Question

A solution containing a large amount of $A$ and water is steam distilled. The condensate hence obtained contains $0.25$ mole fraction of $A$. The external pressure at which distillation is performed is (${P_w} = 740$).
A.$760torr$
B.$791.3torr$
C.$986.67torr$
D.$886.9torr$

Answer 1

Raoult’s law: It states that partial vapour pressure of each component of an ideal mixture of liquids is equal to the product of vapour pressure of the pure substance with the mole fraction of that component in the mixture.

Complete step by step answer:
Let us first define mole fraction.
Mole fraction: It is defined as the ratio of number of moles of the solute or solvent to the total number of moles present in the solution.
If we want to calculate the mole fraction of solute then number of moles of solute is divided by the total number of moles in the solution and if we want to calculate the mole fraction of solvent then number of moles of solvent is divided by the total number of moles in the solution. And the sum of the mole fraction of solute and mole fraction of solvent is always equal to $1$. As by the question we know that mole fraction if solute is given $0.25$ then the mole fraction of the water in the solution will be $0.75$.
Now we know the value of mole fraction of solute and mole fraction of solvent and also we know the vapour pressure of the solute and we have to find the vapour pressure of the solvent.
And the relation between these term are as follows:
$\dfrac{{{P_A}}}{{{P_B}}} = \dfrac{{{x_A}}}{{{x_B}}}$ where ${P_A}$ is vapour pressure of solute $A$, ${P_B}$ is vapour pressure of solvent and ${x_A}$ is the mole fraction of solute and ${x_B}$ is the mole fraction of solvent.
In the question ${P_B} = 740,{x_A} = 0.25,{x_B} = 0.75$
${P_A} = \dfrac{{0.25}}{{0.75}} \times 740 \\\ {P_A} = \dfrac{{740}}{3} \\\$
So the external pressure will be ${P_A} + {P_B}$. So external pressure is
$740 + \dfrac{{740}}{3} = \dfrac{4}{3} \times 740 = 986.67torr$.

So option C is correct.

Note:
Torr is used to measure the pressure. Pressure is defined as force per unit area. So its SI unit is $N/{m^2}$ but its other units which are SI units are as Pascal represented by $Pa$ and $1Pa = 1N/{m^2}$. And one more unit is torr which is $1torr = 133.32Pa$.