You must add 3.1 g of urea.
We use the boiling point elevation expression
#ΔT_b = iK_bm#
where
#ΔT_b# = change in boiling point; #i# is the van’t Hoff factor; #K_b# is the molal boiling point elevation constant for the solvent; and #m# is the molality of the solution.
Step 1. Determine the #i# value.
Since urea is a nonionic compound, #i# = 1.
Step 2. Calculate the molality of the solution.
#ΔT_b =T_b – T_b^o# = (79.6 - 76.5) °C = 3.1 °C
#ΔT_b = iK_bm#
#m = (ΔT_b)/(iK_b) = (3.1" °C")/(1 × 1.22" °C·kg·mol⁻¹")# = 2.5 mol·kg⁻¹
Step 3: Calculate the moles of the urea.
#m = "moles of urea"/"kilograms of ethanol"#
#n# = moles of urea = #m# × kilograms of ethanol = 2.5 mol·kg⁻¹ × 0.0200 kg = 0.051 mol.
Step 4. Calculate the mass of urea.
The formula of urea is NH₂CONH₂ = CH₄N₂O. Molar mass = 60.06 g/mol
Molar mass = #"mass"/"moles"#
Mass = moles × molar mass = 0.051 mol × #(60.06" g")/(1" mol")# = 3.1 g