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Henderson-Hasselbalch Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jan 18, 2024


Our Henderson-Hasselbalch calculator allows you to calculate the pH of a buffer solution, as well as find the concentration of the acid, and conjugate base found within it.

In the article below, we will acquaint you with the theory, and teach you how to use of the Henderson-Hasselbalch equation to calculate the pH of a biochemical process.

To learn more about the pH go to the pH calculator.

How to use the Henderson-Hasselbalch calculator?

To use the Henderson-Hasselbalch equation calculator, you'll need the following data:

  • [A⁻] – the molar concentration of the conjugate base;
  • [HA] – the molar concentration of the acid; and
  • pK – the acid's dissociation constant (the pK is equal to the pH when half of the acid is dissociated).

Now that you have your result, what can you use it for?

  • The method presented in our buffer pH calculator allows you to compute the pH of both arterial and venous blood! 🩸 (Phosphate and bicarbonate ions are the main buffers in these physiological fluids.)

  • You may also use it to calculate the ratio of deprotonated to protonated amino acids. Carboxyl (-COOH) and amine (-NH2) functional groups are acids and bases respectively, which creates a buffer solution.

How to use the Henderson-Hasselbalch equation?

The Henderson-Hasselbalch equation for pH looks like this:

pH = pKₐ + log([A⁻]/[HA])

It's time for a small bit of math revision: p is a symbol for a negative logarithm, with a base of 10 (for example, pH = -log₁₀(H)).

The HH equation is used for calculating the pH and concentration of a buffer – a solution that consists of a strong acid and a weak, conjugate base, or a strong base and a weak, conjugate acid.

  • The acid can be described as a proton donor (contains a particle of hydrogen: H); and
  • The base is a proton acceptor (is willing to accept a particle of hydrogen: ⁻).

Every acid dissociates into anions and cations when dissolved in water, HA ⇌ H⁺ + A⁻. That's how we can create a conjugate pair of acids & bases. The equilibrium constant (K) for this equation looks as follows:

K = [H⁺][A⁻]/[HA]

The p of the K constant (pK), as mentioned above, is equal to the pH of a solution that contains precisely the same amount of dissociated and undissociated acid, [A⁻] = [HA].

Did you know the Henderson-Hasselbalch equation is also crucial in determining the isoelectric point of a substance? Learn more in the isoelectric point calculator.

Henderson-Hasselbalch equation derivation

We must start with the equation presented above:

K = [H⁺][A⁻]/[HA]

Let's divide it by [H⁺] and K:

1/[H⁺] = [A⁻]/([HA][K])

Now let's separate K:

1/[H⁺] = 1/K × [A⁻]/[HA]

It's time to add some logarithms:

log(1/[H⁺]) = log(1/K) × log([A⁻]/[HA])

Substitute log(1/X) to pX:

pH = pKₐ + log([A⁻]/[HA])

That's it! You got it. 👍

You can also modify it a little bit further to receive, for example, the Henderson-Hasselbalch equation for base concentration:

p[A⁻] = pK + log([H⁺]/[HA])

Buffer pH in the calculator's results

The buffer capacity is the ability of the buffer to maintain its pH. The buffer capacity is largest when the pH is not so different from the pK (range: ± 1).

Once you complete everything that the Henderson-Hasselbalch calculator has to offer, you may also want to play with buffers and pH using our titration calculator. ⚗️

FAQ

How do I calculate Henderson-Hasselbalch equation?

Follow along these steps to calculate the Henderson-Hasselbalch equation:

  1. Determine the negative log in base 10 of the acid dissociation constant (Ka).
  2. Divide the concentration of conjugate base([A]) by conjugate acid ([HA]).
  3. Calculate the log of the result from step 2.
  4. Add the result from step 3 to step 1.
  5. The result is the pH of the solution.

How do I find the conjugate base?

The conjugate base of an acid is the acid with one less hydrogen. For instance, hydrochloric acid (HCl), when dissolved in water, produces H+ and Cl ions. Here, the conjugate base of HCl is Cl.

What is the Henderson-Hasselbalch equation used for?

The Henderson-Hasselbalch equation has its uses mainly in determining pH, ranging from a buffer solution to the pH of our blood.

You can also use the equation to determine the ratio of salt to acid. As well as the concentration of acid and salt, or base and salt in a known buffer solution.

If A and HA are 0.7M and 0.5M, what is the pH of the solution?

The pH value of the solution is 5, considering the Ka value is 1.4×10−5.

Let's calculate it using the formula:

pH = pKa + log([A]/[HA])

pH = −log10(Ka) + log([A]/[HA])

pH = −log10(1.4×10−5) + log(0.7/0.5)

pH = 4.854 + 0.146

pH = 5

Łucja Zaborowska, MD, PhD candidate
Conjugate base [A⁻]
M
Acid [HA]
M
Kₐ
pH
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