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.

The Kb for cyclohexane is 2.79 °C/m

Explanation:

Step 1: Data given

Mass of Paradichlorobenzene = 2.00 grams

Mass of cyclohexane = 22.5 grams

Boiling point of the solution = 82.39 °C

Boiling point of pure cyclohexane = 80.70 °C

Molar mass of Paradichlorobenzene = 147 g/mol

Step 2: Calculate moles Paradichlorobenzene

Moles Paradichlorobenzene = mass / molar mass

Moles Paradichlorobenzene = 2.00 grams / 147 g/mol

Moles Paradichlorobenzene = 0.0136 moles

Step 3: Calculate molality

Molality = moles Paradichlorobenzene / mass cyclohexane

Molality = 0.0136 moles / 0.0225 kg

Molality = 0.605 molal

Step 4: Calculate Kb

Kb = change in boiling point / molality of solution  

 ⇒ Change in boiling point = 82.39 - 80.70 = 1.69 °C

⇒ molality = 0.605 molal

Kb = 1.69 °C / 0.605 molal = 2.79 °C/m

The Kb for cyclohexane is 2.79 °C/m