13.2 Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

<p><strong>13.2 </strong>The ideal gas equation relating to pressure (P), volume (V) and absolute temperature (T) is given by the relation</p><p>PV = nRT, where</p><p>R is the universal gas constant = 8.314 J /mol/K</p><p>N = number of moles = 1 (given)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p><p>T = standard temperature = 273 K</p><p>P = standard pressure = 1 atm = 1.013&nbsp;<span title="Click to copy mathml"><math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>5</mn></mrow></mrow></msup></math></span>&nbsp;N/&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span></p><p>Therefore V =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>n</mi><mi>R</mi><mi>T</mi></mrow></mrow><mrow><mrow><mi>P</mi></mrow></mrow></mfrac></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn><mi></mi><mo>*</mo><mn>8.314</mn><mo>*</mo><mn>273</mn></mrow></mrow><mrow><mrow><mn>1.013</mn><mi mathvariant="normal"></mi><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>5</mn></mrow></mrow></msup></mrow></mrow></mfrac></math></span>&nbsp;= 0.02240&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math></span>&nbsp;= 22.4 litres</p><p>Hence the molar volume of a gas at STP is 22.4 litres.</p>

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