Sparingly soluble calcium phosphate dissolves in water to yield an equilibrium calcium ion concentration of \(7.8 \times 10^{-6} \mathrm{M}\). (a) Write the balanced equilibrium equation for calcium phosphate dissolving in water. (b) Write the \(K_{\text {sp }}\) expression for calcium phosphate. (c) What is the equilibrium concentration of phosphate ion? (d) Calculate the value of \(K_{s p}\) for calcium phosphate (show your calculation).

The concept of equilibrium concentration is pivotal to understanding dissolution processes in chemistry. In the context of sparingly soluble minerals like calcium phosphate, equilibrium concentration denotes the amount of ion in solution when the dissolution and precipitation processes occur at equal rates, resulting in a static situation; no net change in concentration of any species in the solution is observed.

When calcium phosphate dissolves, it reaches a point where the rate of its dissolution equals the rate of its reformation into a solid. The concentrations of calcium and phosphate ions present at this point are the equilibrium concentrations. The given problem specifies an equilibrium concentration of calcium ions, and from this information, it's possible to determine other equilibrium concentrations using the stoichiometry of the dissolution reaction.

The balanced equilibrium equation represents the reversible reaction of a compound in a dynamic equilibrium state, with the reactants turning into products and vice versa. It is essential for understanding the proportions at which different ions exist in solution. For soluble salts such as calcium phosphate, the balanced chemical equation provides insight into the number of ions produced upon dissolution.

In practice, calcium phosphate, which has the formula Ca3(PO4)2, separates into its ions when it comes into contact with water. The balanced chemical equation for this dissociation process illustrates that one molecule of calcium phosphate produces three calcium ions and two phosphate ions upon dissolution. This stoichiometry is crucial for calculating the solubility product constant (Ksp) and equilibrium concentrations of the ions.

Understanding calcium phosphate dissolution is crucial when dealing with compounds that have low solubility. Calcium phosphate is classed as sparingly soluble, meaning it does not dissociate completely in water, and only a small portion of it dissolves to reach an equilibrium state. The equilibrium state is the balance between the forward reaction, where the solid dissolves in water, and the backward reaction, where the ions recombine to form the solid.

The dissolution of calcium phosphate in water leads to the creation of calcium ions and phosphate ions. This dissolution process is governed by the solubility product constant (Ksp), which quantifies the degree of solubility of the compound in water. In practical applications, understanding the dissolution behavior of calcium phosphate can be significant for industries such as pharmaceuticals and food production.

Stoichiometric coefficients play an essential role in the balanced equilibrium equation of a chemical reaction. They indicate the ratios in which compounds participate in a chemical reaction. For dissolution reactions, these coefficients tell us how many moles of each ion are produced from the dissolved substance, thus guiding the calculation of the solubility product constant.

In the balanced equation for calcium phosphate dissolution, the stoichiometric coefficients specify that for every mole of calcium phosphate that dissolves, three moles of calcium ions and two moles of phosphate ions are produced. These coefficients are not merely numbers; they reflect the relative amounts of each ion necessary to form calcium phosphate, and they are crucial for making accurate calculations about solution concentrations and Ksp values in chemical equilibrium.