Henderson Hasselbalch Equation

Introduction

Henderson Hasselbalch was derived by Lawrence Joseph Henderson in 1908. The equation is used for the calculation of the pH of the buffer solution. Karl Albert Hasselbalch then in 1917 rewrote the equation in the logarithmic form. The logarithmic form of this equation is more used. A buffer solution is the combination of an acid and a salt. The property of the buffer solution is that the pH of the buffer mixture will not change with the addition of acid or base.

That is, they are resistant to the change in pH. The calculation of hydrogen ion concentration thereby checking the acidity of buffer solution is tough. But it has been made easy by the coming of Henderson Hasselbalch equation.

What is Henderson Hasselbalch Equation?

The Henderson Hasselbalch equation is an important equation in acid-base chemistry that can be used for the calculation of the pH of a buffer solution. Buffer solutions are very resistant to changes in pH. Buffer solution always has a constant Hydrogen ion concentration, and it does not change with the addition of base or acids. The equation gives the relation between the pH of an acid solution and the corresponding acid dissociation constant. And thereby calculating the pH of buffer solutions. The equation is,

$$\mathrm{pH\:=\:pKa\:+\:\log\:([conjugate\:base]/[weak\:acid])}$$

$$\mathrm{pH\:=\:pKa\:+\:\log[A^{-}]/[HA]}$$

The terms demonstrated above are [HA] is the concentration of weak acid and [𝐴−] is the concentration of conjugate base formed by the loss of protons. Only an approximate value of pH is calculated with the help of this equation. The value will not be accurate and varies by a small amount. The calculation of pH of strong acids and bases cannot be evaluated. The main advantage of this equation is that the calculation of pH of buffer solution is impossible because of its resistance against pH change and also, they remain undisturbed by making them dilute but has become possible with the help of this equation. It is commonly known by the name Henderson equation.

Theory for the Henderson Hasselbalch Equation

Henderson Hasselbalch equation is utilized for the estimation of pH of buffer solution by chemists and biologists.

• The equation gives a proper association between pH and pOH of a solution and pKa and pKb.

• The pH of the bicarbonate buffer system in the blood is first determined with the help of this equation.

• It is a kinetic analysis that helps in the calculation of the acidity of a buffer solution that is thought to be impossible.

• It is an important equation in acid-base chemistry.

• This is even used for the calculation of pH needed for making a corresponding buffer solution.

Applications of the Henderson Hasselbalch Equation

There is much application for this equation. Some of the important applications are pointed out below.

• It can be used for the calculation of a pH with the help of the pKa value of different solutions.

• This equation can be used for the calculation of a concentration of unionized and ionized chemicals.

• The pKa value of solutions can be calculated with the help of the pH value.

• Solubility can be calculated with the help of pH obtained from the equation.

• The isoelectric point of a protein is calculated with the help of this equation.

• It is used for the determination of the protonation state of biomolecules.

More About the Henderson Hasselbalch Equation

Henderson Hasselbalch also has some other characteristic properties and are,

• This equation can be used for the determination of the pH effect over a buffer solution when a slight quantity of acid or a base is added to the buffer.

• This equation also describes the buffer solution.

• It will also describe the relative strength of conjugate acids and bases.

• The equation is a breakthrough in acid-base chemistry as it calculates the pH of buffer solutions.

Derivation of the Henderson Hasselbalch Equation

The Henderson Hasselbalch equation can be developed by taking an example of the dissociation of a weak acid, HA. The dissociation is,

$$\mathrm{Ha\:+\:H_{2}O\:\leftrightarrows\:A^{-}\:+\:H_{2}O^{+}}$$

Then the dissociation constant Ka can be calculated as,

$$\mathrm{ka\:=\:[a^{-}][H_{3}O^{+}]/[HA]}$$

$$\mathrm{ka[HA]/[A^{-}]\:=\:[H_{3}O^{+}]}$$

$$\mathrm{[H_{3}O^{+}]\:=\:ka[HA][A^{-}]}$$

Taking logarithm on both sides. The equation changes to,

$$\mathrm{\log\:[H_{3}O^{+}]\:=\:\log\:ka\:+\:\log\:[HA]/[A^{-}]}$$

Multiplying the above equation with -1 will result in the equation,

$$\mathrm{-\log\:[H_{3}O^{+}]\:=\:-\log\:ka\:-\:\log\:[HA]/[A^{-}]}$$

And it is known that,

$\mathrm{pH\:=\:-\log\:[H_{3}O^{+}]}$

And, $\mathrm{pka\:=\:-\log\:ka}$

So the substitution of these values in the above equation results in the equation,

$$\mathrm{pH\:=\:pka\:+\:\log\:[A^{+}]/[HA]}$$

This equation is the Henderson Hasselbalch equation. And is used for the estimation of the pH of buffer solution. When the concentration of acid and conjugate base is the same the pH and pKa will be equal. That is,

$$\mathrm{[HA]\:=\:[A^{+}]}$$

So, $\mathrm{[A^{+}]/[HA]\:=\:1}$

Thus, the Henderson Hasselbalch equation becomes,

$$\mathrm{pH\:=\:pka\:+\:\log\:1}$$

That is,

$$\mathrm{pH\:=\:pka}$$

This is another mathematical relationship obtained from the Henderson Hasselbalch equation and it can be used for the calculation of the pKa of chemical compounds.

Conclusion

The Henderson Hasselbalch equation is one of the important equations in the branch of chemistry, acid-base chemistry. The calculation of pH of buffer solution has become impossible several years ago. But it is made possible with the evolution of this equation. The form of this equation is most widely accepted for the calculation of the pH of the buffer solution. The equation tells a relationship between pH and pKa. It not only calculates the pH of the buffer it can be used for other applications such as concentration calculation, pKa value calculation, etc. It is derived with the help of pH calculation in the case of weak acids. And the equation is, $\mathrm{pH\:=\:pka\:+\:\log\:[A^{+}]/[HA]}$.

FAQs

1. What are the limitations of the Henderson-Hasselbalch equation?

Buffer solution of extremely dilute solution cannot be determined with the help of this equation since the self-dissociation of water is not considered in the equation. And also, it is not applicable for strong acids and bases.

2. Does volume matter in the Henderson-Hasselbalch equation?

The Henderson Hasselbalch equation only considers the concentration of acid and conjugate base. So, the equation is volume independent.

3. Why is buffer capacity important?

Buffer capacity is a term associated with buffer solution which is the resistance to pH change in a buffer solution. This means that how a buffer resists not undergoing any pH change by the addition of 𝐻+ or 𝑂𝐻− ions.

4. Why does diluting a buffer not change the pH?

The pH value of the buffer relies on the Ka and Kb values and these values do not vary with the change in pH. And also, the concentration of acid and salt will not change, so pH doesn't change with dilution.

5. What are the examples of buffers?

Examples of buffers are Carbonic acid with bicarbonate ion, Citric acid with sodium citrate, Acetic acid with sodium acetate, etc.