Calculate pH at Equivalence Point with Kb
Use this premium weak base titration calculator to find the pH at the equivalence point when a weak base is titrated with a strong acid. Enter the base concentration, base volume, base dissociation constant Kb, and acid concentration to compute the conjugate acid concentration and resulting pH.
Results
Enter your values and click the calculate button to see the equivalence point pH, the required acid volume, and the conjugate acid concentration.
Chart shows an estimated titration curve from zero added acid up to twice the equivalence volume. The equivalence point is where all weak base has been converted to its conjugate acid.
How to calculate pH at equivalence point with Kb
When students first learn acid base titrations, one of the biggest surprises is that the pH at the equivalence point is not always 7. That is only true for a strong acid titrated with a strong base, or vice versa, under standard textbook assumptions. If you are titrating a weak base with a strong acid, the solution at the equivalence point becomes acidic, not neutral. Understanding why that happens is the key to solving this entire class of problems quickly and correctly.
This calculator is designed specifically for the case of a weak base plus strong acid. At the equivalence point, every mole of weak base has reacted with the strong acid. The original weak base is gone, and the solution now contains mainly its conjugate acid. That conjugate acid partially ionizes in water, producing hydronium ions and pushing the pH below 7. The strength of that conjugate acid depends directly on the weak base dissociation constant, Kb.
Why Kb matters at the equivalence point
The weak base equilibrium constant tells you how strongly the base reacts with water to produce hydroxide:
B + H2O ⇌ BH+ + OH-
If a weak base has a large Kb, it is relatively stronger as a base. Its conjugate acid will therefore be relatively weaker. If a weak base has a very small Kb, it is a weaker base, and its conjugate acid will be stronger. This inverse relationship is why Kb is the starting point for equivalence point pH calculations.
Core relationship: Ka × Kb = Kw
At 25 C, Kw = 1.0 × 10-14, so Ka = 1.0 × 10-14 / Kb.
Once you convert Kb to Ka, you can treat the solution at equivalence as a weak acid solution of the conjugate acid BH+. That is the whole trick. The hard part is often not the chemistry, but identifying what species remain after neutralization.
The exact step by step method
- Find moles of weak base initially present.
Moles base = Molarity of base × Volume of base in liters. - Find the acid volume needed to reach equivalence.
At equivalence, moles strong acid added = initial moles weak base. - Compute the total volume at equivalence.
Total volume = initial base volume + acid volume added. - Determine the concentration of the conjugate acid.
At equivalence, all of the original base becomes BH+, so concentration of BH+ = initial base moles / total volume. - Convert Kb to Ka.
Ka = Kw / Kb - Solve the weak acid equilibrium for BH+.
BH+ + H2O ⇌ B + H3O+ - Calculate pH.
If [H3O+] = x, then pH = -log10(x).
Many textbooks use the weak acid shortcut x ≈ √(KaC) when Ka is small relative to concentration C. That works well for many classroom problems. A more rigorous method solves the quadratic equation:
x = (-Ka + √(Ka² + 4KaC)) / 2
This calculator uses the exact quadratic form for the equivalence point, which improves accuracy and avoids small approximation errors for dilute systems.
Worked example with ammonia
Suppose you titrate 50.0 mL of 0.100 M NH3 with 0.100 M HCl. The base dissociation constant for ammonia is approximately 1.8 × 10-5 at 25 C.
Step 1: moles of NH3
0.100 mol/L × 0.0500 L = 0.00500 mol NH3
Step 2: acid volume at equivalence
Because HCl reacts 1:1 with NH3, you need 0.00500 mol HCl. At 0.100 M:
Volume = 0.00500 mol / 0.100 mol/L = 0.0500 L = 50.0 mL
Step 3: total volume
50.0 mL base + 50.0 mL acid = 100.0 mL total = 0.1000 L
Step 4: concentration of NH4+
All 0.00500 mol NH3 becomes NH4+, so:
[NH4+] = 0.00500 mol / 0.1000 L = 0.0500 M
Step 5: convert Kb to Ka
Ka = (1.0 × 10-14) / (1.8 × 10-5) = 5.56 × 10-10
Step 6: solve acid equilibrium
NH4+ + H2O ⇌ NH3 + H3O+
Using the weak acid approximation:
x ≈ √(KaC) = √((5.56 × 10-10)(0.0500)) = 5.27 × 10-6
Step 7: pH
pH = -log10(5.27 × 10-6) ≈ 5.28
That is the classic result: the equivalence point for NH3 titrated with strong acid is acidic.
