Boiling Point Elevation Example Problem

This example problem demonstrates how to calculate boiling point elevation caused by adding salt to water. When salt is added to water, the sodium chloride separates into sodium ions and chloride ions. The premise of boiling point elevation is that the added particles raise the temperature needed to bring water to its boiling point. The extra particles interfere with the interactions between solvent molecules (water, in this case).

Boiling Point Elevation Problem

31.65 g of sodium chloride is added to 220.0 mL of water at 34 °C. How will this affect the boiling point of the water?

Assume the sodium chloride completely dissociates in the water.

Given:
density of water at 35 °C = 0.994 g/mL
K_b water = 0.51 °C kg/mol

Solution

To find the temperature change elevation of a solvent by a solute, use the equation:
ΔT = iK_bm
where:
ΔT = Change in temperature in °C
i = van't Hoff factor
K_b = molal boiling point elevation constant in °C kg/mol
m = molality of the solute in mol solute/kg solvent

Step 1. Calculate the Molality of the NaCl

molality (m) of NaCl = moles of NaCl/kg water

From the periodic table:

atomic mass Na = 22.99
atomic mass Cl = 35.45
moles of NaCl = 31.65 g x 1 mol/(22.99 + 35.45)
moles of NaCl = 31.65 g x 1 mol/58.44 g
moles of NaCl = 0.542 mol
kg water = density x volume
kg water = 0.994 g/mL x 220 mL x 1 kg/1000 g
kg water = 0.219 kg
m_NaCl = moles of NaCl/kg water
m_NaCl = 0.542 mol/0.219 kg
m_NaCl = 2.477 mol/kg

Step 2. Determine the Van 't Hoff Factor

The van't Hoff factor, "i," is a constant associated with the amount of dissociation of the solute in the solvent. For substances which do not dissociate in water, such as sugar, i = 1. For solutes that completely dissociate into two ions, i = 2. For this example, NaCl completely dissociates into the two ions, Na⁺ and Cl^-. Therefore, here, i = 2.

Step 3. Find ΔT

ΔT = iK_bm
ΔT = 2 x 0.51 °C kg/mol x 2.477 mol/kg
ΔT = 2.53 °C

Answer

Adding 31.65 g of NaCl to 220.0 mL of water will raise the boiling point by 2.53 °C.

Boiling point elevation is a colligative property of matter. That is, it depends on the number of particles in a solution and not their chemical identity. Another important colligative property is freezing point depression.