Understanding pH in Buffer Solutions: A Comprehensive Guide

Buffer solutions play a crucial role in maintaining a stable pH environment in various scientific and industrial applications. In this article, we will explore the pH calculation of a specific buffer solution, made from a mixture of sodium hydrogen phosphate (NaH2PO4) and sodium dihydrogen phosphate (Na2HPO4), using the Henderson-Hasselbalch equation.

Introduction to Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a widely used formula in chemistry for calculating the pH of buffer solutions. It is particularly useful for understanding the behavior of weak acids and their conjugate bases in equilibrium.

Buffer Solution Composition

Consider a buffer solution prepared by mixing equal volumes of 0.1 M Na2HPO4 and 0.1 M NaH2PO4. This mixture will have equal concentrations of the conjugate base (HPO42-) and the acid (H2PO4-).

Relevant Dissociation and pKa

The relevant dissociation in this buffer system is the reaction of dihydrogen phosphate ion (H2PO4-) to form hydrogen ion (H ) and hydrogen phosphate ion (HPO42-).

H2PO4- H HPO42-

The pKa for this dissociation can be found in standard literature or tables, and it is approximately 7.2.

Calculating the pH using Henderson-Hasselbalch Equation

Step 1: Identifying the Relevant Dissociation

The relevant dissociation for the phosphate buffer system is:

H2PO4- H HPO42-

The pKa for this dissociation from H2PO4- to HPO42- is approximately 7.2.

Step 2: Calculating Concentrations

When equal volumes of 0.1 M Na2HPO4 and 0.1 M NaH2PO4 are mixed, the concentrations of the conjugate base (HPO42-) and the acid (H2PO4-) will be halved due to dilution. Therefore, the new concentrations are:

[HPO42-] 0.1 M × 1/2 0.05 M [H2PO4-] 0.1 M × 1/2 0.05 M

Step 3: Applying the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is:

pH pKa log ([A-] / [HA])

Substituting the known values into the equation:

pH 7.2 log (0.05 / 0.05)

Since the logarithm of 1 is 0:

pH 7.2 0 7.2

Conclusion

Thus, the pH of the buffer solution made from a mixture of 0.1 M Na2HPO4 and 0.1 M NaH2PO4 in equal amounts is 7.2.

Additional Insights

Note: The nominal concentrations of the acid and conjugate base are indeed irrelevant to the calculation of the pH, as long as the pKa value is known. The logarithmic function in the Henderson-Hasselbalch equation ensures that the pH will remain at a stable value when the concentrations are equal in a buffer solution.

References

For further information on buffer solutions and the Henderson-Hasselbalch equation, refer to the following tables and resources:

Base Strength/Table of Acids w Kas and pKas.pdf Wikipedia articles on Henderson-Hasselbalch Equation and Buffer Solutions