With benzene as solvent, RCOOH dimerises.
\(2 \mathrm{RCOOH} \rightleftharpoons(\mathrm{RCOOH})_2\)
\(\therefore \mathrm{i}=\frac{1}{2}\)
\(\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \times \mathrm{K}_{\mathrm{b}} \times \mathrm{m}\)
where, \(\Delta \mathrm{T}_{\mathrm{b}}=\) boiling point elevation,
\(\mathrm{K}_{\mathrm{b}}=\) ebulliscopic constant
\(\mathrm{m}=\) molality
i = van't Hoff factor
\(\Delta \mathrm{T}_{\mathrm{b}}=\frac{1}{2} \times 2.6 \times \frac{1.22 / \mathrm{M}_{\mathrm{W}}}{100 / 1000} \ldots\) (i)
With acetone as solvent, no dimerisation.
\(\therefore \mathrm{I}=1 \)
\(\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \times \mathrm{K}_{\mathrm{b}} \times \mathrm{m} \)
\(0.17=1 \times 1.7 \times \frac{1.22 / \mathrm{M}_{\mathrm{W}}}{100 / 1000} . ..(\text{ii})\)
Eq. (i) divide by Eq. (ii),
\(\frac{\Delta \mathrm{T}_{\mathrm{b}}}{0.17}=\frac{\frac{1}{2} \times 2.6 \times \frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}}{1 \times 1.7 \times \frac{1.22 / \mathrm{M}_{\mathrm{w}}}{100 / 1000}} \)
\( \Rightarrow \Delta \mathrm{T}_{\mathrm{b}}=\frac{0.26}{2}=13 \times 10^{-2} \)
\(\mathrm{x}=13\)