Question

At ${25^o}C$, the vapour pressure of methyl alcohol is 96.0 torr. What is the mole fraction of $C{H_3}OH$ in a solution in which the (partial) vapour pressure of $C{H_3}OH$is 23.0 torr at ${25^o}C$?
A) 0.24
B) 0.25
C) 0.26
D) 0.27

Answer 1

Hint: To answer this question, refer to Raoult's law. The equation given by Raoult’s law is $p = x \times {p^0}$. Here, $p$ is the partial vapour pressure of the volatile component, $x$ is the mole fraction of the respective component and ${p^0}$ is the vapour pressure of the component in its pure state.

Complete step by step solution:
Raoult’s law gives the relationship between the partial vapour pressure of the volatile component and its mole fraction in the solution. According to Raoult's law, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction in the solution. Thus, we can write:
$p \propto x$
And, $p = x \times {p^0}$
Where, $p$ is the vapour pressure of the volatile component, $x$ is the mole fraction of the respective component, ${p^0}$ is the proportionality constant and is equal to vapour pressure of the component in its pure state.
In the question, we are asked to find the mole fraction of the methyl alcohol ($C{H_3}OH$) in a solution and given that partial vapour pressure of $C{H_3}OH$in the solution is 23.0 torr. The vapour pressure of methyl alcohol is 96.0 torr is also given which is the pure vapour pressure.
According to Raoult’s law, the partial vapour pressure of the $C{H_3}OH$ (let, ${p_A}$) is:
${p_A} = {x_A} \times p_A^0$
${p_A}$= 23.0 torr (given)
 ${x_A}$ = Mole fraction of the $C{H_3}OH$ in the solution
$p_A^0$ = Pure vapour pressure of $C{H_3}OH$= 96.0 torr (given)
Therefore, substituting the given values in the above expression
$23.0 = x \times 96.0$
$x = \dfrac{{23.0}}{{96.0}} = 0.24$
Hence, the mole fraction of $C{H_3}OH$ in the solution is 0.24.

Thus, option (A) is correct.

Note: Mole fraction of a component is usually expressed by the symbol $x$ and it is defined as:
${\text{Mole fraction of a component = }}\dfrac{{{\text{Number of moles of the component}}}}{{{\text{Total number of moles of all the components in the solution}}}}$
Knowledge of mole fraction is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution.