Explain what happens to (a) the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)ions in an acetic acid solution when solid sodium acetate is added; (b) the percentage deprotonation of benzoic acid in a benzoic acid solution when hydrochloric acid is added; (c) the \(\mathrm{pH}\) of the solution when solid ammonium chloride is added to aqueous ammonia.

Understanding Le Chatelier's principle is essential when studying chemical reactions and predicting how systems respond to changes. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system responds by counteracting the change to re-establish equilibrium.

Imagine a seesaw where everything is perfectly balanced. If you add more weight to one side, the seesaw will tip to one side. The seesaw will try to balance itself by either removing the added weight or by adding more weight to the opposite side. Similarly, in chemistry, when the concentration of a reactant or product in a reversible reaction is altered, the system will shift its equilibrium point to counteract the change. This shift could result in the increased production of reactants or products, depending on what was initially changed.

When applying this to the common-ion effect seen in acid-base equilibrium, Le Chatelier's principle helps predict how the addition of an ion that is part of the equilibrium will affect the concentrations of other ions and the overall system.

Acid-base equilibrium refers to the balance that exists in a solution between the acid and base forms of a molecule. This equilibrium is crucial in the context of pH and the common-ion effect, as it governs how acids and bases behave in solution.

Let's dive into the acid dissociation equilibrium: When an acid (HA) dissolves in water, it can donate a proton (H+) to form its conjugate base (A-) and hydronium ions (H3O+). The relative strengths of the acid and its conjugate base determine the extent of this dissociation. A strong acid will almost completely dissociate, while a weak acid only partially dissociates, leaving a significant amount of un-dissociated acid in the solution.

To visualize this, imagine a dance floor representing an acid-base system. Several dance pairs (HA molecules) are in constant motion, separating (dissociating) and rejoining (re-associating). The music's rhythm (the pH of the solution) affects how likely it is that a dancer (a proton) will leave their partner (the acid molecule) for a solo performance (being a free H3O+ ion). If a strong dancer (a strong acid) steps onto the floor, it's almost certain they'll go solo. However, a hesitant dancer (a weak acid) might stick close to their partner, only occasionally venturing into a solo.

The pH of a solution is a measure of its acidity or basicity and is a critical aspect of chemistry, primarily when working with acid-base reactions. The pH is calculated as the negative logarithm (base 10) of the concentration of hydronium ions in the solution, expressed in moles per liter (M). The formula for pH is given by: \(\text{pH} = -\log [\mathrm{H}_3\mathrm{O}^+]\).

Picture the pH scale as a ladder, with each rung representing a different level of acidity or basicity. The lower rungs are highly acidic (low pH values), the middle rung is neutral (pH 7, pure water), and the upper rungs are basic or alkaline (high pH values). A slight change in the number of hydronium ions, akin to shifting the weight on a rung, can cause a significant climb or drop on this pH ladder.

To calculate the effect of adding a common ion to a solution on pH, we must consider both the initial pH and the extent to which the added ion will affect the established acid-base equilibrium. This balance directly influences the concentration of hydronium ions, and thus, the pH of the solution shifts correspondingly. For instance, adding a salt that contains a common ion to a weak acid or base can suppress further ionization of the weak acid or base, leading to a change in pH.