Question

\(\mathrm{CaSO}_{4}\left(K_{\mathrm{sp}}=2.4 \times 10^{-5}\right)\) has a larger \(K_{\mathrm{sp}}\) value than that of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\left(K_{\mathrm{sp}}=1.4 \times 10^{-5}\right)\). Does it fol- low that \(\mathrm{CaSO}_{4}\) also has greater solubility \((\mathrm{g} / \mathrm{L}) ?\)

Short answer

No, it does not follow that \(CaSO_{4}\) has greater solubility (in g/L) than \(Ag_{2}SO_{4}\) just because its \(K_{sp}\) value is higher.

Step-by-step solution

Identify solubility product constants

The \(K_{sp}\) value of \(CaSO_{4}\) is given as \(2.4 \times 10^{-5}\) and of \(Ag_{2}SO_{4}\) as \(1.4 \times 10^{-5}\). This indicates that at equilibrium, the product of the concentration of the ions in solution is greater for \(CaSO_{4}\) than for \(Ag_{2}SO_{4}\).

Identify the equilibrium reactions

The salts dissolve in water dissociating into ions: \(CaSO_{4} \rightarrow Ca^{2+} + SO^{2-}_{4}\), contributing 1+1=2 particles for each formula unit dissolved, whereas \(Ag_{2}SO_{4} \rightarrow 2Ag^{+} + SO^{2-}_{4}\), contributing 2+1=3 particles per formula unit dissolved.

Compare the number of ions

From the dissolution reactions, you can observe that \(Ag_{2}SO_{4}\) breaks up into more ions in solutions than \(CaSO_{4}\). This factor can affect the solubility (in g/L) of the salts because it influences the mass of the salt that can be dissolved in the solution.

Conclusion

Given that \(Ag_{2}SO_{4}\) produces more ions when it dissolves and since the solubility depends on the number of moles of ions per liter of solution, it is not certain that \(CaSO_{4}\) has greater solubility just because it has a bigger \(K_{sp}\). Additional information, such as molar mass and temperature, would be needed to accurate determine which of the two salts is more soluble (in g/L).

Key concepts

Understanding Solubility

Solubility is the ability of a substance to dissolve in a solvent to form a homogeneous solution. When discussing solubility in chemistry, typically it's the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. For ionic compounds like calcium sulfate (CaSO₄) and silver sulfate (Ag₂SO₄), solubility is a crucial concept, as it can determine how these compounds behave in different chemical environments.

• A higher solubility means more of the solute can be dissolved in the solvent.
• This is usually expressed in grams per liter (g/L) for solids in liquids.

In the context of the exercise, even though CaSO₄ has a higher solubility product constant ( K_{sp} ), it doesn't automatically guarantee a greater solubility in terms of g/L, since other factors like the number of ions it dissociates into and its molar mass must also be considered.

Exploring Equilibrium Reactions

Equilibrium reactions are fundamental to understanding how substances dissolve in solutions. When a solid dissolves in a liquid, it dissociates into its constituent ions until equilibrium is reached. At this point, the rate at which the solute dissolves equals the rate at which it precipitates out of solution. This state is defined by the solubility product constant, K_{sp} .

• The K_{sp} value is critical because it reflects the concentrations of the ions at equilibrium.
• A larger K_{sp} indicates a greater extent of dissociation into ions.

For the given compounds, CaSO₄ dissociates into two ions ( Ca^{2+} and SO₄^{2-} ), while Ag₂SO₄ dissociates into three ions ( 2Ag⁺ and SO₄^{2-} ). Therefore, the equilibrium dynamics are different even if one compound has a larger K_{sp} value than the other.

Ionic Dissociation Details

Ionic dissociation is the process by which an ionic compound separates into its individual ions in a solution. This process is key to understanding the behavior of ionic compounds in solution and their implications for solubility.

• For CaSO₄, it dissociates into two ions: Ca^{2+} and SO₄^{2-}. This gives us fewer particles compared to Ag₂SO₄.
• Ag₂SO₄ separates into three ions: 2Ag^{+} and SO₄^{2-}, which increases the total ion concentration when dissolved.
• The number of particles (ions) formed affects the solubility and can lead to differences in the weight of the dissolved substance (g/L) even when the K_{sp} is lower.

Thus, evaluating solubility in terms of ionic dissociation requires understanding both the number and type of ions each compound generates. These factors influence the concentration and mass of dissolved ions in the solution, thereby affecting solubility measurements.