Answer to Question #244157 in Chemistry for Kan

Question

4. A compound called pyrene has the empirical formula C8H5. When 4.04 g of pyrene is dissolved in 10.00 g of benzene, the boiling point of the solution is 85.1

Answer 1

A compound called pyrene has the empirical formula C₈H₅. When 4.04 g of pyrene is dissolved in 10.00 g of benzene, the boiling point of the solution is 85.1°C. Calculate the molar mass of pyrene and determine its molecular formula. The molal boiling-point constant for benzene is 2.53°C/m. Its normal boiling point is 80.1°C.

Solution:

A solution will boil at a higher temperature than the pure solvent.

This is the colligative property called boiling point elevation.

An equation has been developed for this behaviour. It is:

Δt = i × K_b × m

K_b for benzene is 2.53°C/m

i = 1 (for nonelectrolyte - pyrene)

m - the molality of the solute

Hence,

(85.1°C - 80.1°C) = (1) × (2.53°C/m) × m

m = (85.1°C - 80.1°C) / (2.53°C/m) = 1.9763 m

Molality of pyrene = 1.9763 m

Molality of solute = Moles of solute / Kilograms of solvent

Kilograms of solvent = Kilograms of benzene = (10.00 g) × (1 kg / 1000 g) = 0.01 kg

Hence,

Moles of pyrene = Molality of pyrene × Kilograms of benzene

Moles of pyrene = (1.9763 mol/kg) × (0.01 kg) = 0.019763 mol

Moles of pyrene = Mass of pyrene / Molar mass of pyrene

Mass of pyrene = 4.04 g

Hence,

Molar mass of pyrene = Mass of pyrene / Moles of pyrene

Molar mass of pyrene = (4.04 g) / (0.019763 mol) = 204.42 g/mol

The molar mass of pyrene is 204.42 g/mol

MM(C₈H₅) = 8×Ar(C) + 5×Ar(H) = 8×(12.0107) + 5×(1.00784) = 101.125 (g/mol)

n = Molar mass of pyrene / MM(C₈H₅) = (204.42 g/mol) / (101.125 g/mol) = 2.02 = 2

Hence,

The molecular formula of pyrene is 2×(C₈H₅) = C₁₆H₁₀

Answer:

The molar mass of pyrene is 204.42 g/mol

The molecular formula of pyrene is C₁₆H₁₀