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 dissolution equation for AgCl in water is: \[\text{AgCl(s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^− (aq) \] (b) The expression for Kc is: \[K_c = [\text{Ag}^+][\text{Cl}^-]\] (c) The dissolution of AgCl in water is an endothermic reaction (ΔH > 0). According to Le Châtelier's principle, increasing the temperature will increase the solubility of AgCl in water.

Step-by-step solution

Part (a): Dissolution Equation

Silver chloride is an insoluble strong electrolyte. When it dissolves in water, it dissociates into its respective ions. The dissolution equation for AgCl can be represented as follows: \[ \text{AgCl(s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^− (aq) \]

Part (b): Expression for Kc

The equilibrium constant, Kc, can be determined by expressing the concentration of products divided by the concentration of reactants. In our case, since AgCl is a solid, it is not included in the Kc expression. So, the expression for Kc can be written as follows: \[K_c = [\text{Ag}^+][\text{Cl}^-]\]

Part (c): Solubility and Temperature

According to Le Châtelier's principle, if we increase the temperature of an endothermic reaction, the equilibrium will shift towards the products side, increasing the solubility. In contrast, if we increase the temperature of an exothermic reaction, the equilibrium will shift towards the reactants side, decreasing the solubility. We need to find out whether the dissolution of AgCl in water is an endothermic or exothermic reaction by referring to the thermochemical data provided in Appendix C. Based on the data, we find that the dissolution of AgCl in water has a positive enthalpy change (ΔH > 0), which indicates that it is an endothermic reaction. Therefore, according to Le Châtelier's principle, increasing the temperature will shift the equilibrium towards the products side and increase the solubility of AgCl in water.