Question

A solution of sucrose (molar mass = 342 g mol⁻¹) has been prepared by dissolving 68.5 g of sucrose in 1000 g of water. The freezing point of the solution obtained will be ______. (k_f for water = 1.86 K kg mol⁻¹)

Options

• −0.372°C

• −0.520°C

• +0.372°C

• −0.570°C

Answer 1

A solution of sucrose (molar mass = 342 g mol⁻¹) has been prepared by dissolving 68.5 g of sucrose in 1000 g of water. The freezing point of the solution obtained will be −0.372°C.

Explanation:

Given: Mass of sucrose = 68.5 g

Molar mass of sucrose = 342 g/mol

Mass of water = 1000 g = 1.0 kg

K_f for water = 1.86 K kg mol⁻¹

Moles of sucrose = `68.5/342 = 0.2` mol

Since solvent = 1 kg,

Molality = 0.2 mol/kg

ΔT_f = K_f m

= 1.86 × 0.2

= 0.372°C

T_f​ = 0°C − 0.372°C

T_f​ = −0.372°C