Chemistry - Ionic Equilibrium Question with Solution | TestHub

Here's a refined solution:

We know $\Delta T_b=i{K}_{b}m$. First, find the molality $m$ of HA. Given $p{K}_a=2$, $K_a=10^{-2}$. Using the approximation for weak acids, $[H^{+}]=\sqrt{K_a\cdot m}$. The van't Hoff factor $i=1+\alpha$, where $\alpha$ is the degree of dissociation. Since $K_a=\frac{{\alpha }^{2}m}{1-\alpha }\approx {\alpha }^{2}m$, then $\alpha =\sqrt{\frac{K_a}{m}}$.

Approximating $i\approx 1.5$, $0.0156=1.5\times 0.52\times m$, so $m=0.02$. Then $i=\frac{m_{theor}}{m_{app}}$, so $m_{app}=\frac{30}{1.5}=20gm/mol$.

Final Answer: The final answer is $\boxed{20}$