An evacuated glass vessel weights 40.0g when empty, 135.0g when filled with a liquid of density 0.95 g mL^-1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mo^-1 is:

(Given: R = 0.082 L atm K^-1 mol^-1)

<p>Wt of liquid = 135 – 40 = 95 gm</p><p>Volume of liquid =&nbsp;<math><mrow><mfrac><mrow><mi>w</mi><mi>t</mi><mo>.</mo></mrow><mrow><mi>d</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>i</mi><mi>t</mi><mi>y</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>9</mn><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>9</mn><mn>5</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mn>0</mn><mn>0</mn><mi>m</mi><mi>l</mi></mrow></math></p><p>Hence volume of vessel = 100 ml = 0.1 lit from ideal gas equation, </p><p><math><mrow><mi>M</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>R</mi><mi>T</mi></mrow><mrow><mi>P</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0</mn><mn>8</mn><mn>2</mn><mn>1</mn><mo>×</mo><mn>2</mn><mn>5</mn><mn>0</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>8</mn><mn>2</mn></mrow></mfrac></mrow></math></p><p><math><mrow><mo>∴</mo><mi>M</mi><mo>=</mo><mn>1</mn><mn>2</mn><mn>5</mn><mtext> </mtext><mtext> </mtext><mi>g</mi><mo>/</mo><mi>m</mi><mi>o</mi><mi>l</mi></mrow></math></p>

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