsp;Approx. atomic mass = 6.4 / Sp. heat = 6.4 /0.15 = 42.67</p>



<p class="has-text-align-center">Now,&nbsp;approx. atomic mass = equivalent mass × valency</p>



<p class="has-text-align-center">∴&nbsp;Valency = approx. atomic mass / equivalent mass = 42.67 / 20&nbsp;= 2.1</p>



<p class="has-text-align-center">∴&nbsp;Valency = 2 (Corrected to nearest whole number)</p>



<p class="has-text-align-center">Now,&nbsp;Corrected atomic mass&nbsp;= Equivalent mass × valency&nbsp;=&nbsp;20 × 2 =40 u</p>



<p class="has-text-align-center"><strong>Ans:</strong> the atomic mass of the metal is 40.</p>



<p>In next article, we shall study the concept of equivalent mass and hydrogen displacement method to determine it.</p>



<p class="has-text-color has-text-align-center has-medium-font-size has-vivid-cyan-blue-color"><strong><a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/law-of-isomorphism/12489/">Previous Topic: Atomic Mass Using Law of Isomorphism</a></strong></p>



<p class="has-text-color has-text-align-center has-medium-font-size has-vivid-cyan-blue-color"><strong><a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/equivalent-mass-by-hydrogen-displacement-method/12667/">Next Topic: Equivalent Mass by Hydrogen Displacement Method</a></strong></p>



<h4 class="wp-block-heading"><strong>Science &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/" target="_blank">Chemistry</a> &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/concept-atomic-mass-and-equivalent-mass/" target="_blank">Concept of Atomic Mass and Equivalent Mass</a> &gt; Atomic Mass by Dulong Petit&#8217;s Law</strong></h4>
<p>The post <a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/dulong-petits-law-atomic-mass/12628/">Atomic Mass by Dulong Petit&#8217;s Law</a> appeared first on <a href="https://thefactfactor.com">The Fact Factor</a>.</p>
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		<title>Atomic Mass Using Law of Isomorphism</title>
		<link>https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/law-of-isomorphism/12489/</link>
					<comments>https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/law-of-isomorphism/12489/#respond</comments>
		
		<dc:creator><![CDATA[Hemant More]]></dc:creator>
		<pubDate>Sat, 23 May 2020 15:03:15 +0000</pubDate>
				<category><![CDATA[Physical Chemistry]]></category>
		<category><![CDATA[Atomic mass]]></category>
		<category><![CDATA[Average of atomic mass]]></category>
		<category><![CDATA[Chemistry]]></category>
		<category><![CDATA[Determination of atomic mass]]></category>
		<category><![CDATA[Eilhard Mitscherlich]]></category>
		<category><![CDATA[GAM]]></category>
		<category><![CDATA[GAW]]></category>
		<category><![CDATA[Gram atomic mass]]></category>
		<category><![CDATA[Isomorphous]]></category>
		<category><![CDATA[Law of isomorphism]]></category>
		<category><![CDATA[Valency]]></category>
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					<description><![CDATA[<p>Science &#62; Chemistry &#62; Concept of Atomic Mass and Equivalent Mass &#62; Law of Isomorphism Method In the last article, we have studied determination of atomic mass by Cannizzaro&#8217;s method. In this article, we shall study the law of isomorphism and its use to find the atomic mass of a substance. This law was given [&#8230;]</p>
<p>The post <a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/law-of-isomorphism/12489/">Atomic Mass Using Law of Isomorphism</a> appeared first on <a href="https://thefactfactor.com">The Fact Factor</a>.</p>
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										<content:encoded><![CDATA[
<h4 class="wp-block-heading"><strong>Science &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/" target="_blank">Chemistry</a> &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/concept-atomic-mass-and-equivalent-mass/" target="_blank">Concept of Atomic Mass and Equivalent Mass</a> &gt; Law of Isomorphism Method</strong></h4>



<p>In the last article, we have studied determination of atomic mass by Cannizzaro&#8217;s method. In this article, we shall study the law of isomorphism and its use to find the atomic mass of a substance. This law was given by a German chemist Eilhard Mitscherlich.</p>



<div class="wp-block-image"><figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://thefactfactor.com/wp-content/uploads/2020/06/Eilhard-Mitscherlich-1.png" alt="" class="wp-image-13104" width="142" height="184"/></figure></div>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Isomorphism:</strong></p>



<p>The phenomenon of two or more substances displaying similarity or identity of crystalline form is called isomorphism. Such substances are called isomorphs or isomorphous to each other.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Characteristics of Isomorphous Substances:</strong></p>



