Question

A solution of 1.5 g benzoic acid (C6H5COOH; MW = 122.123 g/mol) in 100.0 g of carbon tetrachloride (CCl4; MW =153.822 g/mol) has a boiling point of 77.50°C. The boiling point of pure carbon tetrachloride is 76.72°C and the melting point is -22.92°C. Calculate the molecular weight of benzoic acid in the solution. Suggest a reason for the difference between the molar mass based on the formula (listed above) and the molar mass determined in part a.

Answer 1

We will use the formula for boiling point elevation here which is given as

where T_b is the elevation in boiling point, Kb is the ebullioscopic constant or boiling point elevation constant, m is the molality, i is the Van't Hoff factor.

T_b = Boiling point of the solution - boiling point of the pure solvent = 77.50 - 76.72 = 0.78^oC

K_b = 5.03 kg^oC/mol

i = 1 as benzoic acid doesn't dissociate in CCl₄.

m = moles of solute/Mass of solvent(in kg) = mass of solute/(molar mass of solute)*(mass of solvent(in kg))

m = 1.5/(Molar mass of benzoic acid)*(0.1) = 15/Molar mass of benzoic acid (Note : 100 g = 100/1000 = 0.1 kg)

Substituting values in the equation, we get

0.78 = (5.03 X 15)/Molar mass of benzoic acid

Molar mass of benzoic acid = 96.73 g

Given above is the molecular mass of benzoic acid whereas the determined mass is the molar mass. Molecular mass is the sum of atomic masses (mass of the molecule relative to 1/12th of the mass of the carbon-12 atom whereas molar mass is the mass of one mole of the molecule that is pertaining to 1 mole of 1.5 gm of benzoic acid. They are related but their magnitudes are apart because of the same reason.