For a weak monobasic acid, if pK_a = 4, then at a concentration of 0.01 M of the acid solution, the van’t Hoff factor is

$$\begin{gathered} \mathrm{HA} \rightleftharpoons {\mathrm{H}}^{+}+ {\mathrm{A}}^{-} \\ \mathrm{At} \mathrm{equili}, \mathrm{C}(1-\mathrm{\alpha }) \mathrm{C\alpha } \mathrm{C\alpha } \end{gathered}$$

 $$\begin{gathered} \mathrm{Given}, {\mathrm{pk}}_{\mathrm{a}}=4 \Rightarrow {\mathrm{k}}_{\mathrm{a}}={10}^{-4} ; \mathrm{C}=0.01\mathrm{M} \\ {\mathrm{k}}_{\mathrm{a}}={\mathrm{C\alpha }}^2\Rightarrow \mathrm{\alpha }=\sqrt{\frac{{\mathrm{k}}_{\mathrm{a}}}{\mathrm{C}}}=\sqrt{\frac{{10}^{-4}}{{10}^{-2}}}={10}^{-1}=0.1 \\ \mathrm{van}\text{'}\mathrm{t} \mathrm{hoff} \mathrm{factor}, \mathrm{i}=\frac{1+\mathrm{\alpha }}{1}=1+0.1=1.1 \end{gathered}$$