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QJEEM11Ch7152: JEE Main 2011 Chemistry - Class 11 JEEM11Ch7152 Solution: A 5.2 molal aqueous solution of methyl alcohol, CH 3 OH, is…

A 5.2 molal aqueous solution of methyl alcohol, CH3OH, is supplied. What is the mole fraction of methyl alcohol in the solution ?

Multiple Choice Options

  • A 0.19
  • B 0.086
  • C 0.05
  • D 0.1

Step-by-Step Verified Solution

The formula between Mole fraction and Molality is </mo></mrow><mi>m</mi><mo>=</mo><mrowdata−mjx−texclass="ORD"><mfrac><mrowdata−mjx−texclass="ORD"><mrowdata−mjx−texclass="ORD"><msub><mi>X</mi><mrowdata−mjx−texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi>e</mi></mrow></msub></mrow></mrow><mrowdata−mjx−texclass="ORD"><mrowdata−mjx−texclass="ORD"><msub><mi>X</mi><mrowdata−mjx−texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>×</mo><mrowdata−mjx−texclass="ORD"><mfrac><mrowdata−mjx−texclass="ORD"><mn>1000</mn></mrow><mrowdata−mjx−texclass="ORD"><mrowdata−mjx−texclass="ORD"><msub><mi>M</mi><mrowdata−mjx−texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></mrow></msub></mrow></mrow></mfrac></mrow></math></mjx−assistive−mml></mjx−container></mjx−assistive−mml></mjx−container></mjx−assistive−mml></mjx−container></mo></mrow><mi>m</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>X</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi>e</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>X</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>×</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1000</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></mrow></msub></mrow></mrow></mfrac></mrow></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>
mm = molality, Xsolute = Mole fraction of solute, Xsolvent = Mole fraction of solvent, Msolvent = Molar mass of solvent

Here solute is methyl alcohol(CH3OH) and solvent is water(H2O). Here water is solvent because question says solution is aqueous.

Assume mole fraction of methyl alcohol = X

So mole fraction of water = 1 - X

and given molality (m) = 5.2

Msolvent = 18 (as molar mass of H2O = 18)

∴\therefore 5.2 = X1−X×100018{X \over {1 - X}} \times {{1000} \over {18}}

by solving this we get,

X = 0.086

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