Weak Base-Strong Acid Titrations

Introduction

When a strong acid titrates a weak base, added protons progressively convert the base into its conjugate acid. This generates a buffer before equivalence. At the equivalence volume, the conjugate acid remains and can make the solution acidic. The same stoichiometric landmarks as a weak-acid titration appear, but the pH trends downward.

Core explanation

Use ammonia as an example: NH₃ + H₃O⁺ → NH₄⁺ + H₂O. Initially, ammonia partially reacts with water to make OH⁻, so pH is determined by Kb and analytical ammonia concentration. As strong acid enters, nearly each added proton converts one NH₃ into one NH₄⁺. Before equivalence, both forms are present. Using NH₄⁺ as the acid form, pH ≈ pKa(NH₄⁺) + log₁₀([NH₃]/[NH₄⁺]). Alternatively, compute pOH from Kb and the base/acid ratio, then convert to pH at the stated temperature. Do not mix Ka and Kb forms carelessly.

At half-equivalence, equal mole amounts of NH₃ and NH₄⁺ give pH ≈ pKa(NH₄⁺), or pOH ≈ pKb(NH₃) under the familiar approximations. This is not the same as a pH of 7. The equivalence volume comes from the balanced mole ratio: for NH₃ and a monoprotic strong acid, added acid moles equal initial NH₃ moles.

At equivalence, essentially all initial base has become NH₄⁺. The buffer expression cannot be used with essentially zero NH₃. Instead evaluate NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺ and Ka = Kw/Kb. Its hydronium production makes pH below neutral water at 25 °C. The analytical NH₄⁺ concentration is initial NH₃ moles divided by the final mixed volume. Beyond equivalence, excess strong acid controls pH, calculated after mole subtraction and dilution.

The observed curve may be less steep near equivalence than a comparable strong-base/strong-acid titration. The conjugate-acid strength and total concentration influence the jump. An indicator must change color in the acidic steep region, or a pH meter can locate equivalence more directly. Acidic equivalence follows the chemistry of the conjugate acid; it does not mean the strong acid was added in stoichiometric excess.

Step-by-step reasoning

1. Calculate initial base moles and equivalence acid volume. 2. Before equivalence, subtract acid moles from base and add them to conjugate acid. 3. At half-equivalence, set their ratio to one. 4. At equivalence, solve conjugate-acid equilibrium; later, calculate excess strong acid.

Visual explanation

Draw a pH curve descending as strong acid is added. Label a broad NH₃/NH₄⁺ buffer segment, half-equivalence near the conjugate-acid pKa, and an acidic equivalence region.

Real-world analogy

Imagine gradually converting untagged items into tagged items, one tag per item. At halfway, the populations are equal; when all are tagged, the tagged population's own properties determine the outcome.

Real-world example

A solution containing ammonia can be titrated with standardized hydrochloric acid. Its buffer region reflects coexisting NH₃ and NH₄⁺, while the equivalence mixture contains ammonium chloride.

Why?

Why is equivalence acidic despite no excess titrant? NH₄⁺ is the conjugate acid of a weak base and donates some protons to water, generating hydronium.

Common misconception

“Acidic equivalence means too much strong acid was added.” At true equivalence, conjugate-acid hydrolysis alone can lower pH below 7 at 25 °C.

Worked example

Titrate 20.0 mL of 0.100 M NH₃ with 0.100 M HCl. Initial NH₃ = 0.00200 mol, so equivalence occurs after 20.0 mL HCl. At 10.0 mL, 0.00100 mol NH₃ and 0.00100 mol NH₄⁺ coexist. Their ratio is one, so pH is approximately pKa(NH₄⁺), about 9.25 at 25 °C using a representative value. At equivalence, the analytical NH₄⁺ concentration is 0.00200/0.0400 = 0.0500 M and its weak-acid equilibrium controls pH.

Quick check

1. Which species remains at equivalence in an ammonia/HCl titration? Answer: NH₄⁺, together with spectator chloride and water.

Exam focus

Label the acid form in the logarithmic ratio. Do not insert Kb into a pH equation that requires Ka without converting through Kw at the specified temperature.

Advanced insight

At very low concentrations, water autoionization can matter alongside conjugate-acid hydrolysis. A full calculation joins Ka, mass balance, and charge balance rather than relying on a square-root estimate.

Summary

Strong acid converts weak base to conjugate acid. Their mixture buffers before equivalence; equal forms at half-equivalence connect pH to conjugate-acid pKa; hydrolysis makes equivalence acidic.

Practice questions

1. What reaction occurs when H₃O⁺ is added to NH₃? Answer: NH₃ + H₃O⁺ → NH₄⁺ + H₂O. 2. At half-equivalence, how do base and conjugate-acid amounts compare? Answer: They are approximately equal. 3. What controls pH beyond equivalence? Answer: Strong acid left over after all initial weak base is neutralized, with total-volume dilution included.