Problem 37 - Analytical Chemistry

Question

Write the thermodynamic solubility product expressions for the following: (a) \(\mathrm{BaSO}_{4} \rightleftharpoons \mathrm{Ba}^{2+}+\mathrm{SO}_{4}^{2-}\) (b) \(\mathrm{Ag}_{2} \mathrm{CrO}_{4} \rightleftharpoons 2 \mathrm{Ag}^{+}+\mathrm{CrO}_{4}^{2-}\)

Step-by-Step Solution

Answer

(a) \( K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{SO}_{4}^{2-}] \); (b) \( K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CrO}_{4}^{2-}] \).

Step 1: Understanding Solubility Equilibria

The dissolution of a sparingly soluble salt in water reaches an equilibrium between the undissolved solid and its constituent ions in solution. The solubility product constant, denoted as \( K_{sp} \), represents this equilibrium condition for a given salt.

Step 2: Writing the Product Expression for BaSO4

For \( \mathrm{BaSO}_{4} \rightleftharpoons \mathrm{Ba}^{2+} + \mathrm{SO}_{4}^{2-} \), the solubility product expression is derived from the concentration of the ions at equilibrium: \[ K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{SO}_{4}^{2-}] \]. This indicates that the product of the molar concentrations of the barium and sulfate ions at saturation is constant.

Step 3: Writing the Product Expression for Ag2CrO4

For \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \rightleftharpoons 2 \mathrm{Ag}^{+} + \mathrm{CrO}_{4}^{2-} \), note that the dissolution produces two silver ions for each chromate ion. The solubility product expression is \[ K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CrO}_{4}^{2-}] \]. Here, the concentration of silver ions is squared to account for the stoichiometric coefficient in the balanced equation.

Key Concepts

Thermodynamic Solubility

Thermodynamic solubility refers to the maximum amount of a solute that can dissolve in a solvent at a specific temperature to reach equilibrium. This process involves both the dissolution and precipitation of a substance. In the context of sparingly soluble salts like barium sulfate \(\mathrm{BaSO}_{4} \) and silver chromate \(\mathrm{Ag}_{2}\mathrm{CrO}_{4} \), we observe a situation where only a tiny amount of the salt actually dissolves before a balance is achieved.
To quantify this, chemists use the concept of the solubility product constant \( K_{sp} \), which symbolizes the level at which the salt dissolves into its respective ions:

• For \(\mathrm{BaSO}_{4} \), the expression is \( K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{SO}_{4}^{2-}] \).
• For \(\mathrm{Ag}_{2}\mathrm{CrO}_{4} \), it is \( K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CrO}_{4}^{2-}] \).

These expressions help us understand and predict how salts will behave under different conditions, which is essential in fields such as pharmacology and environmental science.

Equilibrium

Equilibrium in the context of solubility is the state where the dissolution of a salt and the precipitation back into solid form occur at the same rate. At equilibrium, no net change is observed in the concentrations of ions in the solution.
This balanced condition is crucial for understanding how much of a salt remains dissolved in a solution at a given temperature. The equilibrium condition can be disrupted by changes in temperature, pressure, or the addition of other solutes, which can either increase solubility or cause more precipitation.
The solubility product \( K_{sp} \) is a representation of this equilibrium:

• It is temperature-dependent, often varying with changes in temperature.
• The higher the \( K_{sp} \), the more soluble the salt in the solution.

Monitoring equilibrium helps in various industrial and laboratory settings to control the formation of scale, improve product yield, or optimize conditions for specific chemical reactions.

Sparingly Soluble Salts

Sparingly soluble salts are those that dissolve to a very limited extent in water, reaching a point where only a few ions enter the solution. Examples include salts like \( \mathrm{BaSO}_{4} \) and \( \mathrm{Ag}_{2}\mathrm{CrO}_{4} \), which are used in medical imaging and analytical chemistry, respectively.
Despite their limited solubility, these salts are pivotal in many applications due to their predictable behavior at equilibrium. When these salts dissolve, they establish a dynamic equilibrium with their undissolved forms, and their solubility product \( K_{sp} \) can be used to calculate the concentrations of ions in solution.
Understanding sparingly soluble salts is important for:

• Predicting the conditions under which a salt will start to precipitate.
• Determining the purity of a sample.
• Designing reactions that require precise control over ion concentrations.

In fields such as water treatment, managing the solubility of these salts helps prevent clogging of pipelines and ensures effective processing.