Calculate the molar solubility of \(\mathrm{CuI}\left(K_{\mathrm{sp}}=1.27 \times 10^{-12}\right)\).

Understanding the solubility product constant, typically represented as \(K_{sp}\), is crucial when discussing the solubility of ionic compounds in solution. It's a value that reflects the extent to which a compound can dissolve in a solvent and is specific to each particular compound under a set of conditions, usually temperature and pressure.

For any given sparingly soluble ionic compound, the solubility product constant represents the maximum product of the molar concentrations of the ions that result from the compound dissolving in water, each raised to the power of its coefficient in the balanced dissolution equation. In simpler terms, \(K_{sp}\) gives us a threshold at which a solution becomes saturated with those ions, and no more of the solid can dissolve.

In the context of the problem, the solubility product constant for CuI is \(1.27 \times 10^{-12}\). This low value indicates a very low solubility, which is characteristic of many ionic compounds containing transition metals or heavy nonmetals. To calculate the molar solubility (\(s\)), which is the amount of solute that can dissolve in a liter of solution before the solution is saturated, we need to square root the value of \(K_{sp}\) because of the 1:1 ratio of ions formed according to the dissociation reaction.

Ionic compounds are composed of positive and negative ions held together by the strong electrostatic forces known as ionic bonds. These compounds often crystallize in a lattice structure and are typically formed from metals and nonmetals, where metals lose electrons to become positively charged cations, and nonmetals gain electrons to become negatively charged anions.

The properties of ionic compounds, such as their melting points, boiling points, solubility, and electrical conductivity, all stem from the strengths of their ionic bonds. However, when it comes to solubility, not all ionic compounds dissolve well in water. Those that do dissociate into their ions when they dissolve, which significantly affects the conductivity and the chemistry of the solution.

Back to our example, CuI is an ionic compound consisting of copper (Cu) ions and iodide (I) ions. Its solubility is subject to various factors, but the primary determinant in a chemical equilibrium scenario is the solubility product constant, a reflection of its limited solubility in water.

A dissociation reaction refers to the process where a compound breaks down into its constituent ions when dissolved in a solvent, such as water. For ionic compounds, this reaction is essential to understand because it portrays how solids turn into free ions that can move and react within a solution.

Notably, the dissociation of an ionic compound is a reversible process, as represented by the double arrow in the chemical equation used in the problem-solving steps. The equation \(\mathrm{CuI} \rightleftharpoons \mathrm{Cu^+} + \mathrm{I^-}\) illustrates that CuI can dissociate to form Cu+ and I- ions, but under equilibrium conditions, some of the ions will recombine to form the solid compound. This state, where the rates of the forward (dissolution) and reverse (precipitation) reactions are equal, is what defines the solubility product constant (\(K_{sp}\)).

The goal in calculating the molar solubility is to ascertain how much of CuI can dissolve to form a saturated solution without forming a precipitate, under the assumption that dissolution is the only significant process occurring. This information is not just useful for theoretical exercises but is also vital for practical applications in chemistry and industry, where solubility plays a role in processes like drug delivery, mineral extraction, and water treatment.