Question

The vapour pressure of two pure liquids a and b are 100 and 80 torr respectively. Total vapour pressure of solution obtained by mixing 2 moles of a and 3 moles of b would be

Answer 1

Answer : The total vapor pressure of the solution will be, 88 torr

Explanation : Given,

Vapor pressure of pure liquid A = 100 torr

Vapor pressure of pure liquid B = 80 torr

Moles of pure liquid A = 2 moles

Moles of pure liquid B = 3 moles

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

$\text{Mole fraction of liquid A}=\frac{\text{Moles of A}}{\text{Moles of A}+\text{Moles of B}}=\frac{2}{2+3}=0.4$

$\text{Mole fraction of liquid B}=\frac{\text{Moles of B}}{\text{Moles of A}+\text{Moles of B}}=\frac{3}{2+3}=0.6$

Now we have to calculate the total  vapor pressure of solution.

According to the Raoult's law,

$P_T=X_A\times p^o_A+X_B\times p^o_B$

where,

$P_T$ = vapor pressure of solution = ?

$p^o_A$ = vapor pressure of pure liquid A

$p^o_B$ = vapor pressure of pure liquid B

$X_A$ = mole fraction of pure liquid A

$X_B$ = mole fraction of pure liquid B

Now put all the given values in the above formula, we get:

$P_T=0.4\times 100torr+0.6\times 80torr$

$P_T=88torr$

Therefore, the total vapor pressure of the solution will be, 88 torr

Answer 2

Answer: Total vapour pressure of solution obtained by mixing 2 moles of a and 3 moles of b would be 88 torr.

Explanation:-

According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.

$p_1=x_1p_1^0$ and $p_2=x_2P_2^0$

where, x = mole fraction

$p^0$ = pressure in the pure state

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_1+p_2$

$p_{total}=x_ap_a^0+x_bP_b^0$

$x_{a}=\frac{\text {moles of a}}{\text {moles of a+moles of b}}=\frac{2}{2+3}=0.4$,  

$x_{b}=\frac{\text {moles of b}}{\text {moles of a+moles of b}}=\frac{3}{3+2}=0.6$,  

$p_{a}^0=100torr$

$p_{b}^0=80torr$

$p_{total}=0.4\times 100+0.6\times 80=88torr$

The total vapor pressure is 88 torr.