91Ó°ÊÓ

When a salt is dissolved in water, it dissociates into its constituent ions. This process is a simple separation of ions in the solid state into their individual components. For the salts given in the exercise, the dissociation can be represented by reversible chemical equations.

For example, silver chromate (\(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0), upon dissolution, breaks into silver ions and chromate ions:

• \(\mathrm{Ag}_2 \mathrm{CrO}_4 (s) \rightleftharpoons\) 2 \(\mathrm{Ag}^{+} (aq)\) + \(\mathrm{CrO}_4^{2-} (aq)\)

Similarly, silver oxalate (\(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0) dissociates into silver ions and oxalate ions:

• \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4 (s) \rightleftharpoons\) 2 \(\mathrm{Ag}^{+} (aq)\) + \(\mathrm{C}_2 \mathrm{O}_4^{2-} (aq)\)

The dissociation equations describe how the salts interact with water to release ions, a critical step in understanding their solubility.

The solubility product constant (\(K_{sp}\)\u00a0) is a key concept in determining how much of a salt can dissolve in a solution. This constant expresses the equilibrium concentration of the ions in a saturated solution.

For each salt in the exercise, the \(K_{sp}\)\u00a0expression relates the concentrations of the ions produced upon dissociation:

• For \(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0: \(K_{sp} = [\mathrm{Ag}^{+}]^2 [\mathrm{CrO}_4^{2-}]\)
• For \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0: \(K_{sp} = [\mathrm{Ag}^{+}]^2 [\mathrm{C}_2 \mathrm{O}_4^{2-}]\)

These expressions help us calculate the maximum concentration of ions at which the salts remain in equilibrium. The \(K_{sp}\)\u00a0is unique to each salt and indicates its capacity to dissociate in water.

The concentration of silver ions (\([\mathrm{Ag}^{+}]\)\u00a0) in solution is a pivotal element in handling the solubility and dissociation of silver-based salts. When both \(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0 and \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0 are present in the same solution and saturation has been reached, tasks involve determining which salt provides the higher \([\mathrm{Ag}^{+}]\)\u00a0.

To solve this, we use the \(K_{sp}\)\u00a0values to find solubilities (\(s\)\u00a0 for \(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0 and \(t\)\u00a0 for \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0), then compute \(2s\)\u00a0 and \(2t\)\u00a0 for \([\mathrm{Ag}^+]\)\u00a0.

• Calculate \(s = \sqrt[3]{\frac{K_{sp}}{4}}\)\u00a0 for \(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0
• Calculate \(t = \sqrt[3]{\frac{K_{sp}}{4}}\)\u00a0 for \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0

The lower \(K_{sp}\)\u00a0 tends to limit the dissolved \([\mathrm{Ag}^{+}]\)\u00a0, impacting how much of the salt can dissolve significantly in the solution without forming a precipitate.

Saturation refers to the point at which no more solute can dissolve in the solution at a given temperature. When this occurs, we have reached the maximum concentration of ions that a solution can hold without precipitating.

In our case, both \(\mathrm{Ag}_2 \mathrm{CrO}_4\)\u00a0 and \(\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4\)\u00a0 can only dissolve until they reach their respective saturation points. Once saturated, the salts are in dynamic equilibrium — ions are dissolving from and precipitating into their solid forms at the same rate.

• Saturation depends on the \(K_{sp}\)\u00a0 of each salt, influencing how much solute dissolves.
• Higher \(K_{sp}\)\u00a0 values indicate greater solubility and thus higher saturation limits.

Understanding saturation helps us predict behaviors in solutions where multiple salts are present, ensuring accurate calculation of ion concentrations.