<p>The crystals of isomorphous substances have the same shape.</p>



<ul class="wp-block-list"><li>If crystals of one substance are suspended in a saturated solution of another, the former continuous to grow as latter is deposited all over it. Thus they form overgrowth on each other.</li><li>They can form a mixed crystal with each other.</li></ul>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Examples:</strong></p>



<ul class="wp-block-list"><li>Ferrous sulphate (FeSO<sub>4</sub>.7H<sub>2</sub>O) and magnesium sulphate (MgSO<sub>4</sub>.7H<sub>2</sub>O).</li><li>Potassium perchlorate (KClO<sub>4</sub>)and potassium permangnate (KMnO<sub>4</sub>).</li><li>Potassium chromate (K<sub>2</sub>CrO<sub>4</sub>)and potassium sulphate (K<sub>2</sub>SO<sub>4</sub>).</li><li>Ammonium alum ((NH<sub>4</sub>)<sub>2</sub>SO<sub>4</sub>.Al<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>.24H<sub>2</sub>O) and potash alum (K<sub>2</sub>SO<sub>4</sub>.Al<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>.24H<sub>2</sub>O)</li></ul>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Law of Isomorphism:</strong></p>



<p>This law was given by Mitscherlich in 1819. It states that “Substance having similar internal structure exhibit identity of crystalline form”.</p>



<p>Thus we can conclude that</p>



<ul class="wp-block-list"><li>isomorphous substances should have similar chemical formulae.</li><li>the elements forming isomorphous substances must have the same valency</li><li>In isomorphous compounds, the ratio between masses of two elements which combine with the same combined mass of all other elements is the same as the ratio between their atomic masses. Mathematically.</li></ul>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="340" height="38" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-01-1.png" alt="Law of Isomorphism" class="wp-image-12500" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-01-1.png 340w, https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-01-1-300x34.png 300w" sizes="auto, (max-width: 340px) 100vw, 340px" /></figure></div>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>To Find Atomic Mass Using Law of Isomorphism: (Steps Involved):</strong></p>



<ul class="wp-block-list"><li>Find percentage composition of a compound containing an element whose atomic mass is to be found.</li><li>Write the formula of the compound using given the formula of the isomorphous substance.</li><li>Calculate molecular mass of the compound.</li><li>Assume atomic mass of the element as ‘x’.</li><li>Write percentage formula for the element.</li><li>Find the value of x. Which gives the atomic mass of the element.</li></ul>



<p class="has-text-color has-background has-medium-font-size has-luminous-vivid-orange-color has-very-light-gray-background-color"><strong>Nunerical Problems:</strong></p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 01:</strong></p>



<p><strong>The sulphate of metal contains 20.9 % of the metal and is isomorphous with ZnSO<sub>4</sub>.7H<sub>2</sub>O. What is the probable atomic mass of the metal?</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">The sulphate is isomorphous with &nbsp;ZnSO<sub>4</sub>.7H<sub>2</sub>O.</p>



<p class="has-text-align-center">Hence by the law of isomorphism, its chemical formula should be &nbsp;MSO<sub>4</sub>.7H<sub>2</sub>O.</p>



<p class="has-text-align-center">Let atomic mass of metal M be ‘x’</p>



<p class="has-text-align-center">∴ &nbsp;The molecular mass of metal sulphate = (x + 32 + 16 × 4) + 7(1 × 2 + 16)</p>



<p class="has-text-align-center">∴ The molecular mass of metal sulphate = (x + 32 + 64) + 7(18) = x + 96 + 126 = x + 222</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="329" height="38" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-02-1.png" alt="Law of Isomorphism" class="wp-image-12502" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-02-1.png 329w, https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-02-1-300x35.png 300w" sizes="auto, (max-width: 329px) 100vw, 329px" /></figure></div>



<p class="has-text-align-center">∴ &nbsp;100x = 20.9x + 20.9 × 222</p>



<p class="has-text-align-center">∴ 100x &#8211; 20.9x = 4639.80</p>



<p class="has-text-align-center">∴ 79.1x = 4639.80</p>



<p class="has-text-align-center">∴ &nbsp;x = 4639.80&nbsp;/ 79.1 = 58.65</p>



<p class="has-text-align-center">Thus the probable atomic mass of the metal is 58.65.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 02:</strong></p>



<p><strong>The oxides of two elements A and B are isomorphous. The metal A whose atomic mass is 52, forms a chloride whose vapour density is 79. The oxide B contains 47.1 % of oxygen. Calculate the atomic mass of B.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Let valency of the element be ‘x’. Hence its chloride formula is ACl<sub>x</sub>.</p>



