Question

At a given temperature, total vapour pressure in Torr of a mixture of volatile components A and B is given by
$P_{Total}$ = $120+75X_B$
hence, vapour pressure of pure A and B
respectively (in Torr) are

• A. 120, 75
• B. 120, 195
• C. 120, 45
• D. 75, 45

Answer 1

The correct option is B 120, 195

$P_{Total}=P_A{X}_A+P_B{X}_B$
$P_{Total}$ is the total vapor pressure of the mixture
$P_A$ and $X_A$ are the pure vapour pressure and mole fraction of component $A$
$P_B$ and $X_B$ are the pure vapour pressure and mole fraction of component $B$

$X_A+X_B=1$

$X_A=1-X_B$

It is given that
$P_{Total}$ = $120+75X_B$ $\to$1
Hence $P_{Total}=P_A{X}_A+P_B{X}_B$
=$P_A(1-X_B)+P_B{X}_B$

=$P_A+(-P_A+P_B)X_B$ $\to$2

So from 1 and 2
$P_A$= 120 Torr
$-P_A+P_B$=75
$P_B$=75+$P_A$
=195 Torr