Question #e2397

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Answer 1 · 2014-08-10T17:42:19

The mass of urea is 26.1 g.

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

Step 1. Calculate #T_"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 = "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 = #"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.