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Henderson-Hasselbalch Equation

Henderson-Hasselbalch Equation- Core Concepts

In this tutorial, you will learn what the Henderson-Hasselbalch equation is, how to use the equation to determine the pH of a buffer, how to derive the equation, and how to solve some example problems

What is the Henderson Hasselbalch Equation?

The Henderson-Hasselbalch equation is used to determine the pH of a buffer system.

The Ka is the acid dissociation constant, and pKa is the negative log of Ka. [Conjugate Base] is also commonly written as [A-]. And [Weak Acid] may be seen as [HA]. These values refer to the equilibrium concentration.

If you have the same concentration of acid and conjugate base, then the pH will be the same as the pKa because the log(1) = 0.

If [HA] = [A], then

Derivation of the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation can be derived from the Ka of a weak acid. Here we will assume we have a weak acid, HA, and its conjugate base, A. In water the following dissociation occurs:

derivation Henderson-Hasselbalch equation

Therefore, the acid dissociation constant is defined as

Which can be rearranged to

Then take the log of both sides

Henderson-Hasselbalch equation derivation

Multiply by -1 so that in the next step we can substitute in for pH.

Henderson-Hasselbalch equation derivation log

Based on the definition of pH = -log [H3O+] we can substitute into our equation

pH Henderson-Hasselbalch equation derivation

And then use logarithm rules to simplify the right side

derivation of Henderson-Hasselbalch equation pH

Knowing that pKa = -log(Ka), we can substitute that into our previous equation to arrive at the Henderson-Hasselbalch equation

Henderson-Hasselbalch equation

Example Problems of Henderson Hasselbalch Equation

Determining Buffer Ratio

Suppose we are making a buffer solution of ammonium (NH4+) and ammonia (NH3). In this example, ammonium is our weak acid and ammonia is the conjugate base. The reaction is as follows.

ph Buffer Henderson-Hasselbalch equation example

If the pKa of ammonium is 9.3 and we want a pH of 10. What ratio of ammonia to ammonium should be added to the solution?

The problem asks for a ratio, so we are looking for the value of , or  for this specific buffer solution. To solve the problem, start by plugging in the known values– pH and pKa.

ph Buffer Henderson-Hasselbalch equation example

Subtract 9.3 from each side to simplify

ph Buffer Henderson-Hasselbalch equation example

The ratio we are looking for is within the logarithmic term. To get rid of the log we can use logarithmic rules to simplify.

ph Buffer Henderson-Hasselbalch equation example

Therefore, the ratio is about 5 times the amount of ammonia as ammonium to get a buffer solution with a pH of 10.

Determining pH

Use the Henderson-Hasselbalch equation to determine the pH of a buffer solution made up of 0.15 M CH3COO and 0.20 M CH3COOH. The pKa of acetic acid (CH3COOH) is 4.75.

To solve this example problem, we want to start with the Henderson-Hasselbalch equation since we are looking at a buffer solution of a weak acid and conjugate base.

determining ph Buffer example Henderson-Hasselbalch equation

Then plug the known values into our equation

determining ph Buffer example Henderson-Hasselbalch equation

Then simplify and solve

determining ph Buffer example Henderson-Hasselbalch equation

Our buffer solution of acetic acid has a pH of 4.63.

Limitations of the Henderson-Hasselbalch Equation

  1. When using the Henderson-Hasselbalch to make a buffer solution the ratio of [A]/[HA] should be close to one. This makes the most stable solution. When the ratio moves far away from one, the capacity to buffer the solution decreases as a small disturbance changes the pH dramatically.
  2. This pH equation does not account for the self-dissociation of water. At very low concentrations of buffer, water can contribute to the pH
  3. If an acid can easily dissociate more than one hydronium ion (H+) the equation does not account for that and may not work well.
  4. Practically when making specific pH buffers, it is important to have the pKa be close to the target pH to have the biggest range of buffering capability.

Fun Facts:

  1. The equation is named after Lawrence Joseph Henderson and Karl Albert Hasselbalch. Henderson made the original equation in 1908. Then in 1917 Hasselbalch put the formula into logarithmic terms and the way it is most seen today.
  2. The Henderson-Hasselbalch equation has important biological relevance. Many biological samples must be kept at a specific pH. So, when samples are prepared the Henderson-Hasselbalch equation is used to prepare a buffer that will help proteins and other pH sensitive molecules to maintain their structure.
  3. The equation can also be written for the pOH of a buffer system.
Henderson-Hasselbalch equation for pOH buffer

The [Conjugate Acid] is also referred to as [HB+]. And the [Weak Base] is also referred to as [B]. Try checking your understanding by going through the derivation for the pOH version of the equation.

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