Problem 95 - Chemistry The Molecular Science

Question

What is the effect on the equilibrium if more solid \(\mathrm{AgCl}\) is added to a solution saturated with \(\mathrm{Ag}^{+}\) and \(\mathrm{Cl}^{-}\) ions?

Step-by-Step Solution

Answer

Adding more solid AgCl does not alter the equilibrium concentrations of the ions in solution.

Step 1: Understanding the Saturated Solution

A solution is saturated when it contains the maximum concentration of ions that can coexist with the undissolved solid without any change in concentration. For \[ \mathrm{AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)}, \]it represents a dynamic equilibrium between the solid salt and its ions in solution.

Step 2: Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In the case of adding more solid, it is important to identify which component is changing.

Step 3: Effect of Adding More Solid AgCl

Adding more solid \( \mathrm{AgCl(s)} \)to the equilibrium does not affect the concentration of \( \mathrm{Ag^+(aq)} \)and \( \mathrm{Cl^-(aq)} \)ions because the solubility product \( K_{sp} \)only applies to the ions in solution and not the amount of solid present.

Step 4: Conclusion

Since the addition of more solid \( \mathrm{AgCl} \)only increases the amount of undissolved solid without affecting the concentrations of \( \mathrm{Ag^+} \)or \( \mathrm{Cl^-} \),the equilibrium position remains unchanged.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps us understand how equilibrium systems respond to changes. When an external change is applied to a system in equilibrium, the system will adjust to minimize that change and restore a new equilibrium. This can involve changes in concentrations, pressure, volume, or temperature. For example, if you increase the concentration of one reactant in a reaction at equilibrium, the system will shift to consume some of that added reactant. This means more products will be formed to counterbalance the change. In cases like adding more solid to a saturated solution, the principle helps us realize that certain changes, like the amount of solid added, may not disrupt the equilibrium state. This is because the equilibrium is dictated by the concentrations of solutes in solution, not the amount of solid present.

Solubility Product (K_sp)

The solubility product, denoted as \(K_{sp}\), is a specialized form of the equilibrium constant used for sparingly soluble salts. It reflects the maximum product of the ionic concentrations that can be present in a solution at equilibrium with its undissolved solid.When looking at the equilibrium \[\mathrm{AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)},\]\(K_{sp}\) is expressed as:\[K_{sp} = [Ag^+][Cl^-].\]This expression shows that \(K_{sp}\) only involves the concentrations of the ions in solution, not the solid.Understanding \(K_{sp}\) helps in determining how much of a solute can dissolve before the solution becomes saturated. Any addition of solid does not change \(K_{sp}\) because it concerns equilibrium between the ions.

Saturated Solution

A saturated solution exists when a solute is in equilibrium with its dissolved ions and undissolved solid. It represents a state where the solution cannot dissolve any more solute at a given temperature. It’s a dynamic equilibrium because while individual ions may continue to dissolve and precipitate out of solution, the overall concentration remains constant.In the context of silver chloride, a saturated solution can dissolve only up to a certain concentration of \(\mathrm{Ag^+}\) and \(\mathrm{Cl^-}\) ions. Adding more \(\mathrm{AgCl(s)}\) does not change the solubility provided the system is already saturated. This is because the rates of dissolution and precipitation of the ions in the solution are equal.