What Is A Weak Acid-Weak Base Titration? (pH Curve & Ka)

A weak acid–weak base titration tracks how pH changes as a weak base reacts with a weak acid. Its curve depends on both (K_a) and (K_b), not just the volume added. At the formal equivalence point, the solution contains two ions that can react with water, so its pH is not automatically 7.

If you are checking a lab result or trying to understand a pH curve, the key challenge is knowing which equilibrium controls each part of the titration. The same shortcut does not work from the first drop to the last. First identify the acid and base, then track the mole amounts, and finally account for the ions that react with water.

I use one worked example below to show how those steps fit together. The numbers also show why a weak acid–weak base curve is often less useful for finding an endpoint with an indicator than a strong acid–strong base curve.

Weak Acid–Weak Base Titration: Reaction, Assumptions, and Curve Overview

A weak acid–weak base titration is a reaction between an acid that only partly ionizes in water and a base that also reacts only partly with water. The main reaction transfers a proton from the acid to the base. The measured pH reflects both this reaction and the later reactions of its products with water.

Write the acid as (HA), its conjugate base as (A^-), and the base as (B). The base’s conjugate acid is (BH^+). The net proton-transfer reaction is:

[ HA+B\rightleftharpoons A^-+BH^+ ]

A conjugate acid–base pair differs by one proton. For example, (HA/A^-) is one pair, and (BH^+/B) is another.

The acid dissociation constant, (K_a), describes how much (HA) ionizes in water. The base dissociation constant, (K_b), describes how much (B) reacts with water to form (BH^+) and (OH^-). Larger values mean stronger acids or bases within their respective categories.

One important detail: the equilibrium constant for the proton-transfer reaction is

[ K_{\mathrm{net}}=\frac{K_a(HA)K_b(B)}{K_w} =\frac{K_a(HA)}{K_a(BH^+)} ]

Here, (K_w) is the ion-product constant of water, about (1.0\times10^{-14}) at (25^\circ\text{C}). This relation helps show whether proton transfer strongly favors products. It is not generally (K_a/K_b).

The formal equivalence point is the volume at which the initial acid and added base have reacted in equal mole amounts according to the balanced reaction. It does not mean every molecule has reacted, nor does it guarantee neutral pH.

For a clear calculation, record the acid and base identities, their concentrations, the initial acid volume, the volume added, and the temperature. The titration curve plots pH on the vertical axis against added titrant volume on the horizontal axis. Its shape depends on these details as well as on (K_a) and (K_b).

pH Calculations by Titration Region: Initial, Pre-Equivalence, Equivalence, and Post-Equivalence

A titration curve is best calculated in sections because the main pH-controlling species change as base is added. Before equivalence, the acid and its conjugate base may form a buffer. At equivalence, both product ions can affect pH. After equivalence, the added weak base and its conjugate acid often control the solution.

Initial solution

For a weak acid alone at concentration (C), use its ionization equilibrium:

[ K_a=\frac{[H^+][A^-]}{[HA]} ]

If the acid ionizes only slightly, the common approximation is

[ [H^+]\approx\sqrt{K_aC} ]

Then calculate (\mathrm{pH}=-\log[H^+]). If the approximation would use a large fraction of the starting acid, solve the equilibrium equation instead.

Before equivalence

First calculate the reacting mole amounts. If the reaction is sufficiently product-favored, subtract the moles of base added from the starting moles of acid to estimate remaining (HA), and treat the same amount as formed (A^-). When both are present in meaningful amounts, the Henderson–Hasselbalch equation can estimate pH:

[ \mathrm{pH}\approx\mathrm{p}K_a+\log\left(\frac{[A^-]}{[HA]}\right) ]

Because both concentrations share the same total volume, their ratio can be calculated from their mole amounts. At the half-equivalence volume, those amounts are equal, so this approximation gives (\mathrm{pH}\approx\mathrm{p}K_a).

That shortcut is not automatic for a weak base titrant. The product (BH^+) can also donate a proton to water. Use the buffer estimate when its effect is small; otherwise, include both conjugate pairs in the equilibrium calculation.

At equivalence

At formal equivalence, the main solutes are (A^-) and (BH^+). Each can react with water:

[ A^-+H_2O\rightleftharpoons HA+OH^- ]

[ BH^++H_2O\rightleftharpoons B+H_3O^+ ]

Their relevant constants are

[ K_b(A^-)=\frac{K_w}{K_a(HA)}, \qquad K_a(BH^+)=\frac{K_w}{K_b(B)} ]

For a dilute solution with equal amounts of the two ions, a useful estimate is

[ \mathrm{pH}_{eq}\approx 7+\frac12\log\left(\frac{K_b(B)}{K_a(HA)}\right) ]

Thus, (K_b(B)>K_a(HA)) predicts an equivalence pH above 7; (K_b(B)<K_a(HA)) predicts one below 7. Similar values predict a pH near 7 under the stated assumptions.

This estimate may fail for very dilute solutions, unequal ion concentrations, or conditions where water’s own ionization matters. In those cases, solve the mass balances, charge balance, and both hydrolysis equilibria together.

