You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a \(K_{\text {sp }}\) value of zero in water at \(25^{\circ} \mathrm{C}\). What does this mean?

The solubility product constant, \(K_{\text{sp}}\), is an equilibrium constant that describes the degree to which a solid compound dissolves in water. It is specifically used for sparingly soluble salts and represents the product of the concentrations of the ions of the salt in its saturated solution, each raised to the power of their stoichiometric coefficients. For a general equation of a sparingly soluble salt, \(\text{A}_{\text{x}}\text{B}_{\text{y}} \rightleftharpoons \text{x A}^{\text{+}} + \text{y B}^{\text{-}}\), the \(K_{\text{sp}}\) can be represented as the following expression: \[K_{\text{sp}} = [\text{A}^+]^{\text{x}} [\text{B}^-]^{\text{y}}\] A higher value of \(K_{\text{sp}}\) indicates that more of the solid will dissolve in water, while a lower value indicates that less of the solid will dissolve.

Given that the solid has a \(K_{\text{sp}}\) value of zero in water at \(25^{\circ} \mathrm{C}\), this means that the solid does not dissolve in water at all. The concentrations of the ions in the solution would be zero, indicating that the solid is completely insoluble in water.

In conclusion, a \(K_{\text{sp}}\) value of zero for a solid means that the compound does not dissolve in water at all and is considered insoluble at \(25^{\circ} \mathrm{C}\).