Question

Paradichlorobenzene, C6H4Cl2, is a component of mothballs. A solution of 2.00 g in 22.5 g of cyclohexane boils at 82.39 ∘C. The boiling point of pure cyclohexane is 80.70 ∘C. Calculate Kb for cyclohexane. Express the constant numerically in degrees Celsius per molal.

Answer 1

Answer:

2.79 °C/m

Explanation:

When a nonvolatile solute is dissolved in a pure solvent, the boiling point of the solvent increases. This property is called ebullioscopy. The temperature change (ΔT) can be calculated by:

ΔT = Kb*W*i

Where Kb is the ebullioscopy constant for the solvent, W is the molality and i is the van't Hoff factor.

W = m1/(M1*m2)

Where m1 is the mass of the solute (in g), M1 is the molar mass of the solute, and m2 is the mass of the solvent (in kg).

The van't Hoff factor represents the dissociation of the elements. For an organic molecule, we can approximate i = 1. Thus:

m1 = 2.00 g

M1 = 147 g/mol

m2 = 0.0225 kg

W = 2/(147*0.0225)

W = 0.6047 mol/kg

(82.39 - 80.70) = Kb*0.6047*1

0.6047Kb = 1.69

Kb = 2.79 °C/m