Question

Propionic acid, C₂H₅CO₂H (Kₐ = 1.34 × 10^−5), is used in the manufacture of calcium propionate, a food preservative. What is the pH of a 0.698-M solution of C₂H₅CO₂H?

a) 2.91
b) 4.72
c) 5.34
d) 7.45

Answer 1

The pH of a 0.698-M solution of propionic acid, with a given Kᵁ of 1.34 × 10⁻⁵, is approximately 3.07, which is not listed among the answer choices provided.

Step-by-step explanation:

The student asks about the pH of a 0.698-M solution of propionic acid (C₂H₅CO₂H) with a given acid dissociation constant (Kᵁ) of 1.34 × 10⁻⁵. To calculate the pH, we first need to write the dissociation reaction of propionic acid in water:

CH₃CH₂COOH(aq) + H₂O(l) → CH₃CH₂COO⁻(aq) + H₃O⁺(aq)

We then apply the equilibrium expression for the dissociation.

Kᵁ = [CH₃CH₂COO⁻][H₃O⁺] / [CH₃CH₂COOH]

Assuming initial concentration of H₃O⁺ is close to zero and the change in concentration of propionic acid is minimal, we have:

Kᵁ = x² / (0.698 - x) ≈ x² / 0.698

Solving for x (concentration of H₃O⁺), x ≈ √(1.34 × 10⁻⁵ × 0.698) ≈ 8.59 × 10⁻⁴

The pH of the solution is calculated using the equation:

pH = -log[H₃O⁺]

pH = -log(8.59 × 10⁻⁴) ≈ 3.07

Therefore, none of the options a) 2.91 b) 4.72 c) 5.34 d) 7.45 match the calculated pH. The correct pH value of the 0.698-M solution of propionic acid is approximately 3.07.