A$$_3$$B$$_2$$ is a sparingly soluble salt of molar mass M (g mol$$^{-1}$$) and solubility x g L$$^{-1}$$. The solubility product satisfies K$$_{sp}$$ = $$a\left(\frac{x}{M}\right)^5$$. The value of a is _________. (Integer answer)

When the sparingly soluble salt $$A_3B_2$$ dissolves, it dissociates into its constituent ions based on its stoichiometry:

$$A_3B_2(s) \rightleftharpoons 3A(aq) + 2B(aq)$$

If the molar solubility of the entire salt is $$s$$ (which is equal to $$\frac{x}{M}$$), then at equilibrium, the concentrations of the individual ions will be proportional to their coefficients:

• Concentration of $$A$$ ions: $$[A] = 3s$$
• Concentration of $$B$$ ions: $$[B] = 2s$$

he $$K_{sp}$$ expression is the product of the ion concentrations, each raised to the power of their stoichiometric coefficients from the balanced equation:

$$K_{sp} = [A]^3[B]^2$$ = $$108 \times s^5$$ = $$108 \times \frac{x}{M}$$.