Question

A solution containing $0.5$ g of naphthalene in $50$ g $CC{l}_4$ yield a boiling point elevation of $0.4$ K, while a solution of $0.6$ g of an unknown solute in the same mass of the solvent gives a boiling point elevation of $0.65$ K. Find the molar mass of the unknown solute.

Answer 1

Napthlene $C_{10}{H}_8,M=12\times 10+8=128g$

Molality of Naphthalene in $CC{l}_4,m=\frac{0.5}{128}\times \frac{1000}{50}$

$\Delta T_b=K_{b}m$

$0.4=K_b\frac{0.5}{128}\times \frac{1000}{50}$ ...(i)

Let the molar mass of unknown solute be M.

The molality of unknown solute in $CC{l}_4,m=\frac{0.6}{M}\times \frac{1000}{50}$

$\Delta T_b=K_{b}m$

$0.65=K_b\times \frac{0.6}{M}\times \frac{1000}{50}$ ...(ii)

Divide equation (i) by (ii)

$\frac{0.4}{0.65}=\frac{0.5\times M}{0.6\times 128}$

$M=\frac{0.4\times 0.6\times 128}{0.65\times 0.5}=94.523$