# Buffer pH Calculator

Created by Davide Borchia
Last updated: Jul 10, 2022

Nature — and chemistry — provided us with a handy tool to keep in check the acidity of a solution: discover what it is and how to calculate a pH buffer solution.

• What is pH: a really brief introduction to acids and bases;
• What are pH buffer solutions;
• How to calculate the pH of a buffer solution: calculate the Henderson-Hasselbalch equation; and
• How to use our pH buffer solution calculator.

## What is pH?

The pH is a measure of the acidity or basicity of an aqueous solution. The pH is defined through the concentration of $\text{H}^+$ ions in the solution:

$pH = -\log{[\text{H}^+]}$

The presence of the $\text{H}^+$ ions is due to the dissociation of water in the presence of certain chemical species:

$2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$

We won't enter the details of acids and bases. It will suffice for you to know that:

• An acid is a chemical species that tends to donate protons to the solution;
• Water is neither acid nor basic (amphoteric); and
• A base is a species that accepts the protons.

## Acids and bases: introduction to pH buffer solutions

A pH buffer solution is an aqueous solution capable of maintaining its pH stable against the addition of small quantities of strong acids and bases.

This behavior is of fundamental importance in biological systems, where an ideal range of pH is often required to allow certain processes. The presence of a buffer solution ensures stability around the operating point of the reaction.

From a chemical point of view, a pH buffer solution is a mixture of a weak conjugate acid-base pair; there are two possible cases: a weak acid and its conjugate base or a weak base and its conjugate acid.

When we talk of conjugate acids and bases, we mean chemical species that, by transfer of a proton ($\text{H}^+$), can change their "nature" from acid to base.

To create a buffer solution, add an aqueous solution of the weak acid (base) plus a solution containing the salt of its conjugate base (acid). The result is a chemical equilibrium in the form:

$\text{A}\text{H}+\text{H}_2\text{O}\rightleftharpoons \text{A}^-+\text{H}_3\text{O}^+$

for an acid buffer solution. The chemical equation for a buffer solution created from a base is:

$\text{B}+\text{H}_2\text{O}\rightleftharpoons\text{BH}^++\text{OH}^-$

We call it alkaline buffer solution.

In both cases, we need to add a salt (usually either sodium or chlorine) to the solution in order to increase the molarity of the conjugates (they don't come only from the dissociation of the acid/base).

Let's now see how a pH buffer solution works and how it is stable against additions of acids and bases.

## How does a pH buffer solution work

Consider an acidic buffer solution. We can add a small amount of a diluted solution of a strong acid (which corresponds to a sharp increase in the concentration of $\text{H}^+$.

Our buffer solution will react to this addition by shifting its equilibrium. We can see the change in this part of the pH buffer solution equation:

$\text{A}^-+\text{H}^+\rightleftharpoons \text{AH}$

Thanks to the addition of hydronium ions, the equilibrium is highly moved towards the right: we added a strong acid, but the reaction returned us a weak one, effectively counteracting the reduction of pH.

Similarly, an addition of a base would cause an increase in the concentration of hydroxide ions. In this case, the following reaction helps reduce the effect of the addition:

$\text{AH}+\text{OH}^-\rightleftharpoons \text{A}^-+\text{H}_2\text{O}$

We added a strong base, and in return, we got the weak conjugate base of our pH buffer solution.

## How to use the Henderson-Hasselbalch equation to calculate the pH of a buffer solution

The operating range of a pH buffer solution is pretty limited: the counteracting abilities only work for certain values of pH, after which the solution would experience sharp changes in acidity.

This small range means that you have to carefully plan and calculate the pH of your buffer solution beforehand. The Henderson-Hasselbalch equation calculates exactly this.

The Henderson-Hasselbalch equation is:

$\text{pH}\approx\text{pK}_{\text{a}} +\log{\left(\frac{[\text{A}^-]}{[\text{AH}]}\right)}$

Where the pH of the buffer solution is calculated through the acid dissociation constant, $\text{pK}_{\text{a}}$, and the concentrations of the pair of conjugate acid and base.

🙋 Henderson had the idea to calculate the pH of a buffer solution using the acid dissociation constant; Hesselbalch put the math in it, later introducing the logarithm, making the approximation way more accurate.

We can define a similar equation for an alkaline buffer solution:

$\text{pOH}\approx\text{pK}_{\text{b}} +\log{\left(\frac{[\text{HB}^+]}{[\text{B}]}\right)}$

Don't worry about $\text{pOH}$: it's nothing but the complementary of $\text{pH}$:

$\text{pOH}=14-\text{pH}$

Since the acid and basic dissociation constant are specific values identifying the strength/weakness of the acidity/alkalinity of a chemical species, we can use these values to find the $\text{pH}$ of the final buffer solution.

However, it's likely that the best use of the Henderson-Hasselbalch equation is to calculate the desired values of the constants, which buffer at a definite value of $\text{pH}$.

## How to use our pH buffer solution calculator

We implemented the Henderson-Hesselbalch equation in a neat and easy-to-use tool: in a second, you will find out what the desired dissociation constant is, or you can calculate the $\text{pH}$ of a buffer solution if you already know the chemical species that will appear in it.

Select the nature of your buffer solution first: alkaline or acidic?

This choice will allow you to insert the correct values of at least three of the four variables. You can use our pH buffer calculator in many ways, directly to calculate the $\text{pH}$, or in reverse:

• Insert the $\text{pK}$ and the concentrations to find the $\text{pH}$;
• Insert the $\text{pH}$ and the concentrations to find the $\text{pK}$; or
• Insert $\text{pH}$, $\text{pK}$, and a concentration to find the concentration of the other member of the pair.

Davide Borchia
Check out our list of popular buffers and their pK's in the article to your right 👉
Buffer type
Acid
Ka
pKa
Acid concentration
M
Salt concentration
M
pH
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