Question

What is the vapor pressure of isopropanol (MW = 60.1) in a closed container of 70% isopropanol in water (MW = 18.0) at 25oC? Such a mixture contains 70 g of isopropanol and 30 g of water. The vapor pressure of pure isopropanol at 25oC = 50 torr

Answer 1

Answer:

The vapor pressure of the 70% isopropanol solution is 21 Torr.

Explanation:

Relative lowering of vapor pressure for solution with non volatile solute is given by :

$\frac{p^o-p}{p^o}=\chi_{solute}$

Where:

$p^o$ = Vapor pressure of pure solvent

p = Vapor pressure of solution

$\chi_{solute}$ =  Mole fraction of solute

We have, 70% isopropanol solution which menas 70 grams of isopropanol (solvent) and 30 grams of water (solute).

Mass of water = 30 g

Moles of water = $n_w=\frac{30 g}{18.0 g/mol}=1.667 mol$

Mass of isopropanol = 70 g

Moles of isopropanol =$n_i=\frac{70 g}{60.1 g/mol}=1.165 mol$

Mole fraction of solute that is water :

$\chi_w=\frac{1.667 mol}{1.667 mol+1.165 mol}=0.5886$

Vapor pressure of the pure isopropanol =$p^o=50 Torr$

Vapor pressure of the solution = p

$\frac{50 Torr-p}{50 Torr}=0.5886$

Solving for p:

p = 20.57 Torr ≈ 21 Torr

The vapor pressure of the 70% isopropanol solution is 21 Torr.