Molality Example Problem

Question: A 4 g sugar cube (Sucrose: C₁₂H₂₂O₁₁) is dissolved in a 350 ml teacup of 80 °C water. What is the molality of the sugar solution?
Given: Density of water at 80° = 0.975 g/ml

Definition

Molality is the number of moles of solute per kilogram of solvent.

Step 1 - Determine number of moles of sucrose in 4 g Solute is 4 g of C₁₂H₂₂O₁₁

C₁₂H₂₂O₁₁ = (12)(12) + (1)(22) + (16)(11)
C₁₂H₂₂O₁₁ = 144 + 22+ 176
C₁₂H₂₂O₁₁ = 342 g/mol
divide this amount into the size of the sample
4 g /(342 g/mol) = 0.0117 mol

Step 2 - Determine mass of solvent in kg.

density = mass/volume
mass = density x volume
mass = 0.975 g/ml x 350 ml
mass = 341.25 g
mass = 0.341 kg

Step 3 - Determine molality of the sugar solution.

molality = mol_solute / m_solvent
molality = 0.0117 mol / 0.341 kg
molality = 0.034 mol/kg

Answer:

The molality of the sugar solution is 0.034 mol/kg.