What mass of urea, a nonionic compound, must be added to 20.0 g of ethanol to make the boiling point of ethanol 79.6 ºc? kb = 1.22 ºc/m the normal boiling point of ethanol is 76.5 ºc.

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 ; and ##m## is the 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