After equivalence

Once the formal equivalence volume has passed, added (B) is in excess. If (B) and (BH^+) are both present in useful amounts, estimate pOH with

[ \mathrm{pOH}\approx\mathrm{p}K_b+ \log\left(\frac{[BH^+]}{[B]}\right) ]

Then use (\mathrm{pH}+\mathrm{pOH}=14.00) at (25^\circ\text{C}). This is a buffer approximation, not a universal post-equivalence formula. Close to equivalence, or when the concentrations are very low, solve the full equilibria.

Interpreting (K_a), (K_b), the Equivalence Point, and Experimental Curve Quality

The values of (K_a) and (K_b) help predict the equivalence pH, while the full curve also depends on concentration and volume. A weak–weak titration often has a smaller pH jump near equivalence than a strong-acid–strong-base titration, so the endpoint may be hard to detect with an indicator.

Use the table to match each region with a suitable first calculation.

Worked example: formic acid titrated with ammonia

Suppose (50.0\ \mathrm{mL}) of (0.100\ \mathrm{M}) formic acid is titrated with (0.100\ \mathrm{M}) ammonia at about (25^\circ\text{C}). Use (K_a=1.8\times10^{-4}) for formic acid and (K_b=1.8\times10^{-5}) for ammonia.

The starting amount of formic acid is

[ 0.0500\ \mathrm{L}\times0.100\ \mathrm{mol/L}=0.00500\ \mathrm{mol} ]

Equal concentrations mean the formal equivalence volume is (50.0\ \mathrm{mL}). At half-equivalence, (25.0\ \mathrm{mL}) of ammonia has been added. A buffer estimate gives (\mathrm{pH}\approx\mathrm{p}K_a\approx3.74), provided the ammonium ion’s effect is small enough for this estimate.

At equivalence, the approximate pH is

[ 7+\frac12\log\left(\frac{1.8\times10^{-5}}{1.8\times10^{-4}}\right) =6.50 ]

The prediction is below 7 because the formate ion is a stronger base than ammonium is an acid under these conditions. This value is an estimate based on the dilute-solution approximation, not a measured result.

This example is a calculation case, not a claim that every weak–weak titration follows the same curve. Changing either concentration or equilibrium constant can change the curve and the endpoint’s usefulness.

Applications in Analytical Chemistry: Endpoint Selection and Measurement

An endpoint is the observed signal used to decide that a titration is complete; it may be a color change or a pH-meter reading. The equivalence point is the calculated stoichiometric point. They are related, but they are not identical. A suitable method depends on how sharply the curve changes near equivalence.

Because the pH jump can be modest in a weak acid–weak base titration, do not choose an indicator by habit. Compare its color-transition range with the steep portion of the actual curve. If that portion is too small or unclear, a calibrated pH meter can provide a more useful record of pH versus added volume. A meter still requires careful technique and does not remove errors in concentrations or volume measurements.

To build and check a curve:

• Record the starting volume, solution concentrations, temperature, and (K_a) and (K_b).
• Calculate the formal equivalence volume from mole stoichiometry.
• Choose representative volumes before, near, and after equivalence.
• Use the equilibrium model that fits each region; do not extend one shortcut across the whole curve.
• Plot pH against volume and check whether the calculated equivalence region is sharp enough for the planned endpoint method.

A curve that looks too flat to support a clear color change may still be useful for studying equilibria, but it may not provide a precise visual endpoint. The key takeaway is to calculate the curve before selecting an indicator.

Conclusion and FAQ

A weak acid–weak base titration requires more than counting added milliliters. Track the mole balance, identify the species present in each region, and use (K_a), (K_b), and water’s ionization constant to describe their equilibria. Treat the equivalence pH as a result to calculate, not a fixed value.

Is the equivalence-point pH always 7?
No. The ions (A^-) and (BH^+) can react with water, so the pH depends on their relative acid and base strengths.

What does (K_a) tell me?
It measures how readily a weak acid donates a proton in water. A larger (K_a) means a stronger acid.

What does (K_b) tell me?
It measures how readily a weak base reacts with water to form its conjugate acid and hydroxide. A larger (K_b) means a stronger base.

When can I use Henderson–Hasselbalch?
Use it as an approximation when a conjugate acid–base pair is present in substantial amounts and other equilibria do not strongly affect pH. It is not a universal equation for every point on the curve.

What is the half-equivalence point?
It is the point where half the starting acid has reacted by the formal mole calculation. When the acid/conjugate-base buffer approximation applies, pH is close to the acid’s (\mathrm{p}K_a).

Why is the curve less steep near equivalence?
Both reactants are weak, and the product ions can buffer the solution through hydrolysis. As a result, the pH change may be smaller than in a strong-acid–strong-base titration.

How do I find the equivalence volume?
Use the balanced reaction and match the reacting mole amounts. For a one-to-one reaction, equal acid and base concentrations give an equivalence volume equal to the initial acid volume.

Which indicator should I use?
Choose one whose transition range overlaps the steep section of the calculated or measured curve. If there is no clear steep section, consider measuring pH with a calibrated meter instead.

What should I do if the equivalence estimate seems unreliable?
Solve the mass balances, charge balance, and hydrolysis equilibria together. This is especially important at very low concentrations or when water autoionization may matter.

Does temperature affect the result?
Yes. Equilibrium constants, including (K_w), depend on temperature. Use values that match the stated temperature when precision matters.

(This article was written by one of our staff writers, Nathan Sterling. Visit our Meet the Team page.)