The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively:

Step 1: Identify a Clear Coordinate Point from the Graph

By examining the equilibrium curve, we can identify a distinct, well-defined point where the concentrations of both ions intersect cleanly at integer grid marks:

• $$[\text{X}] = 1\text{ mM} = 1 \times 10^{-3}\text{ M}$$
• $$[\text{Y}] = 2\text{ mM} = 2 \times 10^{-3}\text{ M}$$

Step 2: Determine the Stoichiometry

The ratio of the molar concentrations of the ions in the saturated solution gives the stoichiometric coefficients of the salt formula:

$$\frac{[\text{Y}]}{[\text{X}]} = \frac{2\text{ mM}}{1\text{ mM}} = 2$$

This means that for every 1 mole of $$\text{X}$$ ions that dissolves, 2 moles of $$\text{Y}$$ ions are released into the solution. Therefore, the empirical formula of the salt is $$\text{XY}_2$$.

Step 3: Calculate the Solubility Product ($$K_{sp}$$)

The dissolution equation for the salt $$\text{XY}_2$$ is written as:

$$\text{XY}_2(s) \rightleftharpoons \text{X}^{2+}(aq) + 2\text{Y}^-(aq)$$

The expression for its solubility product constant ($$K_{sp}$$) is:

$$K_{sp} = [\text{X}][\text{Y}]^2$$

Substituting the equilibrium concentration values from Step 1 into the expression:

$$K_{sp} = \left(1 \times 10^{-3}\text{ M}\right) \times \left(2 \times 10^{-3}\text{ M}\right)^2$$

$$K_{sp} = \left(1 \times 10^{-3}\right) \times \left(4 \times 10^{-6}\right)$$

$$K_{sp} = 4 \times 10^{-9}\text{ M}^3$$

Conclusion:

The stoichiometry corresponds to $$\text{XY}_2$$ and the calculated solubility product is $$4 \times 10^{-9}\text{ M}^3$$.

Answer: Option B — $$\text{XY}_2, 4 \times 10^{-9}\text{ M}^3$$