Calcium sulfate is found in plaster. At \(25^{\circ} \mathrm{C}\) the value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaSO}_{4}\) is \(4.9 \times 10^{-5}\). What is the calculated molar solubility of \(\mathrm{CaSO}_{4}\) in water?

Understanding the solubility product constant, often denoted as the Ksp, is central to grasping the solubility behaviors of ionic compounds in solutions. The Ksp is a type of equilibrium constant exclusive to the dissolution of sparingly soluble salts. When a slightly soluble ionic compound is in equilibrium with its ions in a saturated solution, the product of the molar concentrations of its ions, each raised to the power of its stoichiometric coefficient, gives us the Ksp value.

For instance, for a general salt represented by AB that dissociates into A+ and B-, the Ksp expression would be written as \[K_{sp} = [A^+][B^-]\].In the context of \[\mathrm{CaSO}_{4}\], the Ksp expression is specifically \[K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{SO}_{4}^{2-}]\].The Ksp is intrinsic to a compound and is affected by temperature but not by the concentrations of the ions. It's essential for calculating the molar solubility, which tells us how much of the compound can dissolve in a certain amount of solvent. A smaller Ksp value suggests a lower solubility, indicating that a substance is less soluble in water.

The dissociation of calcium sulfate in water is an example of a dissolution process where the solid phase \[\mathrm{CaSO}_{4}\] separates into its constituent ions. When \[\mathrm{CaSO}_{4}\] is added to water, it dissociates to form \[\mathrm{Ca}^{2+}\] and \[\mathrm{SO}_{4}^{2-}\] ions in the solution.

The balanced chemical equation demonstrating this dissociation is written as:\[\mathrm{CaSO}_{4}(s) \rightleftharpoons \mathrm{Ca}^{2+}(aq) + \mathrm{SO}_{4}^{2-}(aq)\].This reversible reaction reaches equilibrium when the rate of dissolution equals the rate of precipitation. At equilibrium, the concentrations of \[\mathrm{Ca}^{2+}\] and \[\mathrm{SO}_{4}^{2-}\] are stable, which allows us to use the Ksp to calculate their concentrations in solution.

When solving for the concentration of ions in a solution, stemming from a dissolved sparingly soluble compound like calcium sulfate, it's integral to know the stoichiometry of the dissociation reaction. For every mole of \[\mathrm{CaSO}_{4}\] that dissolves, one mole of \[\mathrm{Ca}^{2+}\] ions and one mole of \[\mathrm{SO}_{4}^{2-}\] ions are formed. This 1:1:1 ratio is crucial in establishing the relationship between the molar solubility of the compound and the concentration of each ion.

Let's denote the molar solubility of \[\mathrm{CaSO}_{4}\] as 's'. Solving equilibrium problems involves setting up an equation using the Ksp value where \[s\] represents the concentration of \[\mathrm{Ca}^{2+}\] and \[\mathrm{SO}_{4}^{2-}\] ions at equilibrium. At this point, the expression \[K_{sp} = s^2\] holds true because each dissociated ion contributes to the product of concentrations used in Ksp. After calculating 's', you can directly state the concentration of each ion in the solution as equal to 's', as they are present in a 1:1 ratio.