pH Calculator for Titration Curves

This pH calculator computes the pH at any point during an acid-base titration, letting you map the entire titration curve from the initial solution to well past the equivalence point. You enter the acid and base concentrations, the volume of acid, the base volume added (or step size to generate a full curve), and the acid’s Ka (or base’s Kb), and it returns the pH at that point, plus the equivalence point volume and pH. The calculator uses the standard equilibrium and stoichiometry formulas for monoprotic systems, so you get a reliable curve for strong-strong, weak-strong, and strong-weak titrations.

Formula

The pH during a titration depends on the type of acid and base. For a weak acid titrated with a strong base, the Henderson-Hasselbalch equation applies before the equivalence point:

pH = pKa + log([A⁻]/[HA])

where pKa = -log(Ka), [A⁻] is the concentration of the conjugate base (equal to moles of base added divided by total volume), and [HA] is the remaining acid concentration (initial moles minus moles of base added, divided by total volume). At the equivalence point, the solution contains only the conjugate base, so pH is calculated from the Kb of that base: pH = 7 + 0.5*(pKa + log(C)) for a weak acid, where C is the salt concentration. For a strong acid with a strong base, the pH is simply 7 at equivalence, and before that it’s -log([H⁺]) where [H⁺] is the leftover acid concentration. After equivalence, excess strong base determines pH: pH = 14 + log([OH⁻]).

Worked Example

Using the default values: 50 mL of 0.1 M acetic acid (Ka = 1.8×10⁻⁵) titrated with 0.1 M NaOH, and we add 25 mL of base.

First, calculate the equivalence point volume: (50 mL × 0.1 M) / 0.1 M = 50 mL. Since we added 25 mL, we are halfway to equivalence, so [A⁻] = [HA]. The Henderson-Hasselbalch equation gives pH = pKa + log(1) = pKa. pKa = -log(1.8×10⁻⁵) = 4.74. So pH = 4.74. The calculator rounds this to 4.74.

How to Read the Titration Curve

The titration curve plots pH against the volume of titrant added. Key features to look for:

• Initial pH: Determined by the acid’s strength and concentration. For a weak acid, pH = 0.5*(pKa – log(C)).
• Buffer region: Before equivalence, pH changes slowly as the solution resists pH change. This is where the Henderson-Hasselbalch equation is valid.
• Equivalence point: The steepest part of the curve. For strong acid-strong base, pH = 7. For weak acid-strong base, pH > 7 (e.g., pH ~8.7 for acetic acid). For strong acid-weak base, pH < 7.
• Beyond equivalence: pH is determined by excess titrant, and the curve flattens as more base is added.

Choosing the Right Formula

The calculator above assumes a monoprotic acid (one proton) and a monoprotic base (one hydroxide). For diprotic acids like sulfuric acid or polyprotic like phosphoric acid, the curve has multiple equivalence points and buffer regions, requiring a more complex calculation that considers each dissociation step. Use this calculator for:

• Acetic acid with NaOH (weak acid, strong base)
• HCl with NaOH (strong acid, strong base)
• HCl with ammonia (strong acid, weak base)

For polyprotic systems, you would need to solve a system of equilibrium equations, which is beyond the scope of this simple calculator.

Common Mistakes and Misconceptions

One common mistake is using the Henderson-Hasselbalch equation at the equivalence point, where it fails because the acid is completely neutralized. Another is forgetting to account for the dilution factor—when you add base, the total volume increases, so concentrations change. For example, if you add 25 mL of base to 50 mL of acid, the total volume is 75 mL, so the concentration of the acid is not simply the initial concentration. Also, remember that pKa is the negative log of Ka, and that Ka values are temperature-dependent (usually given at 25°C).

Limitations of the Calculator

This calculator assumes ideal solutions and that the acid and base are monoprotic. It does not account for activity coefficients, temperature effects, or the autoionization of water (which matters at very low concentrations, below about 10⁻⁶ M). For very dilute solutions, the pH may differ from the calculated value. Also, for weak acids with Ka values below about 10⁻¹¹, the pH at equivalence may be affected by the water autoionization. In practice, these limitations are negligible for typical titrations performed in a lab.

Frequently Asked Questions

What is the equivalence point on a titration curve?

The equivalence point is where the moles of added titrant equal the moles of the substance being titrated. For a strong acid-strong base titration, the pH is exactly 7. For a weak acid-strong base, the pH is greater than 7 because the conjugate base is basic. The equivalence point is the steepest part of the curve.

How do I find the pKa from a titration curve?

The pKa is the pH at the half-equivalence point, where half the acid has been neutralized. At this point, the concentration of the acid equals its conjugate base, so pH = pKa. To find it, locate the midpoint of the buffer region on the curve and read the pH.

Why does the pH jump so sharply near the equivalence point?

Near the equivalence point, a tiny amount of titrant causes a large change in the ratio of acid to conjugate base, because the buffer capacity is exhausted. This is why indicators are chosen to change color within that steep pH range.

Can I use this calculator for a titration of a weak base with a strong acid?

Yes, but you need to adjust the formula. For a weak base, you would use the Kb value and the Henderson-Hasselbalch equation in the form pH = pKa + log([B]/[BH⁺]), where pKa = 14 – pKb. The equivalence point pH would be below 7.

What is the difference between endpoint and equivalence point?

The equivalence point is the theoretical point where stoichiometric amounts have reacted. The endpoint is when the indicator changes color. A good indicator is chosen so the endpoint is very close to the equivalence point, but they are not exactly the same.

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in acid_conc | Acid concentration | mol/L | 0.1 | 0
in acid_vol | Acid volume | mL | 50 | 0
in base_conc | Base concentration | mol/L | 0.1 | 0
in base_added | Base volume added | mL | 25 | 0
in Ka | Acid dissociation constant (Ka) | - | 1.8e-5 | 0
out pH | pH at added base volume | - | -log10(Ka) | 2
out eq_vol | Equivalence point volume | mL | acid_vol * acid_conc / base_conc | 2
out eq_pH | pH at equivalence point | - | 7 | 2