For a concentrated solution of a weak electrolyte ( K _ eq =...

Given that concentration of ${A}_{2}{B}_{3}$ is $C$ and degree of dissociation is $\alpha$

The equilibrium reaction of weak electrolyte ${A}_{2}{B}_{3}$ is

$\begin{cases}{A}_{2}{B}_{3} & ⇌ 2{A}^{3 +} & + 3{B}^{2 -} \\ C & - & - \\ ↓ & ↓ & ↓ \\ C ( 1 - \alpha ) & 2C\alpha & 3C\alpha\end{cases}$

Now, The equilibrium constant is the ratio of the concentrations of reactants and products raised to the stoichiometric coefficients.

${K}_{eq} = \dfrac{( 2C \alpha{)}^{2} ( 3C \alpha{)}^{3}}{C ( 1 - \alpha )} = 108{C}^{4}{\alpha}^{5}$

$\dfrac{{K}_{eq}}{108{C}^{4}} = {\alpha}^{5} ⇒ \alpha = \left(\dfrac{{K}_{eq}}{108{C}^{4}}\right)\dfrac{1}{5}$