A solution of an unknown acid had a pH of 3.70. Titration of a 25.0 mL aliquot of the acid solution required 21.7 mL of 0.104 M sodium hydroxide for complete reaction. Assuming that the acid is monoprotic, what is its ionization constant? A) 9.0 × 10^-2 B) 2.0 × 10^-4 C) 4.4 × 10^-7 D) 3.6 × 10^-9 E) 2.7 × 10^-11

Question

Quizplus · Accepted Answer

Step 1: Calculate the initial concentration of H+ ions in the solution.

pH = -log[H+]
3.70 = -log[H+]
[H+] = 2.0 × 10^-4 M

Step 2: Calculate the moles of H+ ions present in the solution.

moles H+ = concentration × volume
moles H+ = 2.0 × 10^-4 × 0.025
moles H+ = 5.0 × 10^-6

Step 3: Calculate the moles of NaOH required to neutralize the H+ ions.

moles NaOH = concentration × volume
moles NaOH = 0.104 × 0.0217
moles NaOH = 2.2608 × 10^-3

Step 4: Calculate the concentration of OH- ions in the solution after the neutralization.

moles OH- = moles NaOH
moles OH- = 2.2608 × 10^-3

volume of solution after neutralization = volume of acid solution = 25.0 mL

concentration of OH- = moles / volume
concentration of OH- = 2.2608 × 10^-3 / 0.025
concentration of OH- = 0.090432 M

Step 5: Calculate the ionization constant (Ka) of the acid.

Ka = [H+][OH-] / [acid]
Ka = (5.0 × 10^-6)(0.090432) / (2.0 × 10^-4)
Ka = 1.10 × 10^-7

The closest value to the answer is C, 4.4 × 10^-7, so the correct choice is (C).

A Solution of an Unknown Acid Had a PH of 3.70