# Question e2397

##### 1 Answer
Aug 10, 2014

The mass of urea is 26.1 g.

This is a freezing point depression problem.

In your problem, we have to work backwards from the freezing point to calculate the mass of solute.

Step 1. Calculate ${T}_{\text{f}}$

ΔT_"f" = T_"f"° - T_"f" = 0.00 °C – (-2.38) °C = 2.38°C

Step 2. Calculate $i$.

Since urea is a nonelectrolyte, $i$ = 1.

Step 3. Calculate the molality

ΔT_"f" = iK_"f"m

m = (ΔT_"f")/(iK_"f") = (2.38"°C")/( 1 × 1.86"°C·kg·mol⁻¹")# = 1.28 mol·kg⁻¹

Step 4. Calculate the moles of urea

$m = \text{moles of urea"/"kilograms of water}$

Moles of urea = $m$ × kilograms of water = 1.28 mol·kg⁻¹ × 0.340 kg = 0.435 mol

Step 5. Calculate the mass of urea

The formula of urea is NH₂CONH₂. The molar mass is 60.06 g·mol⁻¹.

Moles = $\text{mass"/"molar mass}$

Mass = moles × molar mass = 0.435 mol × 60.06 g·mol⁻¹ = 26.1 g

The mass of urea is 26.1 g.