# Henderson-Hasselbalch Equation Calculator

Estimates the pH of a buffer solution when the Ka numerical value of the acid dissociation constant is known.

Refer to the text below the calculator for more information about the Henderson-Hasselbalch equation.

This equation was originally derived in 1908 by Lawrence Joseph Henderson and subsequently, in 1917, Karl Albert Hasselbalch re-expressed the formula in logarithmic terms.

It’s purpose is to help calculate the pH of a solution containing the acid and one of its salts, that is, of a buffer solution.

The Henderson-Hasselbalch equation is derived from the definition of the acid dissociation constant:

`pH = pK`

_{a} + log_{10}([A−] / [HA])

Where: `pK`

_{a} = - log_{10} (K_{a})

When the concentrations of the acid and the conjugate base are the same, i.e, when the acid is 50% dissociated, the pH of the solution is equal to the pKa of the acid.

The Henderson-Hasselbalch equation is an approximation, with a certain region of validity. Remember that it does not take into account the self-dissociation of water, which becomes increasingly important in dilute solutions.

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1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

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## About the Henderson-Hasselbalch equation

A simple buffer solution, that in 1908 Lawrence Joseph Henderson created an equation to determine the pH of, consists of a solution of an acid and a salt of the conjugate base of the acid.

One common example would be a buffer solution where the acid may be acetic acid and the salt may be sodium acetate.

The Henderson-Hasselbalch equation is derived from the definition of the acid dissociation constant and relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka, and the concentrations of the two components.

`pH = pK`

_{a} + log_{10}([A−] / [HA])

Where: `pK`

_{a} = - log_{10} (K_{a})

When the concentrations of the acid and the conjugate base are the same, i.e, when the acid is 50% dissociated, the pH of the solution is equal to the pKa of the acid.

The Henderson-Hasselbalch equation is an approximation, with a certain region of validity.

There are also some assumptions to be made:

- It does not take into account the self-dissociation of water, which becomes increasingly important in dilute solutions. This assumption is not valid with pH values more than about 10. For such instances the mass-balance equation for hydrogen must be extended to take account of the self-ionization of water.
- The acid is monobasic and dissociates according to the equation: HA = H
^{+}+ A^{-}where H^{+}stands for hydrated hydronium ion. - The salt MA is completely dissociated in solution.

## Reference

Henderson LJ. Concerning the relationship between the strength of acids and their capacity to preserve neutrality. Am. J. Physiol. 1908;21 (2): 173–179.

Specialty: Miscellaneous

No. Of Variables: 3

Article By: Denise Nedea

Published On: May 4, 2020

Last Checked: May 4, 2020

Next Review: May 4, 2025