# 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.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## 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 · 12:00 AM

Last Checked: May 4, 2020

Next Review: May 4, 2025