A 0.0010 M solution of a weak acid,HA,with K_a = 2 * 10^-10 produces [H₃O⁺]

Question

A 0.0010 M solution of a weak acid,HA,with K_a = 2 * 10^-10 produces [H₃O⁺] < 10^-6 M.Which of the following equations can be used to determine [H₃O⁺]? A)The acid is so weak that the pH is about 7. B)[H₃O⁺]² + K_a [H₃O⁺] - [HA]_initialK_a = 0 C)[H₃O⁺] = (K_w + K_a[HA]_initial)^½ D)[H₃O⁺] = [HA]_initial E)[H₃O⁺] = (K_a[HA]_initial)^½

Quizplus · Accepted Answer

The equation given in choice C is the correct expression for calculating the concentration of the conjugate base, [HSO4-], in a solution of sulfuric acid, which is a strong acid. However, the question is about a weak acid, and the equation given in choice C is incorrect in this case. 
Therefore, the correct choice is C, as it gives the correct equation for calculating the concentration of the conjugate base of a strong acid, which is not relevant to the question at hand.

A 00010 M Solution of a Weak Acid,HA,with Ka = 2

A 00010 M Solution of a Weak Acid,HA,with K_a = 2