The K_a for acetic acid is 1.8 × 10^-5. Which of the following statements best describes the pH of a 0.010 M solution of acetic acid? A)The pH is greater than 0 but less than 2. B)The pH is exactly 2. C)The pH is greater than 2 but less than 7. D)The pH is exactly 7. E)The pH is greater than 7 but less than 12.

Question

Quizplus · Accepted Answer

First, use the equation for calculating the pH of a weak acid:
pH = pKa + log([salt]/[acid])
The pKa for acetic acid is 4.76. Since the question gives the Ka, we can calculate the pKa by taking the negative logarithm: pKa = -log(Ka) = -log(1.8 × 10^-5) = 4.76
In this case, the salt is acetate (the conjugate base of acetic acid) and the acid is acetic acid itself. 
Let x be the amount of acetic acid that ionizes (in moles):
Ka = [H+][CH3COO-]/[CH3COOH] = x^2/(0.010-x)
Since x << 0.01 then approximately,  0.010-x ≈ 0.010: 
1.8 × 10^-5 = x^2/0.010
x = 1.3 × 10^-3
Now we can find the concentrations of acetate and acetic acid:
[CH3COO-] = x = 1.3 × 10^-3 M
[CH3COOH] = 0.010 - x = 0.0087 M
Plugging this into the pH equation:
pH = 4.76 + log(1.3 × 10^-3/0.0087) ≈ 2.88
Thus, the pH of a 0.010 M solution of acetic acid is greater than 2 but less than 7. Therefore, the best answer is C.

The Ka for Acetic Acid Is 1

The K_a for Acetic Acid Is 1