Calculate the \(\mathrm{pH}\) of \(0.05 \mathrm{M}\) sodium acetate solution if the \(p K_{a}\) of acetic acid is \(4.74\)

The relationship between pKa and pH is foundational to understanding acid-base chemistry. The pKa value is a measure of the strength of an acid; it's the negative logarithm of the acid dissociation constant (Ka). It indicates at what pH level half of the acid molecules are deprotonated (lose a hydrogen ion).

In the context of sodium acetate solutions, acetic acid's pKa helps us assess the degree to which the conjugate base (CH3COO-) can attract a hydrogen ion from water, creating hydroxide ions (OH-) and thus affecting the pH. Since pH is a measure of hydrogen ion concentration, and pKa provides a way to calculate the equilibrium concentrations, by knowing the pKa of acetic acid, we can determine the pH of its corresponding salt solution after hydrolysis.

Moreover, a lower pKa means a stronger acid; thus the conjugate base would be weaker and its solution less basic. This relationship enables us to predict how the pH will shift when an acid or its conjugate base is in solution.

Hydrolysis of salts occurs when salt ions react with water to form the acid or base. In the case of sodium acetate, the acetate ion (CH3COO-) is a conjugate base of acetic acid and can undergo hydrolysis to form hydroxide ions (OH-) and acetic acid.

This reaction is crucial because it directly impacts the pH of the solution. Since sodium acetate is derived from a weak acid and a strong base, the hydrolysis of the acetate ion will tend to make the solution more basic (higher pH). The extent to which this happens depends on the acid-base properties of the ions involved, which is determined by their respective pKa and pKb values.

Understanding the hydrolysis mechanism helps us predict the behavior of a solution and the dominant species at equilibrium. It is a perfect demonstration of how salts can affect the acidity or basicity of a solution, even though they might be neutral themselves.

The ICE (Initial, Change, Equilibrium) table method is an indispensable tool for solving equilibrium problems in chemistry. 'I' stands for the initial concentration of reactants and products, 'C' represents the change in concentration as reactants are converted to products, and 'E' stands for the equilibrium concentrations.

For sodium acetate hydrolysis, the ICE table helps quantify the hydrolysis process by outlining the initial concentrations of acetate ions and water, the changes as equilibrium is established, and the resulting concentrations of acetic acid and hydroxide ions.

This method simplifies dealing with complex equilibrium calculations by providing a structured approach. By assuming that the change in concentration of the hydrolyzed species (often labeled as 'x') is small, we can solve for 'x' essentially the concentration of OH- ions in a solution of a weak base like acetate.

Acid-base equilibrium refers to the state in which the rates of the forward and reverse reactions of acid and base are equal, leading to constant concentrations of all species in solution. This equilibrium is governed by the acid dissociation constant (Ka) for acids or the base dissociation constant (Kb) for bases.

In the sodium acetate example, the equilibrium focuses on the hydrolysis reaction of the acetate ion. Using the known pKa of acetic acid, we can determine the Kb for the acetate ion and then use the ICE table approach to find the equilibrium concentrations of all species. It is important to consider the self-ionization of water as well, which provides a basis for calculating the hydroxide ion concentration and, subsequently, the pH of the solution.

The calculations based on this state of equilibrium help us understand the extent to which a substance can alter the pH of a solution. A strong grasp of acid-base equilibrium concepts allows students to predict the direction and extent of pH changes in any aqueous system.