<p class="has-text-align-center">The molecular mass of chloride = 2 × its vapour density = 2 × 79 = 158 g</p>



<p class="has-text-align-center">The molecular mass of chloride ACl<sub>x</sub>. = 52 + 35.5 &nbsp;x = 158</p>



<p class="has-text-align-center">∴ &nbsp; 35.5 &nbsp;x = 158 &#8211; 52 = 106</p>



<p class="has-text-align-center">∴ &nbsp;x &nbsp;= 106 / 35.5 = 3 (Nearest whole number)</p>



<p class="has-text-align-center">Thus valency of element A is 3.</p>



<p class="has-text-align-center">The oxides of two elements A and B are isomorphous.</p>



<p class="has-text-align-center">Hence the valency of A and B should be the same. Hence valency of element B is also 3.</p>



<p class="has-text-align-center">The oxide of B contains 47.1 % of oxygen.</p>



<p class="has-text-align-center">i.e. it contains 100 &#8211; 47. 1= 52.9 % of element B.</p>



<p class="has-text-align-center">Mass of oxygen = 47.1 g Mass of element = 52.9 g</p>



<p class="has-text-align-center">Equivalent mass of B = (52.9 x 8)/47.1 = 8.99</p>



<p class="has-text-align-center">Atomic mass of B = Equivalent mass x valency = 8.99 x 3 = 26.97</p>



<p class="has-text-align-center">Thus the atomic mass of the element B is 26.97.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 03:</strong></p>



<p><strong>A metal has 22.64% of metal in its sulphate. The metallic sulphate is isomorphous with MgSO<sub>4</sub>.7H<sub>2</sub>O. Calculate the atomic mass of the metal.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">The sulphate is isomorphous with MgSO<sub>4</sub>. 7H<sub>2</sub>O..</p>



<p class="has-text-align-center">Hence by the law of isomorphism, its chemical formula should be MSO<sub>4</sub>. 7H<sub>2</sub>O..</p>



<p class="has-text-align-center">Let atomic mass of metal M be ‘x’</p>



<p class="has-text-align-center">The molecular mass of metal sulphate = (x + 32 + 16 × 4) + 7(1 × 2 + 16)</p>



<p class="has-text-align-center">The molecular mass of metal sulphate = (x + 32 + 64) + 7(18) = x + 96 + 126 = x + 222</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="273" height="33" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-03-1.png" alt="Law of Isomorphism" class="wp-image-12504"/></figure></div>



<p class="has-text-align-center">∴ 100x = 22.64x + 22.64 × 222</p>



<p class="has-text-align-center">∴ 100x &#8211; 22.64x = 5026.08</p>



<p class="has-text-align-center">∴ 77.36x = 5026.08</p>



<p class="has-text-align-center">∴ x = 5026.08/ 77.36 = 64.97 = 65</p>



<p class="has-text-align-center">Thus the probable atomic mass of the metal is 65.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 04:</strong></p>



<p><strong>Magnesium sulphate contains 9.75% of magnesium and 39.02% of sulphate whereas zinc sulphate contains 22.6% of zinc and 35.5% sulphate. If the atomic mass of zinc is 65, find that of magnesium, if both the sulphates are isomorphous.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Let formula of zinc sulphate be ZnSO<sub>4</sub>.xH<sub>2</sub>O.</p>



<p class="has-text-align-center">% of zinc = 22.6, % of sulphate = 35.5, % of water = 100 -(22.6 + 35.5) = 100 &#8211; 58.1 = 41.9</p>



<p class="has-text-align-center">The molecular mass of zinc sulphate = (65+ 32 + 16 × 4) + x(1 × 2 + 16)</p>



<p class="has-text-align-center">The molecular mass of zinc sulphate =(65 +32 + 64) + 18x = 161 + 18x</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="318" height="36" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-04.png" alt="Law of Isomorphism" class="wp-image-12505" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-04.png 318w, https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-04-300x34.png 300w" sizes="auto, (max-width: 318px) 100vw, 318px" /></figure></div>



<p class="has-text-align-center">∴ 1800x = 41.9(18x + &nbsp;161)</p>



<p class="has-text-align-center">∴ 1800x = 754.2x + &nbsp;6745.9</p>



<p class="has-text-align-center">∴ 1800x &#8211; 754.2x = 6745.9</p>



<p class="has-text-align-center">∴ 1045.8x = 6745.9</p>



<p class="has-text-align-center">∴ x = 6745.9 / 1045.8 = 6.5 = 7</p>



<p class="has-text-align-center">The sulphate is isomorphous with &nbsp;magnesium sulphate.</p>



