**Henderson–Hasselbalch Equation**

*How to Derive Henderson Hasselbalch Equation?*

Henderson-Hasselbalch equation is a simple expression which relates the * pH*,

*and the buffer action of a weak acid and its conjugate base. The Henderson-Hasselbalch equation also describes the characteristic shape of the titration curve of any weak acid such as acetic acid, phosphoric acid, or any amino acid. The titration curve of a weak acid helps to determine the buffering*

**pKa***pH*which is exhibited around the

*pKa*of that acid. For example, in the case of acetate buffer, the

*pKa*is 4.76. This is the best buffering

*pH*of acetic acid. Besides, at this

*pH*the acetic acid (CH

_{3}COOH) and acetate ions (CH

_{3}COO¯) will be at equimolar concentration in the solution. This equimolar solution of a weak acid and its conjugate base will resist the change in

*pH*by donating or taking up the H⁺ ions.

*(*

*pH is the negative logarithm of hydrogen ion concentration in a medium.The pKa is the negative logarithm of Ka. The Ka is the dissociation constant (similar to the equilibrium constant) for the ionization reaction of an acid.)*

**Learn more:** Titration Curve of a Weak Acid (Acetic Acid)

In the present post, we will see the derivation of Henderson-Hasselbalch equation from the ionization reaction of a weak acid. We also discuss the significance of Henderson-Hasselbalch equation.

**Deriving Henderson-Hasselbalch Equation**

Take the ionization reaction of a weak acid (HA):

The dissociation constant ** Ka **of the above reaction will be:

*Dissociation constant is the ratio of the concentration of products by the concentration of reactants. The square brackets, [ ], denote ‘concentration’.*

Then from the equation (2) take out the** [H⁺]** to the left side (solve for H⁺):

Then take the negative logarithm of both sides:

We know that the – log [H⁺] is * pH* and the – log Ka is

**pKa.**Substitute the ** pH **and

**in the equation (4):**

*pKa*Now invert the **-log [HA]/[A¯]**, which involves changing its sign to obtain the **Henderson-Hasselbalch** equation.

**[A¯]** is the concentration of proton acceptor (it can accept the proton in a buffer)

**[HA]** is the concentration of proton donor (it can donate a proton in the buffer)

Thus the equation (6) can be better stated as:

The above equation is called the **Henderson-Hasselbalch** equation.

**Uses of Henderson-Hasselbalch Equation**

**Uses of Henderson-Hasselbalch Equation**

The Henderson–Hasselbalch is mainly used for calculating the pH or pKa of a solution containing known quantities of a weak acid and its conjugate base.

**Learn more:** Biochemistry Solved Problems – pH, pKA and Henderson-Hasselbalch Equation.

At the midpoint of the titration curve of a weak acid, the concentration HA (proton donor) equals the concentration of A¯ (proton acceptor). We have already stated that for a buffer the best buffering *pH* is at its *pKa.* (Also remember, the buffer is a mixture of equimolar concentration of weak acid and its conjugate base).

Let’s put it in the Henderson-Hasselbalch equation

Since the concentration of proton acceptor **(A¯)** and proton donor **(HA)** is uniform in the midpoint of titration, the value becomes log 1.

Thus the equation becomes **pH = pKa + log 1**

**log 1 = 0**

Thus **pH = pKa + 0**

= **pH = pKa**

**This also proved that for a buffer, the best buffering activity is obtained at the pH value equal to its pKa value.**

* References: *Lehninger A.B., (2018), Textbook of Biochemistry, Ed. 5, Pearson International, New York

**<< Back to Biochemistry Lecture Notes**

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@. Titration Curve of Weak Acid

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