Question

$1.22g$ of an organic acid is separately dissolved in $100g$ of benzene $\left(K_b=2.6Kkgmo{l}^{-1}\right)$ and $100g$ of acetone $\left(K_b=1.7Kkgmo{l}^{-1}\right)$. The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by $0.17^{\circ }C$. The increase in boiling point of solution in benzene in ${}^{\circ }C$ is $x\times 10^{-2}$. The value of $x$ is ______ (Nearest integer) [Atomic mass : $C=12.0,H=1.0,O=16.0$ ]

Answer 1

Answer: 13

With benzene as solvent
$\Delta T_b=i{K}_{b}m$
$\Delta T_b=\frac{1}{2}\times 2.6\times \frac{1.22/M_w}{100/1000}....$(1)
With Acetone as solvent
$\Delta T_b=i{K}_{b}m$
$0.17=1\times 1.7\times \frac{1.22/M_w}{100/1000}.....$(2)
$(1)/(2)$
$\frac{\Delta T_b}{0.17}=\frac{\frac{1}{2}\times 2.6+\frac{1.22/M_w}{100/1000}}{1\times 1.7\times \frac{1.22/M_w}{100/1000}}$
$\Delta T_b=\frac{0.26}{2}$
$\Delta T_b=13\times 10^{-2}$
$\Rightarrow x=13$