Question

Explain, using Le Châtelier's principle, what happens to the \(\left[\mathrm{H}^{+}\right]\) of a 0.10 \(\mathrm{M}\) solution of acetic acid when a drop of NaOH solution is added.

Short answer

In summary, when a drop of NaOH is added to a 0.10 M acetic acid solution, it reacts with the acetic acid, decreasing its concentration. According to Le Châtelier's principle, the equilibrium shifts to the left to counteract this disturbance, causing the concentration of hydrogen ions [H+] to decrease, and the concentration of acetate ions [CH3COO-] to increase.

Step-by-step solution

Write the balanced equation for the dissociation of acetic acid in water

Consider the dissociation of acetic acid (CH3COOH) in water: \[CH_3COOH(aq) \rightleftharpoons CH_3COO^-(aq) + H^+(aq)\] The equilibrium constant expression for this reaction is: \[K_a = \frac{\left[ CH_3COO^- \right] \left[ H^+ \right]}{\left[ CH_3COOH \right]}\]

Taking acetic acid as a weak acid

Acetic acid is a weak acid, which means that it does not dissociate completely in water. Therefore, at equilibrium, there will still be some undissociated acetic acid in the solution: \[[CH_3COOH]_0 = [CH_3COOH]_{eq} + [CH_3COO^-]_{eq}\]

Identifying the role of NaOH

When NaOH is added to the acetic acid solution, the following reaction occurs: \[NaOH(aq) + CH_3COOH(aq) \rightarrow CH_3COONa(aq) + H_2O(l)\] Notice that the base NaOH reacts with acetic acid to produce sodium acetate (CH3COONa) and water. This reaction consumes both the base NaOH and acetic acid, effectively decreasing the concentration of CH3COOH in the solution.

Applying Le Châtelier's principle

According to Le Châtelier's principle, the equilibrium will shift to counteract the disturbance caused by the addition of NaOH. Because the concentration of acetic acid has decreased due to the reaction with NaOH, the equilibrium will shift in the direction that increases the [CH3COOH] to restore equilibrium. In this case, the equilibrium will shift to the left, favoring the formation of more acetic acid: \[CH_3COOH(aq) \leftarrow CH_3COO^-(aq) + H^+(aq)\] As the reaction shifts to the left, the concentration of hydrogen ions [H+] will decrease, while the concentration of acetate ions [CH3COO-] will increase.

Conclusion

In conclusion, when a drop of NaOH solution is added to a 0.10 M solution of acetic acid, the equilibrium shifts to the left to counteract the disturbance caused by the NaOH. As a result, the concentration of hydrogen ions [H+] decreases, and the concentration of acetate ions [CH3COO-] increases. This demonstrates the application of Le Châtelier's principle in understanding the effect of adding a base to a weak acid solution.

Key concepts

Chemical Equilibrium

Chemical equilibrium refers to a state in a chemical reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of the reactants and products over time. It's essential to understand that equilibrium doesn't mean the reactants and products are present in equal amounts, but rather that their concentrations have stabilized at a certain ratio. Let's break down this concept using the context of acetic acid in water.

In the exercise, we introduced the balanced equation for acetic acid dissociating in water. At equilibrium, the reaction reaches a state where the rate at which acetic acid molecules dissociate into acetate ions and hydrogen ions is equal to the rate at which these ions recombine to form acetic acid. This dynamic process is represented by the constant movement, but no net change in concentrations. Equilibrium can be disturbed by changes in concentration, temperature, or pressure, which brings into play the Le Châtelier's principle.

Acetic Acid Dissociation

In the context of the exercise, the dissociation of acetic acid is crucial to understand its behavior in solution. As a weak acid, acetic acid only partially dissociates into acetate ions (\( CH_3COO^- \) and hydrogen ions (\( H^+ \) in water. This partial dissociation is represented by a reversible reaction, meaning it can proceed in both the forward (dissociating) and reverse (reassociating) directions.

As a weak acid, the concentration of acetic acid (\( [CH_3COOH] \) remains significantly higher than the concentrations of its ions. The equilibrium constant (\( K_a \) for this reaction is thus typically less than one. The exercise walks us through what happens when NaOH, a strong base, is introduced to the mixture. NaOH reacts with acetic acid to create water and sodium acetate, disturbing the established equilibrium. This is a concrete example of how external changes, such as adding another reactant, can influence an established chemical equilibrium.

Weak Acid Behavior

Weak acids like acetic acid only partially ionize in water, which is a defining characteristic of their behavior. Unlike strong acids that disassociate completely, weak acids create an equilibrium mixture of the undissociated acid form and its ions. This weak acid behavior is the basis for an acid's strength and dictates the pH of the solution.

When an acid doesn't fully dissociate, the resulting solution is less acidic compared to a solution of strong acid at the same concentration. The provided exercise illustrates this concept by showing how the addition of NaOH, a base, leads to the consumption of acetic acid molecules and a corresponding shift in the equilibrium position. Le Châtelier's principle predicts the direction of this shift, aiming to lessen the impact of the disturbance by reducing the concentration of hydrogen ions, which contributes to maintaining the acid's weak dissociation and preserving the overall chemical equilibrium.