An acetic acid solution has a pH of 5.80. What is its [H₃O⁺]? A) 1.6 × 10⁻²⁰ M B) 6.3 × 10⁻⁹ M C) 1.6 × 10⁻⁶ M D) 6.3 × 10⁵ M

Question

Quizplus · Accepted Answer

Acetic acid, CH3COOH, is a weak acid that undergoes partial dissociation in water:
CH3COOH + H2O ⇌ CH3COO- + H3O+
The equilibrium constant expression for this reaction is Keq = [CH3COO-][H3O+] / [CH3COOH]
The pH of the solution is 5.80, so the concentration of H3O+ is:
[H3O+] = 10^-pH = 10^-5.80 = 1.58 x 10^-6 M
Since acetic acid is a weak acid, we can assume that the concentration of CH3COO- is equal to the concentration of [HS1U1B13S1U1B0O]-- so let's call both of these concentrations "x":
x^2 / (0.10-x) = 1.8 x 10^-5 (Note: 0.10 is the initial concentration of acetic acid)
Using the quadratic formula, we find that x = 1.6 x 10^-6 M
Therefore, the concentration of [HS1U1B13S1U1B0O]-- is 1.6 x 10^-6 M, and the concentration of [HS1U1B13S1U1B0OS1U1P1+] is equal to the concentration of H3O+, or 1.58 x 10^-6 M. Adding these two values together gives us the answer of 3.18 x 10^-6 M. However, the question is asking for the concentration of only [HS1U1B13S1U1B0OS1U1P1+S1S1P0]. Therefore, the answer is 1.6 x 10^-6 M, which is choice C.

An Acetic Acid Solution Has a PH of 5