# Solve this following

Question:

$1.22 \mathrm{~g}$ of an organic acid is separately dissolved in $100 \mathrm{~g}$ of benzene $\left(\mathrm{K}_{\mathrm{b}}=2.6 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$ and $100 \mathrm{~g}$ of acetone $\left(\mathrm{K}_{\mathrm{b}}=1.7 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$. 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 $0.17^{\circ} \mathrm{C}$.

The increase in boiling point of solution in benzene

in ${ }^{\circ} \mathrm{C}$ is $\mathrm{x} \times 10^{-2}$. The value of $\mathrm{x}$ is

(Nearest integer)

[Atomic mass: $\mathrm{C}=12.0, \mathrm{H}=1.0, \mathrm{O}=16.0]$

Solution:

With benzene as solvent

$\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \mathrm{K}_{\mathrm{b}} \mathrm{m}$

$\Delta \mathrm{T}_{\mathrm{b}}=\frac{1}{2} \times 2.6 \times \frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}$ ...............(1)

With Acetone as solvent

$\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \mathrm{K}_{\mathrm{b}} \mathrm{m}$

$0.17=1 \times 1.7 \times \frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}$   ..................(2)

(1) / ( 2 )

$\frac{\Delta \mathrm{T}_{\mathrm{b}}}{0.17}=\frac{\frac{1}{2} \times 2.6+\frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}}{1 \times 1.7 \times \frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}}$

$\Delta \mathrm{T}_{\mathrm{b}}=\frac{0.26}{2}$

$\Delta \mathrm{T}_{\mathrm{b}}=13 \times 10^{-2}$

$\Rightarrow x=13$