Question

The slightly soluble solute \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) is most soluble in (a) pure water; (b) \(0.10 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ;\) (c) \(0.25 \mathrm{M} \mathrm{KNO}_{3}\); (d) \(0.40 \mathrm{M} \mathrm{AgNO}_{3}\).

Short answer

(a) \(Ag_{2}CrO_{4}\) is most soluble in pure water, as there are no common ions present to reduce its solubility due to the common ion effect.

Step-by-step solution

Understanding Solubility and Common Ion Effect

Solubility is the amount of solute that can be dissolved in a solvent at a given temperature. The common ion effect refers to the decrease in solubility when a compound is mixed with a solution already containing one of its constituent ions. When \(Ag_{2}CrO_{4}\) dissolves, it dissociates into its ions \(2Ag^+\) and \(CrO_{4}^{2-}\).

Determining Solubility in Pure Water

In pure water, there are no common ions present. Consequently, there would be no restrictions on the solubility of the \(Ag_{2}CrO_{4}\) due to the common ion effect. So it can be dissolved to its maximum capacity.

Determining Solubility in \(0.10M K_{2}CrO_{4}\)

The \(K_{2}CrO_{4}\) solution contains the common ion \(CrO_{4}^{2-}\). Presence of this ion will reduce the solubility of \(Ag_{2}CrO_{4}\) in this solution due to the common ion effect.

Determining Solubility in \(0.25M KNO_{3}\)

The \(KNO_{3}\) solution does not have a common ion with \(Ag_{2}CrO_{4}\). However, it will not increase the solubility of \(Ag_{2}CrO_{4}\) as in the case of pure water. The solubility will be similar to that in pure water.

Determining Solubility in \(0.40M AgNO_{3}\)

In this case, \(AgNO_{3}\) shares a common ion \(Ag^+\) with \(Ag_{2}CrO_{4}\). Therefore, due to the common ion effect, the solubility of \(Ag_{2}CrO_{4}\) will be further reduced in this solution.

Key concepts

Common Ion Effect

The common ion effect is a fundamental concept in chemistry that affects the solubility of compounds. It's all about how the presence of an ion, that's already in solution, can influence the dissolution of a compound that contains the same ion. This happens because introducing more ions of the same type into the solution disturbs the equilibrium of the dissolution process.
When a slightly soluble compound dissolves in a solvent, it reaches an equilibrium state represented as:

• \[Ag_2CrO_4(s) \rightleftharpoons 2Ag^+(aq) + CrO_4^{2-}(aq)\]

Adding either \[Ag^+\] or \[CrO_4^{2-}\] into the solution shifts the equilibrium to the left as per Le Chatelier’s principle. This means that instead of more dissolving, the solution will reach equilibrium with less dissolving of the compound. Essentially, having a common ion pushes the reaction toward creating more of the solid, thereby reducing overall solubility. Understanding this can help predict which solutions will inhibit or have negligible impact on solubility.

Slightly Soluble Compounds

Slightly soluble compounds are those that do not dissolve readily in a solvent. This limited dissolving capacity is often indicated by a small solubility product constant, \(K_{sp}\), which defines the product of the molar concentrations of its ions at equilibrium.
Such compounds, like silver chromate \(Ag_2CrO_4\), have a delicate balance, dissolving to a limited extent to reach a saturated solution. This specific \(K_{sp}\) value is a benchmark for the amount of ions present in solution when equilibrium is achieved.
Many slightly soluble compounds are influenced by the common ion effect, leading to further reduced solubility when a common ion is present. For instance, \(Ag_2CrO_4\) dissociates into \(2Ag^+\) and \(CrO_4^{2-}\), and any added excess of \(Ag^+\) or \(CrO_4^{2-}\) will lead to the reformation of the solid compound. This carefully balanced interaction underscores the sensitivity of slightly soluble compounds to their chemical environment and the ion concentration of the solutions they are in.

Dissolution and Ionization

Dissolution and ionization are key processes in understanding how substances interact in solutions. Dissolution is a physical process where a compound separates into its constituent parts or ions when mixed with a solvent. Ionization, on the other hand, is a type of dissolution for ionic compounds where an ionic solid breaks down into its ions in a solvent.
When \(Ag_2CrO_4\) dissolves, it ionizes to form \(2Ag^+\) and \(CrO_4^{2-}\) ions, reaching equilibrium between the solid and these ions in solution.
The process reaches equilibrium when the rate of dissolution equals the rate of precipitation, meaning no net change in the concentration of ions occurs. This balance is affected by various factors, including temperature, the nature of the solvent, and notably, the presence of common ions. By analyzing these processes, we gain insight into predicting the behavior of slightly soluble compounds in different solutions. Understanding these principles is essential to mastering topics in chemistry that involve solubilities and saturation levels.