- The equilibrium for AgCl dissociation is \(AgCl_{(s)} \rightleftharpoons Ag^+_{(aq)} + Cl^-_{(aq)}\).
- Adding \(AgNO_3\) introduces extra \(Ag^+\) ions, increasing the concentration of a product in the equilibrium.
- Le Chatelier's principle dictates that increasing the product concentration shifts the equilibrium to the left to counteract the change.
- Consequently, the system shifts towards the reactant side, leading to option \(\boxed{a}\).
Explanation
- Analysis of the System and Equilibrium Disturbance
The chemical equilibrium of a saturated solution of silver chloride (AgCl) is given by the reaction:
\[AgCl_{(s)} \rightleftharpoons Ag^+_{(aq)} + Cl^-_{(aq)}\]
This equilibrium is governed by the solubility product constant, defined as \(K_{sp} = [Ag^+][Cl^-]\). Silver nitrate (\(AgNO_3\)) is a strong electrolyte, meaning it dissociates completely in water according to:
\[AgNO_3_{(aq)} \rightarrow Ag^+_{(aq)} + NO_3^-_{(aq)}\]
Adding \(AgNO_3\) to the saturated AgCl solution significantly increases the concentration of silver ions (\([Ag^+]\)) in the solution.
- Application of Le Chatelier's Principle
According to Le Chatelier's principle, if a system at equilibrium is subjected to a disturbance, the system will adjust to counteract that disturbance. In our case, the disturbance is an increase in the concentration of one of the products, the \(Ag^+\) ion. When the concentration of \(Ag^+\) increases, the reaction quotient \(Q = [Ag^+][Cl^-]\) becomes greater than the solubility product constant \(K_{sp}\) (\(Q > K_{sp}\)). To restore equilibrium and satisfy the constant \(K_{sp}\), the system must reduce the concentration of the product ions (\(Ag^+\) and \(Cl^-\)). This is achieved by the reaction proceeding in the reverse direction, shifting towards the formation of more solid AgCl.
- Conclusion and Final Result
Because the reaction shifts towards the formation of solid AgCl to consume the excess \(Ag^+\) ions, we conclude that the equilibrium shifts to the left (the side of the reactants). This phenomenon is a classic example of the "common ion effect," where the solubility of an ionic compound is decreased by the addition of a common ion. Comparing this to our options, we find that option (a) correctly describes this shift. Therefore, the addition of \(AgNO_3\) causes the equilibrium to shift to the left.
Examples
The common ion effect is crucial in industrial and environmental processes. For instance, in wastewater treatment, it is used to precipitate heavy metals out of water by adding salts that contain common ions, reducing the concentration of the hazardous metal ions in the effluent. Similarly, it plays a role in analytical chemistry when chemists want to minimize the dissolution of a precipitate during a washing step by using a wash solution that already contains a common ion. Understanding these shifts allows for more precise control over chemical reactions in both laboratory and large-scale industrial settings.