Question

Silver chloride, \(\mathrm{AgCl}(s)\), is an insoluble strong electrolyte. (a) Write the equation for the dissolution of \(\mathrm{AgCl}(s)\) in \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Write the expression for \(K_{c}\) for the reaction in part (a). (c) Based on the thermochemical data in Appendix \(\mathrm{C}\) and Le Châtelier's principle, predict whether the solubility of \(\mathrm{AgCl}\) in \(\mathrm{H}_{2} \mathrm{O}\) increases or decreases with increasing temperature.

Short answer

(a) The equation for the dissolution of AgCl in water is: \[ \mathrm{AgCl} \left( s \right) \rightleftharpoons \mathrm{Ag^+} \left( aq \right) + \mathrm{Cl^-} \left( aq \right) \] (b) The expression for \(K_{c}\) is: \[ K_c = \left[ \mathrm{Ag^+} \right] \left[ \mathrm{Cl^-} \right] \] (c) As the dissolution of AgCl is endothermic (\(\Delta H^\circ > 0\)), the solubility of AgCl increases with increasing temperature according to Le Châtelier's principle.

Step-by-step solution

Write the dissolution equation

To write the equation for the dissolution of AgCl in water, we need to consider that it is an ionic compound and dissociates into its constituent ions when it dissolves in water. The equation for this process is: \[ \mathrm{AgCl} \left( s \right) \rightleftharpoons \mathrm{Ag^+} \left( aq \right) + \mathrm{Cl^-} \left( aq \right) \]

Write the expression for \(K_{c}\)

According to the balanced chemical equation, the equilibrium constant (\(K_c\)) can be defined as the ratio of the product of concentrations of ions in the solution to the concentration of undissolved AgCl. Since the undissolved AgCl is a solid, its concentration will not affect the equilibrium and hence does not come into the equation. The expression for \(K_{c}\) is: \[ K_c = \left[ \mathrm{Ag^+} \right] \left[ \mathrm{Cl^-} \right] \]

Predict the solubility change with temperature

To predict whether the solubility of AgCl increases or decreases with increasing temperature, we need to consider the following: - Thermochemical data from Appendix C: If the dissolution of silver chloride is exothermic (releases heat), then the heat can be considered as a product of the reaction. If it is endothermic (absorbs heat), then the heat can be considered as a reactant. - Le Châtelier's principle: If a system at equilibrium is disturbed by a change in temperature, the system will adjust the position of the equilibrium to counteract the change. If the dissolution of AgCl is exothermic: \[ \mathrm{AgCl} \left( s \right) + \text{heat} \rightleftharpoons \mathrm{Ag^+} \left( aq \right) + \mathrm{Cl^-} \left( aq \right) \] By Le Châtelier's principle, the solubility of AgCl decreases with increasing temperature as the system will attempt to counteract the increased temperature by favoring the side that absorbs heat, in this case, the reverse reaction that forms solid AgCl. If the dissolution of AgCl is endothermic: \[ \mathrm{AgCl} \left( s \right) \rightleftharpoons \mathrm{Ag^+} \left( aq \right) + \mathrm{Cl^-} \left( aq \right) + \text{heat} \] By Le Châtelier's principle, the solubility of AgCl increases with increasing temperature as the system will try to counteract the increased temperature by favoring the side that releases heat, in this case, the forward reaction that dissolves AgCl. Looking at the thermochemical data in Appendix C, we find that the dissolution of AgCl is endothermic (\(\Delta H^\circ > 0\)). Therefore, the solubility of AgCl increases with increasing temperature.

Key concepts

Dissolution of AgCl

Understanding the process of dissolution is fundamental when analyzing the behavior of silver chloride (AgCl) in water. When AgCl is placed in water, it dissociates into silver ions (Ag+) and chloride ions (Cl-). This dissolution can be represented by a chemical equation:
\[ \mathrm{AgCl} \left( s \right) \rightleftharpoons \mathrm{Ag^+} \left( aq \right) + \mathrm{Cl^-} \left( aq \right) \]
During this equilibrium process, some of the solid AgCl remains undissolved due to its low solubility. This soluble-precipitate equilibrium plays a crucial role in the solubility dynamics of AgCl and its interaction with environmental factors such as temperature and the presence of other chemical species.

Equilibrium Constant (Kc)

Once we have established the equilibrium between the dissolved ions and the undissolved AgCl, we can examine the quantitative aspect of this equilibrium, which is described by the equilibrium constant, denoted as \(K_c\). The equilibrium constant for the dissolution is a ratio of the concentrations of the products (silver and chloride ions) to the reactants (solid AgCl). However, because the concentration of a solid is constant, it does not appear in the expression. Hence, the \(K_c\) for the dissolution of AgCl is given by:
\[ K_c = \left[ \mathrm{Ag^+} \right] \left[ \mathrm{Cl^-} \right] \]
The value of \(K_c\) is a crucial indicator of the extent to which AgCl will dissolve; a small \(K_c\) value corresponds to low solubility.

Le Châtelier's Principle

Le Châtelier's principle provides insight into how a system at equilibrium responds to external stresses. In the context of AgCl solubility, these stresses could be changes in concentration, pressure, or temperature. According to this principle, the system will adjust to partially counteract the stress. If temperature increases, the equilibrium will shift to favor either the exothermic or endothermic direction, based on the thermochemical nature of the process. This shift affects the concentration of ions in the solution, thereby influencing the solubility of the substance. It is a perfect illustration of the dynamic nature of chemical equilibria and the interplay between different factors that affect a system.

Thermochemical Data

Thermochemical data, such as enthalpy changes (\(\Delta H^\circ\)), provide valuable details on the heat involved in chemical processes. This data is essential when analyzing solubility trends, especially in conjunction with Le Châtelier's principle. An endothermic process (with positive \(\Delta H^\circ\)) indicates that the substance absorbs heat during dissolution, while an exothermic process (with negative \(\Delta H^\circ\)) implies heat release. Understanding whether the dissolution of AgCl is endothermic or exothermic helps predict how changes in temperature will affect its solubility.

Solubility and Temperature

Solubility often varies with temperature, and for AgCl, this relationship is directly influenced by the endothermic nature of its dissolution. As we heat the solution, Le Châtelier's principle explains that the system will adjust to minimize the effect of this temperature increase. Since the dissolution of AgCl is endothermic, increasing temperature will drive the equilibrium toward further dissolution, enhancing the solubility of AgCl. Therefore, students can expect that as the temperature rises, more AgCl will dissolve in the water, a prime example of practical chemistry that we can observe and measure.