Sodium benzoate (C6H5CO2Na) is used as a food preservative. Calculate the pH and the concentrations of all species present (Na+, C6H5COO-, C6H5COOH, H3O+, and OH-) in 0.050 M sodium benzoate; Ka for benzoic acid (C6H5COOH) is 6.5 * 10^-5.

Verified step by step guidance

1. Step 1: Recognize that sodium benzoate (C6H5CO2Na) is a salt of the weak acid benzoic acid (C6H5COOH) and will dissociate completely in water to form C6H5COO- and Na+ ions.
2. Step 2: Write the hydrolysis reaction for the benzoate ion (C6H5COO-) in water: C6H5COO- + H2O ⇌ C6H5COOH + OH-. This reaction will establish an equilibrium in the solution.
3. Step 3: Use the given Ka for benzoic acid to find the Kb for the benzoate ion using the relation Kb = Kw / Ka, where Kw is the ion-product constant of water (1.0 x 10^-14 at 25°C).
4. Step 4: Set up an ICE (Initial, Change, Equilibrium) table for the hydrolysis reaction to express the concentrations of all species at equilibrium in terms of x, where x is the change in concentration of OH-.
5. Step 5: Use the expression for Kb and the equilibrium concentrations from the ICE table to solve for x, which represents the concentration of OH-. Then, calculate the pOH and use it to find the pH of the solution.

Key Concepts

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, sodium benzoate acts as the conjugate base of benzoic acid, allowing the solution to maintain a relatively stable pH despite the presence of additional acids or bases.

Acid-Base Equilibrium

Acid-base equilibrium involves the balance between the concentrations of acids and their conjugate bases in a solution. The dissociation of benzoic acid (C6H5COOH) into its ions establishes this equilibrium. The equilibrium constant, Ka, quantifies the strength of the acid, and is essential for calculating the concentrations of all species in the solution, including H3O+ and OH-.

pH Calculation

The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm of the hydrogen ion concentration (pH = -log[H3O+]). In this scenario, calculating the pH involves determining the concentration of H3O+ ions produced from the dissociation of benzoic acid in equilibrium with sodium benzoate. This requires applying the Henderson-Hasselbalch equation or the equilibrium expression for Ka.