What is the concentration of \(\mathrm{F}^{-}\) ions in a saturated solution that is 0.10 \(\mathrm{M}\) in \(\mathrm{Ca}^{2+}\) ? The \(K_{s p}\) of \(\mathrm{CaF}_{2}\) is \(1.6 \times 10^{-10} .\)

In chemistry, a dissociation reaction occurs when a compound separates into its component ions upon dissolving in a solvent like water. This process forms the basis for understanding the behavior of ionic compounds in solution.

Using the example from the exercise, \(\mathrm{CaF}_{2}\) is an ionic compound that, when in water, dissociates into \(\mathrm{Ca^{2+}}\) ions and \(\mathrm{F}^{-}\) ions. The chemical equation for this dissociation reaction is represented as: \[\mathrm{CaF}_{2} \leftrightarrow \mathrm{Ca^{2+}} + 2 \mathrm{F}^{-}\] The double arrow (\leftrightarrow) indicates that the reaction can proceed forward and backward, meaning it can reach a dynamic equilibrium. At this point, the rate of dissolution equals the rate of crystallization, leading to a saturated solution.

The ion concentration in a solution refers to the molarity of the ions that are present, which is a measure of the number of moles of ions per liter of solution. It is a key factor in determining the extent of a dissociation reaction in a saturated solution and is directly related to the solubility product constant \(K_{sp}\).

For the given exercise, the \(K_{sp}\) of \(\mathrm{CaF}_{2}\) provides the relationship between the concentrations of \(\mathrm{Ca^{2+}}\) and \(\mathrm{F}^{-}\) in a saturated solution. If the concentration of one ion type is known, the \(K_{sp}\) can be used to calculate the concentration of the other. For instance, when \(\mathrm{Ca^{2+}}\) is at 0.10 M, the concentration of \(\mathrm{F}^{-}\) ions can be calculated, using the \(K_{sp}\), to find the point at which the solution is saturated.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction, allowing us to predict the amounts of substances consumed and produced. It is based on the conservation of mass and the concept of the mole.

In the context of our problem, stoichiometry indicates that for every one mole of \(\mathrm{CaF}_{2}\) that dissociates, one mole of \(\mathrm{Ca^{2+}}\) ions and two moles of \(\mathrm{F}^{-}\) ions are produced. This stoichiometric ratio is crucial when calculating ion concentrations from the solubility product constant (\(K_{sp}\)). It's reflected in the \(K_{sp}\) expression as the concentration of fluoride ions is squared, consistent with its 2:1 stoichiometric ratio to calcium ions.