Question

An element $X$ (Atomic mass $=25$) exists as $X_4$ is benzene. $51g$ of saturated solution of $X$ in benzene was added to $50.0g$ of pure benzene. The resulting solution showed a depression of freezing point of $0.55K$. Find the solubility of $X$ per $100g$ of benzene. ($K_f$ for benzene $=5.5Kkgmo{l}^{-1}$)

Answer 1

Answer: 2

Let $xg$ be the mass of element in $51.0g$ of saturated solution.
Mass of benzene in $51.0g$ of saturated solution$=51.0-xg$
Total mass of benzene containing $xg$ of solute$=50+51-x=\left(101-x\right)g$
$\Delta T_f=\frac{1000K_f{W}_B}{M_B{W}_A}=\frac{1000\times 5.5\times x}{4\times 25\times \left(101-x\right)}$
$=0.55$ (given)
$\Rightarrow x=1.0g$
Hence, solubility
$=\frac{W_B\times 100}{W_A}=\frac{1}{\left(51-1\right)}\times 100=2.0g$