Question

Mole fraction of the component $A$ in vapour phase is $x_1$ and the mole fraction of component $A$ in liquid mixture is $x_2$. The total vapour pressure of liquid mixture is.
Here,
$p_A^{\circ }=$ vapour pressure of pure $A$
$p_B^{\circ }=$ vapour pressure of pure $B$

• A. $\frac{p_B^{\circ }\times x_1}{x_2}$
• B. $\frac{p_A^{\circ }\times x_1}{x_2}$
• C. $\frac{p_B^{\circ }\times x_2}{x_1}$
• D. $\frac{p_A^{\circ }\times x_2}{x_1}$

Answer 1

The correct option is D $\frac{p_A^{\circ }\times x_2}{x_1}$

By Raoult's law,
$p_A=p_A^{\circ }\times x_2$
where,
$p_A\Rightarrow \text{Vapour pressure of}A$

From Dalton's law,
$p_A=P_T\times x_1$
where,
$P_T\Rightarrow \text{Total pressure of the liquid mixture}$
Thus,
$p_A=x_2\times p_A^{\circ }=x_1\times P_T$

$\Rightarrow x_1=\frac{x_2\times p_A^{\circ }}{P_T}$

$\Rightarrow P_T=\frac{x_2\times p_A^{\circ }}{x_1}$
Hence, option A is correct.