How to Calculate pH of Salt of Weak Acid and Strong Base?

To calculate the pH of a salt solution formed from a weak acid and a strong base, you use the following formula:

The pH Formula

The pH of a salt solution of a weak acid and strong base is given by:

pH = 1/2 pK_w + 1/2 pK_a + 1/2 logC

This formula is found in Reference 1. A. provided in the prompt.

Let's break down what each term in the formula represents:

• pH: This is the measure of the acidity or basicity of the solution. A pH above 7 indicates a basic solution (which is expected for a salt of a weak acid and strong base).
• pK_w: This is the negative logarithm of the ion product constant for water (K_w). At 25°C, K_w = 1.0 x 10^-14, so pK_w = 14. The value of pK_w changes with temperature.
• pK_a: This is the negative logarithm of the acid dissociation constant (K_a) for the weak acid from which the salt is derived. A smaller pK_a (or larger K_a) indicates a stronger weak acid.
• C: This is the initial molar concentration of the salt in the solution.

Why is the Solution Basic?

When a salt of a weak acid (HA) and a strong base (like NaOH) dissolves in water, it dissociates into ions, for example, NaA. The Na⁺ ion is the conjugate acid of a strong base (NaOH), making it a neutral spectator ion in terms of pH. However, the A⁻ ion is the conjugate base of the weak acid (HA). This A⁻ ion reacts with water in a process called hydrolysis:

A⁻(aq) + H₂O(l) ⇌ HA(aq) + OH⁻(aq)

This reaction produces hydroxide ions (OH⁻), which increases the concentration of OH⁻ in the solution, making it basic (pH > 7). The formula pH = 1/2 pK_w + 1/2 pK_a + 1/2 logC accounts for this hydrolysis effect.

Example Calculation

Let's calculate the pH of a 0.05 M solution of sodium benzoate (C₆H₅COONa) at 25°C. Benzoic acid (C₆H₅COOH) is a weak acid with K_a = 6.3 x 10^-5.

1. Find pK_a:
   pK_a = -log(K_a) = -log(6.3 x 10^-5) ≈ 4.20
2. Identify pK_w:
   At 25°C, pK_w = 14.
3. Identify C:
   The salt concentration C = 0.05 M.
4. Plug values into the formula:
   pH = 1/2 pK_w + 1/2 pK_a + 1/2 logC
   pH = 1/2 (14) + 1/2 (4.20) + 1/2 log(0.05)
   pH = 7 + 2.10 + 1/2 (-1.30)
   pH = 7 + 2.10 - 0.65
   pH = 8.45

The pH of the 0.05 M sodium benzoate solution is approximately 8.45, which is basic, as expected.

Factors Influencing pH

The pH of the salt solution is influenced by:

• Strength of the Weak Acid (pK_a): A weaker acid (higher pK_a) has a stronger conjugate base (A⁻). A stronger conjugate base undergoes more hydrolysis, producing more OH⁻ and resulting in a higher (more basic) pH.
• Salt Concentration (C): A higher concentration of the salt means a higher concentration of the conjugate base (A⁻). This leads to more hydrolysis and a higher pH.
• Temperature (pK_w): As temperature changes, K_w changes, which in turn changes pK_w, affecting the pH.

This formula provides a good approximation for the pH of such solutions, particularly when the salt concentration is not extremely low or high, and the weak acid is not extremely weak.