Question

A water solution containing an unknown quantity of a

nonelectrolyte solute is found to have a freezing point of

–0.23°C. What is the molal concentration of the solution?​

Answer 1

The molal concentration of the solution is approximately 0.124 molal

Step-by-step explanation:

The given parameters are;

The reduced freezing point of the water = -0.23°C

For freezing point depression of a solution, we have;

`\Delta T_f` =
`K_f`· b·i

Where;

`\Delta T_f` = The freezing point depression

`K_f` = Cyroscopic constant (The freezing-point depression constant) = 1.86° Cm⁻¹ for water

b = The molality of the solution

i = van't Hoff factor = 1

Therefore;

`\Delta T_f` =
`T^(\circ)_f - T_f`

Where;

`T^(\circ)_f` = The freezing point of pure water = 0°C

`T_f` = The freezing point of the solution = -0.23°C

∴
`\Delta T_f` =
`T^(\circ)_f - T_f` = 0°C - (-0.23°C) = 0.23 °C

From,
`\Delta T_f` =
`K_f`· b·i, we have;

0.23°C = 1.86°C/m × b × 1

∴ b = (0.23°C/1.86°C/m) ≈ 0.124 molal

Therefore, the molal concentration of the solution, b ≈ 0.124 molal.