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QUESTION

# 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