Question

A solution of sodium chloride in water has a vapor pressure of 19.6 torr at 25 ⁰C. What is the mole fraction of NaCl in this solution? What would be the vapor pressure of this solution at 45 ⁰C? The vapor pressure of pure water is 23.8 torr at 25 ⁰C and 71.9 torr at 45 ⁰C.

Short answer

Mole fraction of NaCl= 0.173

Vapor pressure of the solution at 45 ⁰C=59.461 torr

Step-by-step solution

Step 1:

The vapor pressures of solutions containing non-volatile solutesare given by

Raoult’s law states

$p_{sol}=x_{solvent}\times p_{solvent}^0$

Where

$\begin{array}{l}{p}_{sol}=\text{vaporpressureofthesolution}\\ x_{solvent}=\text{molefractionofthesolvent}\\ p_{solvent}^0=\text{vaporpressureofpuresolvent}\end{array}$

Given that

Vapor pressure of pure water at 25 ⁰C= 23.8 torr

Vapor pressure of solution = 19.6 torr

So, the mole fraction of the solvent is calculated by putting the values in the above

Equation

mole fraction of solvent(water) = $\frac{19.6}{23.7}$=0.827

We know that the solution contains only water and NaCl

So, the mole fraction of water + mole fraction of NaCl should be equal to 1

mole fraction of NaCl = 1-0.827 = 0.173

Also, it is given that

Vapor pressure of pure water at 45 ⁰C=71.9 torr

So, the vapor pressure of this solution at 45 ⁰C would be =0.82771.9 torr

=59.46 torr