91Ó°ÊÓ

The solubility product, often represented as \(K_{sp}\), is a special type of equilibrium constant that applies to sparingly soluble salts. It describes the equilibrium between a solid substance and its ions dissolved in a solution. For silver chloride, \(\text{AgCl (s)} \rightleftharpoons \text{Ag}^+ \text{ (aq)} + \text{Cl}^- \text{ (aq)}\), the solubility product reflects how easily the solid dissolves into these ions in water.

• A low \(K_{sp}\) means the compound is less soluble in water.
• A high \(K_{sp}\) suggests more ions are released into the solution, meaning higher solubility.

Knowing the \(K_{sp}\) is essential for predicting whether a precipitate will form in a chemical reaction involving ionic compounds.

Enthalpy change, denoted as \(\Delta H\), represents the heat absorbed or released during a chemical reaction at constant pressure. It is a crucial concept when studying energy changes in reactions.
In this exercise, we determine \(\Delta H^{\circ}\) using the Van't Hoff equation, which connects it to temperature changes and equilibrium constants:
\[\ln \left( \frac{K_2}{K_1} \right) = \frac{-\Delta H^{\circ}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)\]

• Positive \(\Delta H\) indicates an endothermic reaction, which absorbs heat.
• Negative \(\Delta H\) indicates an exothermic reaction, releasing heat.

For silver chloride, \(\Delta H^{\circ}\) was found to be \(21.2 \text{ kJ/mol}\), suggesting the dissolution absorbs heat slightly, an endothermic process.

Equilibrium constants, including \(K_{sp}\), indicate the ratio of product concentrations to reactant concentrations at equilibrium.
They apply to reversible reactions, where forward and backward reactions occur simultaneously at equal rates:

• An equilibrium constant greater than 1 implies products are favored.
• An equilibrium constant less than 1 suggests the reactants are favored.

For the dissociation of silver chloride, knowing the equilibrium constant at different temperatures helps us understand the temperature’s effect on solubility.
The increase from \(1.782 \times 10^{-10}\) to \(4.159 \times 10^{-10}\) with temperature signifies increased solubility as the temperature rises.

Gibbs free energy, \(\Delta G\), assesses a reaction's spontaneity at constant temperature and pressure. A negative \(\Delta G\) implies a spontaneous process, while positive \(\Delta G\) means non-spontaneity.
In this exercise, we calculate \(\Delta G^{\circ}\) for silver chloride at two temperatures:

• At \(298.15 \text{ K}\), \(\Delta G^{\circ}\) is \(57.9 \text{ kJ/mol}\)
• At \(308.15 \text{ K}\), \(\Delta G^{\circ}\) is \(55.2 \text{ kJ/mol}\)

These positive values tell us that under standard conditions, the dissolution of silver chloride is not favored without external input. Connecting \(\Delta G\) to \(\Delta H\) and \(\Delta S\) through \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \) also helps in calculating the change in entropy \(\Delta S^{\circ}\), which gives further insights into the disorder of the system.