Titration of 25.0 mL of 0.100 M NH3 (Kb = 1.8×10^-5) with 0.100 M HCl. What is the pH at the equivalence point?

• A. 7.00
• B. 3.50
• C. 4.63
• D. 9.00

Answer: (C)

At the equivalence point of titrating a weak base with a strong acid, all the base has been converted to its conjugate acid. Here, ammonia (NH3) becomes ammonium (NH4+). The pH is governed by the hydrolysis of NH4+, not by remaining OH− or base.

First find the conjugate acid’s dissociation constant. For NH3, Kb = 1.8 × 10−5. Using Kw = 1.0 × 10−14, Ka for NH4+ is Ka = Kw / Kb ≈ 1.0 × 10−14 / 1.8 × 10−5 ≈ 5.56 × 10−10. The pKa of NH4+ is about 9.25, indicating NH4+ is a weak acid.

At equivalence, the total volume is 25.0 mL of NH3 plus 25.0 mL of HCl = 50.0 mL, and moles NH3 initially are 0.0250 L × 0.100 M = 2.50 × 10−3 mol. Thus, the NH4+ concentration in the solution is 2.50 × 10−3 mol / 0.0500 L = 0.0500 M.

For a weak acid HA with concentration C and Ka, the [H+] is approximately sqrt(Ka × C). Here, [H+] ≈ sqrt(5.56 × 10−10 × 0.0500) ≈ sqrt(2.78 × 10−11) ≈ 5.3 × 10−6 M. The pH is then −log(5.3 × 10−6) ≈ 5.28.

So, the pH at the equivalence point is about 5.3. This is acidic because the conjugate acid NH4+ dominates the solution, unlike a strong acid–base titration where the equivalence point would be neutral.