Consider a 0.50 M solution of HNO₂, a weak acid with K_a = 4.5 × 10^-4. Which statement is true? A) [H₃O⁺] = 0.50 M. B) The acid is mostly ionized. C) pH = 3.35. D) pH = 0.32. E) pH 0.32.

Question

Consider a 0.50 M solution of HNO₂, a weak acid with K_a = 4.5 × 10^-4. Which statement is true? A) [H₃O⁺] = 0.50 M. B) The acid is mostly ionized. C) pH = 3.35. D) pH = 0.32. E) pH > 0.32.

Quizplus · Accepted Answer

Since the acid is weak, it is not completely ionized in solution. Therefore, the concentration of H₃O⁺ cannot be equal to the initial concentration of the acid (choice A is incorrect). The acid is not mostly ionized since it is a weak acid (choice B is incorrect). To determine the pH of the solution, we can use the expression: K_a = [H₃O⁺][O₃O^-] / [H+] where [H+] is the concentration of hydrogen ions in solution. At equilibrium, the concentration of H₃O⁺ is equal to x, so we have: 4.5 x 10^-4 = x2 / (0.50 - x) Solving for x gives x = 2.1 x 10^-3 M. Since the acid is a weak acid, we can assume that the change in concentration of H₃O⁺ is negligible compared to the initial concentration, so [H₃O⁺] ≈ 2.1 x 10^-3 M. Finally, we can use the expression: pH = -log[H+] where [H+] = K_a / [H₃O⁺] to find the pH of the solution. Plugging in the values gives: pH = -log(4.5 x 10^-4 / 2.1 x 10^-3) ≈ 3.35 Therefore, choice C is incorrect and the correct answer is choice E, pH > 0.32.