Question

The normal boiling point of methanol is$64.78°C$ . A solution containing a non-volatile solute dissolved in methanol has a vapor pressure of 556.0 torr atrole="math" localid="1663821787160" $64.78°C$ . What is the mole fraction of methanol in this solution?

Short answer

$\chi methanol=0.830$The mole fraction of methanol in the solution is

Step-by-step solution

Step 1:

Raoult’s law defines that the vapor pressure of a solvent, which is in equilibrium with a dilute solution, is directly proportional to the molar fraction of solvent in a given solution.

$P_{so\ln }={\chi }_{solvent}\times {P_{solvent}}^{\text{'}}$

Step 2:

Calculate the mole fraction of methanol from the ratio of the vapor pressure of the solution and the vapor pressure of pure methanol at $64.78°C$.

$\chi methanol=\frac{P_{so\ln }}{{P°}_{methanol}}=\frac{556.0torr}{670.0torr}=\chi methanol=0.830$