Question

Vapor pressure of pure water at ${25}^{o}C$ is $20.0$ mm of $Hg$. And the lowering of vapor pressure of a sugar solution is $0.070$ mm of $Hg$. What will be the mole fraction of water?

• A. $0.9965$
• B. $0.0035$
• C. $0.0024$
• D. $0.7785$

Answer 1

The correct option is A $0.9965$

Vapour pressure of the pure solvent, that is water, is $20.0$ mm of $Hg$, that is $p_A^o$ equals to $20.0$ mm of $Hg$.

Lowering of vapor pressure of the sugar solution is $0.070$ mm of $Hg$, that is $(p_A^o-p_A)$ equals to $0.070$

From the relative lowering of vapour pressure we know:

$\frac{p_A^o-p_A}{p_A^o}=X_B$, where $X_B$ is the mole fraction of the solute which is sugar in this case.

Thus $X_B=\frac{0.070}{20.0}$ that is $0.0035$

Thus mole fraction of solute or sugar is $0.0035$.

Mole fraction of solvent or water will be $(1-0.0035)$ that is $0.9965$.