Question

An aqueous solution containing 36.2 g of an unknown molecular (non-electrolyte) compound in 152.4 g of water was found to have a freezing point of -1.4 ∘C.

Calculate the molar mass of the unknown compound.

Express your answer using two significant figures.

Answer 1

We know that ΔT _f = iK_f x m
Where

ΔT _f = depression in freezing point

        = freezing point of pure solvent – freezing point of solution

        = 0 -(-1.4) ^oC

        = 1.4 ^oC

K _f = depression in freezing constant of water = 1.86 ^oC/m

I = vanthoff’s factor = 1 ( since it is non-electrolyte)

m = molality of the solution

    = ( mass / Molar mass ) / weight of the solvent in Kg

    = (36.2g / M ) / 0.1524 kg

    = 237.5 / M

Plug the values we get

1.4 = 1x1.86x(237.5/M)

M = 315.6 g/mol

Therefore the molar mass of unknown compound is 315.6 g/mol