Question

If $P_o$ and $P_s$ are the vapour pressures of the solvent and solution respectively, $n_1$ and $n_2$ are the mole fractions of the solvent and solute respectively, then:

• A. $P_s=P_o{n}_1$
• B. $P_s=P_o{n}_2$
• C. $P_o=P_s{n}_2$
• D. $P_s=P_o\left(n_1/n_2\right)$

Answer 1

Answer: (A)

$P_s=P_o{n}_1$

If $P_o$ and $P_s$ are the vapour pressures of the solvent and solution respectively, $n_1$ and $n_2$ are the mole fractions of the solvent and solute respectively, then $P_s=P_o{n}_1$.

According to Raoult's law, the vapour pressure of a solvent above a solution is equal to the vapour pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present.

$\frac{P_o-P_s}{P_o}=\frac{n}{n+N}$
$\frac{P_o-P_s}{P_o}=n_2$ (as given)
$1-\frac{P_s}{P}=n_2$
$\frac{P_s}{P_o}=1-n_2=n_1$
$P_s=P_o\times n_1$

Hence, the correct option is $A$