Common weak bases and their effect on equivalence point pH
The stronger the weak base, the weaker its conjugate acid, and the closer the equivalence point pH is to 7. The table below compares several commonly discussed weak bases using the same starting condition: 50.0 mL of 0.100 M base titrated to equivalence with 0.100 M strong acid at 25 C.
| Weak base | Kb at 25 C | Conjugate acid Ka | [Conjugate acid] at equivalence | Approximate pH at equivalence |
|---|---|---|---|---|
| Ammonia, NH3 | 1.8 × 10-5 | 5.56 × 10-10 | 0.0500 M | 5.28 |
| Methylamine, CH3NH2 | 5.6 × 10-4 | 1.79 × 10-11 | 0.0500 M | 6.02 |
| Ethylamine, C2H5NH2 | 4.4 × 10-4 | 2.27 × 10-11 | 0.0500 M | 5.97 |
| Pyridine, C5H5N | 3.0 × 10-6 | 3.33 × 10-9 | 0.0500 M | 4.89 |
| Dimethylamine, (CH3)2NH | 6.4 × 10-4 | 1.56 × 10-11 | 0.0500 M | 6.05 |
This comparison highlights a useful exam rule: if Kb is larger, the equivalence point pH usually rises closer to neutral, assuming similar concentrations and volumes.
How temperature changes the calculation
Many classroom problems assume 25 C, where Kw is 1.0 × 10-14. In more advanced chemistry, analytical chemistry, or environmental science work, temperature matters because Kw changes with temperature. That means the Ka derived from Kb also shifts when temperature changes. If your instructor or lab manual gives a nonstandard temperature, do not automatically use 1.0 × 10-14 unless you are told to do so.
| Temperature | Typical pKw value | Typical Kw value | Neutral pH at that temperature |
|---|---|---|---|
| 0 C | 14.94 | 1.15 × 10-15 | 7.47 |
| 25 C | 14.00 | 1.00 × 10-14 | 7.00 |
| 37 C | 13.62 | 2.40 × 10-14 | 6.81 |
| 50 C | 13.26 | 5.50 × 10-14 | 6.63 |
If the problem specifically states 25 C, use the standard Ka = 1.0 × 10-14 / Kb relation exactly as shown in this calculator. If not, ask whether a different Kw must be used.
Most common mistakes students make
- Assuming pH = 7 at equivalence. This is incorrect for weak base plus strong acid titrations.
- Using the original base concentration after mixing. At equivalence, dilution matters. Always use total volume.
- Using Kb directly to calculate pH. At equivalence, the base is gone. You must calculate the acid behavior of the conjugate acid with Ka.
- Forgetting the 1:1 stoichiometry. In most simple monoprotic strong acid titrations of a weak base, moles acid added at equivalence equal initial moles base.
- Ignoring units. Volumes must be converted from mL to L before using molarity equations.
- Applying Henderson-Hasselbalch at equivalence. The buffer equation works before equivalence when both base and conjugate acid are present in meaningful amounts. At equivalence, the original weak base has been fully consumed.
Practical interpretation of the titration curve
A weak base titration curve starts above pH 7 because the solution is initially basic. As strong acid is added, a buffer region forms where both the weak base and its conjugate acid coexist. Near half equivalence, the pOH equals pKb, which is a useful checkpoint when sketching or verifying the curve. As you approach equivalence, the pH drops more sharply. However, unlike a strong base titration, the vertical jump is centered below 7 because the solution at equivalence contains an acidic salt.
After equivalence, any additional strong acid directly controls the pH, and the pH falls rapidly as excess hydronium accumulates. The chart generated by this calculator illustrates exactly that shape. It is especially useful for checking whether your answer makes chemical sense. If your graph suggests a basic pH at equivalence for a weak base titrated by strong acid, you should review your setup.
Quick formula summary
- Initial moles of weak base: n = Cb × Vb
- Equivalence acid volume: Va,eq = n / Ca
- Total volume at equivalence: Vtotal = Vb + Va,eq
- Conjugate acid concentration: Cacid = n / Vtotal
- Convert Kb to Ka: Ka = Kw / Kb
- Hydronium from conjugate acid: x = (-Ka + √(Ka² + 4KaCacid)) / 2
- Final pH: pH = -log10(x)
If you memorize only one idea, memorize this: at the equivalence point of a weak base and strong acid titration, calculate the pH from the conjugate acid formed, not from the original weak base.
Authoritative references for deeper study
If you want to study acid base equilibrium, water ionization, and pH concepts from trusted institutions, these resources are useful starting points:
These references are valuable for confirming broader acid base principles, standard pH behavior, and equilibrium concepts that support the equivalence point calculation shown above.