<p class="has-text-align-center">Hence formula of magnesium sulphate is MgSO<sub>4</sub>.7H<sub>2</sub>O.</p>



<p class="has-text-align-center">Let atomic mass of magnesium be be ‘x’</p>



<p class="has-text-align-center">The molecular mass of magnesium sulphate = (x + 32 + 16 × 4) + 7(1 × 2 + 16)</p>



<p class="has-text-align-center">The molecular mass of magnesium sulphate&nbsp;= (x + 32 + 64) + 7(18) = x + 96 + 126 = x + 222</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="328" height="38" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-05-1.png" alt="Law of Isomorphism" class="wp-image-12507" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-05-1.png 328w, https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-05-1-300x35.png 300w" sizes="auto, (max-width: 328px) 100vw, 328px" /></figure></div>



<p class="has-text-align-center">∴ 100x = 9.75x + 9.75 × 222</p>



<p class="has-text-align-center">∴ 100x &#8211; &nbsp;9.75x = 2164.5</p>



<p class="has-text-align-center">∴ 90.25x = 2164.5</p>



<p class="has-text-align-center">∴ x = 2164.5/90.25 = 23.98 = 24</p>



<p class="has-text-align-center">Thus the atomic mass of the metal is 24.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 05:</strong></p>



<p><strong>1g of the chloride of a metal when treated with the excess of silver nitrate produced 0.965 g of dry silver chloride. Calculate the atomic mass of the metal, given that it forms a sulphate which is isomorphous with BaSO<sub>4</sub>.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">By double decomposition method</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="312" height="74" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-06-1.png" alt="" class="wp-image-12509" srcset="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-06-1.png 312w, https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-06-1-300x71.png 300w" sizes="auto, (max-width: 312px) 100vw, 312px" /></figure></div>



<p class="has-text-align-center">∴ 0.965 E + 34.26 = 143.5</p>



<p class="has-text-align-center">∴ 0.965 E&nbsp; = 109.24</p>



<p class="has-text-align-center">∴&nbsp; E&nbsp; = 113.2</p>



<p class="has-text-align-center">Now the required sulphate is isomorphous with BaSO<sub>4</sub>,&nbsp;hence the formula for the sulphate is MSO<sub>4</sub>. Hence the valency of metal is 2.</p>



<p class="has-text-align-center">Atomic mass = equivalent mass x valency = 113.2 × 2 = 226.4</p>



<p class="has-text-align-center">Thus atomic mass of the metal is 226.4</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 06:</strong></p>



<p><strong>Potassium selenate is isomorphous with potassium sulphate and contains 35.75% of selenium. Find the atomic mass of selenium (Se).</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Potassium selenate &nbsp;is isomorphous with potassium sulphate K<sub>2</sub>SO<sub>4</sub>,</p>



<p class="has-text-align-center">hence the formula for the Potassium selenate is K<sub>2</sub>SeO<sub>4</sub>.</p>



<p class="has-text-align-center">Let atomic mass of metal selenium be be ‘x’</p>



<p class="has-text-align-center">The molecular mass of metal sulphate =39 × 2 + x + 16 × 4&nbsp; =78 + x + 64 = x + 142</p>



<p class="has-text-align-center">% of selenium in sulphate</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="127" height="36" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-07-1.png" alt="" class="wp-image-12511"/></figure></div>



<p class="has-text-align-center">∴ 100x = 35.75x + 35.75 × 142</p>



<p class="has-text-align-center">∴ 100x &#8211; &nbsp;35.75x = 5076.5</p>



<p class="has-text-align-center">∴&nbsp; 64.25x =5076.5 ∴</p>



<p class="has-text-align-center">x&nbsp; = 79.01</p>



<p class="has-text-align-center">Thus the atomic mass of the seleniumis 79.01.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 07:</strong></p>



<p><strong>Potassium permanganate is isomorphous with potassium perchlorate KClO<sub>4</sub> and contains 34.81 % of manganese. Find the atomic mass of manganese.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Potassium permanganate &nbsp;is isomorphous with potassium perchlorate KClO<sub>4</sub>,</p>



<p class="has-text-align-center">hence the formula for the Potassium permanganate is KMnO<sub>4</sub>.</p>



<p class="has-text-align-center">Let atomic mass of metal selenium be be ‘x’</p>



<p class="has-text-align-center">The molecular mass of ptassium permanganate =39 &nbsp;+ x + 16 x 4&nbsp; =39 + x + 64 = x + 103</p>



