Boiling Point Elevation Example Problem

Calculate Boiling Point Elevation Temperature

The boiling point temperature can be elevated by the addition of a solute to the water.
The boiling point temperature can be elevated by the addition of a solute to the water. David Murray and Jules Selmes / Getty Images

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.

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
Kb water = 0.51 °C kg/mol

Solution:

To find the temperature change elevation of a solvent by a solute, use the equation:

ΔT = iKbm

where
ΔT = Change in temperature in °C
i = van 't Hoff factor
Kb = 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

mNaCl = moles of NaCl/kg water
mNaCl = 0.542 mol/0.219 kg
mNaCl = 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, i = 2 for this example.

Step 3 Find ΔT

ΔT = iKbm

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 2.53 °C.

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Helmenstine, Todd. "Boiling Point Elevation Example Problem." ThoughtCo, Nov. 18, 2016, thoughtco.com/boiling-point-elevation-problem-609464. Helmenstine, Todd. (2016, November 18). Boiling Point Elevation Example Problem. Retrieved from https://www.thoughtco.com/boiling-point-elevation-problem-609464 Helmenstine, Todd. "Boiling Point Elevation Example Problem." ThoughtCo. https://www.thoughtco.com/boiling-point-elevation-problem-609464 (accessed October 22, 2017).