pKa to pH Formula & How to Use It

This calculator converts a given pKa value and the concentrations of a weak acid and its conjugate base into the pH of the buffer solution using the Henderson–Hasselbalch equation. You enter the pKa, the acid concentration, and the base concentration, and you get the resulting pH. The same formula also works in reverse: enter pH and one concentration to find the other.

Formula

The relationship between pKa and pH is given by the Henderson–Hasselbalch equation:

pH = pKa + log�₀([A�] / [HA])

• pH – acidity of the solution (no unit, typically 0–14)
• pKa – acid dissociation constant expressed as a logarithm (no unit)
• [Aâ�»] – molar concentration of the conjugate base (mol/L)
• [HA] – molar concentration of the weak acid (mol/L)

The pKa itself is defined as pKa = –log�₀(Ka), where Ka is the acid dissociation constant. A lower pKa means a stronger acid.

Worked Example

Using the default values from the calculator (pKa = 4.75, acid = 0.10 mol/L, base = 0.10 mol/L):

1. Write the equation: pH = 4.75 + log�₀(0.10 / 0.10)
2. Compute the ratio: 0.10 / 0.10 = 1.0
3. Take the logarithm: log�₀(1.0) = 0
4. Add: pH = 4.75 + 0 = 4.75

So the pH equals the pKa when the acid and base concentrations are equal. That is exactly what the calculator returns: 4.75.

When to Use the Henderson–Hasselbalch Equation

This equation is most useful for buffer solutions—mixtures of a weak acid and its conjugate base (or a weak base and its conjugate acid). It gives a quick estimate of pH without solving a full equilibrium problem. It is widely used in biochemistry labs to prepare buffers at a target pH, in titrations to estimate the pH at the half-equivalence point, and in physiology to understand blood pH regulation (the bicarbonate buffer system uses pKa ≈ 6.1).

You can also use it to find the pKa from a known pH and concentration ratio, or to find the ratio of base to acid needed to achieve a desired pH. For example, to make a buffer at pH 5.00 with acetic acid (pKa 4.75), you would need [A�]/[HA] = 10^(5.00 – 4.75) = 10^0.25 ≈ 1.78.

How to Choose the Right pKa Value

Every weak acid has its own pKa. Common values include:

• Acetic acid: 4.75
• Citric acid (first dissociation): 3.13
• Phosphoric acid (first dissociation): 2.15
• Tris (a common biological buffer): 8.07 at 25°C
• Carbonic acid (first dissociation): 6.35

When selecting a buffer, choose an acid whose pKa is within ±1 unit of the desired pH. Buffers work best near their pKa because the pH changes least when small amounts of acid or base are added. Many pKa values are temperature-dependent, so check the value at your working temperature if precision matters.

Common Mistakes and Misconceptions

• Using the equation for strong acids or bases. The Henderson–Hasselbalch equation assumes a weak acid/base equilibrium. For strong acids (like HCl), the pH is simply –logâ‚�â‚€(concentration), and the pKa is very negative.
• Forgetting that concentrations must be in mol/L. If you use millimolar (mM) values, the ratio still works because the units cancel, but mixing units (e.g., mM for acid and M for base) will give a wrong ratio.
• Assuming pH = pKa always. This is only true when [Aâ�»] = [HA]. At other ratios, the pH differs by the log of the ratio.
• Ignoring the “x is smallâ€� approximation. The equation neglects the small amount of acid that dissociates. For very dilute solutions (<0.001 M) or very strong acids, the approximation fails and you need the full quadratic solution.
• Confusing pKa with pH. pKa is a property of the acid; pH is a property of the solution. They are equal only at the half-equivalence point of a titration.

Limits of the Formula

The Henderson–Hasselbalch equation is an approximation. It works well when the acid is weak (Ka < 10�³) and when both [HA] and [A�] are much larger than the hydronium ion concentration. In very dilute solutions, the autoionization of water becomes significant, and the equation underestimates or overestimates pH. Also, at extreme pH values (below 0 or above 14), the assumptions break down. For precise work, especially in analytical chemistry, you should solve the full equilibrium expressions including charge balance and mass balance.

Practical Tips for Buffer Preparation

1. Decide the target pH and choose a weak acid with pKa within 1 unit of that pH.
2. Calculate the required ratio [A�]/[HA] = 10^(pH – pKa).
3. Prepare solutions of the acid and its conjugate base at the same molarity (e.g., 0.1 M each).
4. Mix them in the volume ratio that gives the desired concentration ratio. For example, if the ratio is 2:1 base:acid, mix 2 volumes of base with 1 volume of acid.
5. Verify the pH with a calibrated pH meter and adjust with small amounts of strong acid or base if needed.

Remember that the buffer capacity—the amount of acid or base the buffer can absorb—is greatest when [A�] = [HA], i.e., when pH = pKa. The useful range is roughly pH = pKa ± 1.

Frequently Asked Questions

How do I calculate pH from pKa and concentration?

Use the Henderson–Hasselbalch equation: pH = pKa + log�₀([A�]/[HA]). Plug in the pKa and the molar concentrations of the conjugate base and weak acid. If you only have the acid concentration and Ka, first compute pKa = –log�₀(Ka), then use the equation.

Can I use the Henderson–Hasselbalch equation for strong acids?

No. Strong acids dissociate completely, so the pH is simply –log�₀(concentration). The equation assumes a weak acid equilibrium where the acid and its conjugate base coexist. Using it for a strong acid gives incorrect results.

What is the difference between pKa and pH?

pKa is a measure of acid strength—it is the pH at which half of the acid is dissociated. It is a constant for a given acid at a given temperature. pH measures the actual acidity of a solution and varies with concentration. They are equal only when the acid and conjugate base concentrations are equal.

Why does pH equal pKa at the half-equivalence point?

At the half-equivalence point of a titration, exactly half of the acid has been neutralized, so [A�] = [HA]. Plugging that into the equation gives log�₀(1) = 0, so pH = pKa. This is a common way to experimentally determine pKa.

Does temperature affect the pKa to pH calculation?

Yes. pKa values change with temperature because the equilibrium constant Ka changes. For example, the pKa of Tris buffer decreases about 0.03 units per degree Celsius increase. Always use the pKa value at your working temperature for accurate pH predictions.

What if I only know the pH and pKa—can I find the ratio of base to acid?

Yes. Rearrange the equation to [A�]/[HA] = 10^(pH – pKa). For instance, if pH = 5.00 and pKa = 4.75, the ratio is 10^0.25 ≈ 1.78. This tells you how many moles of conjugate base you need per mole of acid.

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in pka | pKa | - | 4.75 | 0
in acid | Acid concentration | mol/L | 0.10 | 0
in base | Base concentration | mol/L | 0.10 | 0
out ph | pH | - | pka + log10(base / acid) | 2