This example problem demonstrates how to use Raoult's Law to calculate the change in vapor pressure by adding a strong electrolyte to a solvent.**Problem:**

What is the change in vapor pressure when 52.9 g of CuCl_{2} is added to 800 mL of H_{2}O at 52.0 °C.

The vapor pressure of pure H_{2}O at 52.0 °C is 102.1 torr

The density of H_{2}O at 52.0 °C is 0.987 g/mL.**Solution**

Raoult's Law can be used to express the vapor pressure relationships of solutions containing both volitile and nonvolitile solvents. Raoult's Law is expressed by

P_{solution} = Χ_{solvent}P^{0}_{solvent} where

P_{solution} is the vapor pressure of the solution

Χ_{solvent} is mole fraction of the solvent

P^{0}_{solvent} is the vapor pressure of the pure solvent**Step 1** Determine the mole fraction of solution

CuCl_{2} is a strong electrolyte. It will completely dissociate into ions in water by the reaction:

CuCl_{2}(s) → Cu^{2+}(aq) + 2 Cl^{-}

This means we will have 3 moles of solute added for every mole of CuCl_{2} added.

From the periodic table:

Cu = 63.55 g/mol

Cl = 35.45 g/mol

molar weight of CuCl_{2} = 63.55 + 2(35.45) g/mol

molar weight of CuCl_{2} = 63.55 + 70.9 g/mol

molar weight of CuCl_{2} = 134.45 g/mol

moles of CuCl_{2} = 52.9 g x 1 mol/134.45 g

moles of CuCl_{2} = 0.39 mol

Total moles of solute = 3 x (0.39 mol)

Total moles of solute = 1.18 mol

molar weight_{water} = 2(1)+16 g/mol

molar weight_{water} = 18 g/mol

density_{water} = mass_{water}/volume_{water}

mass_{water} = density_{water} x volume_{water}

mass_{water} = 0.987 g/mL x 800 mL

mass_{water} = 789.6 g

moles_{water} = 789.6 g x 1 mol/18 g

moles_{water} = 43.87 mol

Χ_{solution} = n_{water}/(n_{water} + n_{solute})

Χ_{solution} = 43.87/(43.87 + 1.18)

Χ_{solution} = 43.87/45.08

Χ_{solution} = 0.97**Step 2** - Find the vapor pressure of the solution

P_{solution} = Χ_{solvent}P^{0}_{solvent}

P_{solution} = 0.97 x 102.1 torr

P_{solution} = 99.0 torr**Step 3** - Find the change in vapor pressure

Change in pressure is P_{final} - P_{O}

Change = 99.0 torr - 102.1 torr

change = -3.1 torr**Answer:**

The vapor pressure of the water is reduced by 3.1 torr with the addition of the CuCl_{2}.