# Henderson-Hasselbalch Calculator

By Łucja Zaborowska, MD
Last updated: Jun 01, 2020

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.

## 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 the 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 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 like 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]`.

## Henderson-Hasselbalch equation derivation

`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 logarithm:

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

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