<p class="has-text-align-center">% of selenium in sulphate</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="120" height="34" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-08-1.png" alt="" class="wp-image-12513"/></figure></div>



<p class="has-text-align-center">∴ 100x = 34.815x + 34.81 × 103</p>



<p class="has-text-align-center">∴ 100x &#8211; &nbsp;34.815x = 3585.43</p>



<p class="has-text-align-center">∴ 65.19x = 3585.43</p>



<p class="has-text-align-center">∴ x =&nbsp; 54.99 = 55</p>



<p class="has-text-align-center">Thus the atomic mass of the manganese is 55.</p>



<p class="has-text-color has-medium-font-size has-vivid-red-color"><strong>Example &#8211; 08:</strong></p>



<p><strong>Chrome alum is isomorphous with potash alum, K<sub>2</sub>SO<sub>4</sub>, Al<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>. 24 H<sub>2</sub>O and is found to contain 10.42% of chromium. Find the atomic mass of chromium.</strong></p>



<p><strong>Solution:</strong></p>



<p class="has-text-align-center">Chrome alum is isomorphous with potash alum, K<sub>2</sub>SO<sub>4</sub>, Al<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>. 24 H<sub>2</sub>O,</p>



<p class="has-text-align-center">hence the formula for the chrome alumn is&nbsp;K<sub>2</sub>SO<sub>4</sub>, Cr2(SO<sub>4</sub>)<sub>3</sub>. 24 H<sub>2</sub>O.</p>



<p class="has-text-align-center">Let atomic mass of chromium be be ‘x’</p>



<p class="has-text-align-center">The molecular mass of chrome alum is</p>



<p class="has-text-align-center">= 39 × 2 + 32 + 16 × 4 + 2 x &nbsp;+ (32 + 16 × 4 ) x 3&nbsp; + 24 × (1 ×2 + 16)</p>



<p class="has-text-align-center">molecular mass of chrome alum = 78 + 32 + 64 + 2x + (32 + 64) x3 + 24x (2 + 16)</p>



<p class="has-text-align-center">molecular mass of chrome alum = 78 + 32 + 64 + 2x + 96 x3 + 24x 18</p>



<p class="has-text-align-center">molecular mass of chrome alum = 78 + 32 + 64 + 2x + 96 x3 + 24x 18</p>



<p class="has-text-align-center">molecular mass of chrome alum = 78 + 32 + 64 + 2x + 288 + 432</p>



<p class="has-text-align-center">molecular mass of chrome alum =&nbsp; 2x + 894</p>



<p class="has-text-align-center">% of chromium</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="131" height="35" src="https://thefactfactor.com/wp-content/uploads/2020/05/Law-of-Isomorphism-09-1.png" alt="" class="wp-image-12515"/></figure></div>



<p class="has-text-align-center">∴&nbsp; 200x = 10.42 (2x + 894)</p>



<p class="has-text-align-center">∴&nbsp; 200x = 20.84 x + 9315.48</p>



<p class="has-text-align-center">∴&nbsp; 200x &#8211; 20.84 x = 9315.48</p>



<p class="has-text-align-center">∴&nbsp; 179.16x =9315.48</p>



<p class="has-text-align-center">∴&nbsp; x =&nbsp; 51.99 =52</p>



<p class="has-text-align-center">Thus the atomic mass of the chromium is 52.</p>



<p>In the next article, we shall stdy determination of atomic mass by Dulong Petit&#8217;s law.</p>



<p class="has-text-color has-text-align-center has-medium-font-size has-vivid-cyan-blue-color"><strong><a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/cannizzaros-method-of-determination-of-atomic-mass/12481/">Previous Topic: Atomic Mass by Cannizzaro&#8217;s Method</a></strong></p>



<p class="has-text-color has-text-align-center has-medium-font-size has-vivid-cyan-blue-color"><strong><a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/dulong-petits-law-atomic-mass/12628/">Next Topic: Atomic Mass by Dulong Petit&#8217;s Law</a></strong></p>



<h4 class="wp-block-heading"><strong>Science &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/" target="_blank">Chemistry</a> &gt; <a rel="noreferrer noopener" href="https://thefactfactor.com/chemistry/concept-atomic-mass-and-equivalent-mass/" target="_blank">Concept of Atomic Mass and Equivalent Mass</a> &gt; Law of Isomorphism Method</strong></h4>
<p>The post <a href="https://thefactfactor.com/facts/pure_science/chemistry/physical-chemistry/law-of-isomorphism/12489/">Atomic Mass Using Law of Isomorphism</a> appeared first on <a href="https://thefactfactor.com">The Fact Factor</a>.</p>
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