Question

The vapour pressure of pure liquid a is 70 torr at 27'c. it forms an ideal solution with another liquid

b. the mole fraction of b is 0.2 and total vapour pressure is 84 torr. vapour pressure of pure liquid b is

Answer 1

We will use the simple total vapor pressure equation:

$P = x_{A} P^{o}_{A} + x_{B} P^{o}_{B}$

 $84 = (0.8) (70) + (0.2) P^{o}_{B}$

84 - 56 = 0.2 $P^{o}_{B}$

28 = 0.2 $P^{o}_{B}$

$P^{o}_{B}$ = 140 torr

Answer 2

Answer : The vapor pressure of pure liquid B is, 140 torr.

Solution : Given,

Vapor pressure of pure liquid A = 70 torr

Total vapor pressure = 84 torr

Mole fraction of liquid B = 0.2

First we have to calculate the mole fraction of liquid A.

As we know,

$x_A+x_B=1$

where,

$x_A$ = mole fraction of liquid A

$x_B$ = mole fraction of liquid B

$x_A+0.2=1$

$x_A=0.8$

Mole fraction of liquid A = 0.8

Now we have to calculate the vapor pressure of liquid B.

Formula used :

$P_T=(x_A\times P^o_A)+(x_B\times P^o_B)$

where,

$P_T$ = total vapor pressure

$P^o_A$ = vapor pressure of liquid A

$P^o_B$ = vapor pressure of liquid B

Now put all the given values in this formula, we get

$84=(0.8\times 70)+(0.2\times P^o_B)$

$P^o_B=140torr$

Therefore, the vapor pressure of pure liquid B is, 140 torr.