Question

You have two salts, $\mathrm{AgX}$ and $\mathrm{Ag}\mathrm{Y}$, with very similar $K_{\mathrm{sp}}$ values. You know that $\mathrm{HX}$ is a strong acid and $\mathrm{HY}$ is a weak acid. Which salt is more soluble in an acidic solution? Explain.

Short answer

In conclusion, the salt $\mathrm{AgY}$ is more soluble in acidic solution compared to $\mathrm{AgX}$ salt due to the common ion effect. The excess ${\mathrm{H}}^{+}$ ions in acidic solution react with ${\mathrm{Y}}^{-}$ ions to form the weak acid $\mathrm{HY}$ causing the solubility of $\mathrm{AgY}$ to increase.

Step-by-step solution

Write the solubility product (Ksp) expressions for AgX and AgY

We begin with the given information that $\mathrm{AgX}$ and $\mathrm{AgY}$ have similar $K_{\mathrm{sp}}$ values. To find the solubility of both salts, let's write down their Ksp expressions: For $\mathrm{AgX}$: $K_{sp}=[{\mathrm{Ag}}^{+}][{\mathrm{X}}^{-}]$ For $\mathrm{AgY}$: $K_{sp}=[{\mathrm{Ag}}^{+}][{\mathrm{Y}}^{-}]$ #Step 2: Write the acidic solution ionization equations#

Write the acidic solution ionization equations

Next, we write the equations for ionization of the strong acid $\mathrm{HX}$ and the weak acid $\mathrm{HY}$ in acidic solution, along with their respective dissociation constants: For $\mathrm{HX}$: $\mathrm{HX}\leftrightarrow {\mathrm{H}}^{+}+{\mathrm{X}}^{-}$, since $\mathrm{HX}$ is a strong acid, it dissociates completely. For $\mathrm{HY}$: $\mathrm{HY}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{Y}}^{-}$, since $\mathrm{HY}$ is a weak acid, it will have an acid dissociation constant $K_a:K_a=[{\mathrm{H}}^{+}][{\mathrm{Y}}^{-}]/[\mathrm{HY}]$ #Step 3: Determine the common ion effect on solubility#

Determine the common ion effect on solubility

In the presence of excess ${\mathrm{H}}^{+}$ ions from acidic solutions, $\mathrm{HX}$ will not influence the solubility of $\mathrm{AgX}$ salt, since it dissociates completely and is present in the form of ${\mathrm{H}}^{+}$ and ${\mathrm{X}}^{-}$. So, the solubility product $K_{sp}$ for $\mathrm{AgX}$ does not change. However, for $\mathrm{AgY}$, the excess ${\mathrm{H}}^{+}$ ions from acidic solutions will react with ${\mathrm{Y}}^{-}$ from $\mathrm{HY}$ to form $\mathrm{HY}$ in the solution. This reaction will lead to a decrease in ${\mathrm{Y}}^{-}$ ion concentration in the solution, causing the concentration of ${\mathrm{Ag}}^{+}$ ions to increase so that $K_{sp}$ remains constant (Le Chatelier's principle). Thus, the $\mathrm{AgY}$ salt becomes more soluble in the acidic solution. #Conclusion#

Identify the more soluble salt

In conclusion, the salt $\mathrm{AgY}$ is more soluble in acidic solution compared to $\mathrm{AgX}$ salt due to the common ion effect. The excess ${\mathrm{H}}^{+}$ ions in acidic solution react with ${\mathrm{Y}}^{-}$ ions to form the weak acid $\mathrm{HY}$ causing the solubility of $\mathrm{AgY}$ to increase.

Key concepts

Understanding the Common Ion Effect

The common ion effect is an important concept that can affect solubility and equilibrium in chemical solutions. This phenomenon occurs when two compounds produce the same ion in a solution. The presence of a common ion from one compound will shift the equilibrium of the other compound, affecting its solubility.

For instance, if a salt like AgX, which dissociates into Ag+ and X- ions, is dissolved in a solution that already contains X- ions from a strong acid HX, the additional X- ions will suppress the dissociation of AgX due to the common ion effect. This results in a decrease in the solubility of AgX. Essentially, the equilibrium shifts to the left, aligning with Le Chatelier's principle, which states that the system will adjust to counteract the change.

When it comes to salts in acidic solutions, the common ion effect can make certain salts more soluble. If the corresponding acidic form is a weak acid, like HY, the common ions from the acid will shift back into the acid, leaving more room for the salt to dissolve and increasing its solubility.

Solubility Product (Ksp) and Its Role in Precipitation

Solubility product, denoted as Ksp, is another critical concept in understanding solubility. It represents the maximum product of the ionic concentrations of a salt that can exist in a saturated solution without precipitating. It's a unique value for each compound at a given temperature. When ionic products in a solution exceed the Ksp value, the excess ions combine, forming a precipitate, thereby returning the solution to equilibrium.

The expressions for Ksp typically look like this: for a generic salt AB that dissociates into A+ and B- ions, the Ksp expression would be $K_{\text{sp}}=[{\text{A}}^{+}][{\text{B}}^{-}]$. In the context of our problem, whether or not the Ksp value changes depends on the concentration of ions in the solution. For the salts AgX and AgY, which break down into Ag+ and X- or Y- ions, adding other sources of these ions, like strong or weak acids, can affect the solubility without changing the inherent Ksp value of the salts.

The Acid Dissociation Constant (Ka) and Weak Acids

The acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in a solution. It's specifically crucial while dealing with weak acids, as it indicates the extent to which an acid can donate protons, H+, to the solution. Strong acids have very large Ka values, effectively dissociating completely, while weak acids have much smaller Ka values, partially dissociating in solution.

The formula for the acid dissociation constant is as follows: for an acid HA that dissociates into H+ and A- ions, the Ka is expressed by $K_{\text{a}}=[{\text{H}}^{+}][{\text{A}}^{-}]/[\text{HA}]$. When a weak acid like HY is present in an acidic solution, it doesn't fully dissociate. Instead, an equilibrium is established between HY, H+ and Y- ions. The presence of additional H+ ions from the solution can shift this equilibrium, as predicted by the common ion effect, leading to more undissociated HY and a subsequent increase in the solubility of a corresponding salt like AgY.