Determination of molar mass

Exercise 6

   

To determine the molar mass of an unknown substance $S$ three melting point measurements are done: 1) Pure benzene: $5.45\;^oC$ 2) $5.65\;g$ of a substance $S^{,}$ with molar mass $246\;\frac{g}{mol}$ dissolved in $110.0\;g$ benzene: $4.39\;^oC $ 3) $3.46\;g$ of substance $S$ dissolved in $85.0\;g$ benzene: $4.13\;^oC $ Calculate the molar mass of $S$.

$n_{S^{,}}$ $=$ $\frac{5.65}{246} \; mol$ $\mu_{S^{,}}$ $=$ $\frac{5.65}{246\cdot 0.110} $ = $ 0.209 \frac{mol_{S^{,}}}{kg_{benzene}}$ $K_f$ $=$ $\frac{5.45-4.39}{0.209}$ = $ 5.07 \; ^oC$ $\mu_{S}$ $=$ $\frac{5.45-4.13}{5.07} $ $n_{S}$ $=$ $\frac{5.45-4.13}{5.07} \cdot 0.085 $ = $0.0221 \; mol $ $M_S$ $=$ $\frac{3.46}{0.0221}$ = $156.6 \; \frac{g}{mol}$