Question

Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by 0.2°C. The percentage association of solute A in water is ______.
(Given: Molar mass of A = 93 g mol⁻¹, molal depression constant of water is 1.86 K kg rnol⁻¹)

Options

• 50%

• 60%

• 70%

• 80%

Answer 1

Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by 0.2°C. The percentage association of solute A in water is 80%.

Explanation:

Given: Mass of solute A = 0.7 g

Molar mass of A = 93 g/mol

Mass of water = 42.0 g = 0.042 kg

Depression in freezing point ΔT_f = 0.2°C

K_f = 1.86 K kg/mol

Solute A associates:

Moles of solute A (n) = `0.7/93` = 0.00753 mol

Molality (m) = `0.00753/0.042` = 0.1793 mol/kg

ΔT_f = i K_f m

0.2 = i × 1.86 × 0.1793

`i = 0.2/(1.86 xx 0.1793)`

i = 0.602

For the association of n particles to 1, the van’t Hoff factor:

`i = 1 - alpha (1 - 1/n)`

Assume dimerization (n = 2)

0.602 = `1 - alpha(1 - 1/2)`

0.602 = `1 - alpha/2`

`alpha/2` = 1 − 0.602

`alpha/2` = 0.398

α = `0.398/2`

= 0.796

≈ 80%