Calculating the pH of Sodium Benzoate

Oct 13, 2025 by wbrum.org 127 views

Introduction

In chemistry, calculating the pH of a solution is a crucial task that helps us understand the concentration of hydrogen ions in a given solution. In this article, we will explore how to calculate the pH of a 0.54 M solution of sodium benzoate (NaC6H5CO2) at 25°C, given that benzoic acid (HC6H5CO2) is a weak acid with a pKa of 4.20.

Understanding pH and pKa

Before we dive into the calculation, let's briefly discuss the concepts of pH and pKa. pH is a measure of the concentration of hydrogen ions in a solution, and it is defined as the negative logarithm of the concentration of hydrogen ions:

pH = -log[H+]

On the other hand, pKa is a measure of the strength of an acid, and it is defined as the negative logarithm of the dissociation constant of the acid:

pKa = -log(Ka)

The Henderson-Hasselbalch Equation

To calculate the pH of a weak acid solution, we can use the Henderson-Hasselbalch equation, which is given by:

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

where [A-] is the concentration of the conjugate base (in this case, sodium benzoate) and [HA] is the concentration of the weak acid (in this case, benzoic acid).

Calculating the pH of Sodium Benzoate

Now that we have the Henderson-Hasselbalch equation, let's plug in the values we know:

pH = 4.20 + log([NaC6H5CO2]/[HC6H5CO2])

We are given that the concentration of sodium benzoate is 0.54 M, and we can assume that the concentration of benzoic acid is negligible compared to the concentration of sodium benzoate. Therefore, we can simplify the equation to:

pH = 4.20 + log(0.54)

Using a Calculator to Find the pH

To find the pH, we can use a calculator to evaluate the logarithm:

pH = 4.20 + log(0.54) = 4.20 + (-0.27) = 3.93

Conclusion

In this article, we calculated the pH of a 0.54 M solution of sodium benzoate at 25°C, given that benzoic acid is a weak acid with a pKa of 4.20. We used the Henderson-Hasselbalch equation to calculate the pH, and we found that the pH of the solution is 3.93.

Limitations of the Henderson-Hasselbalch Equation

It's worth noting that the Henderson-Hasselbalch equation assumes that the concentration of the conjugate base is much greater than the concentration of the weak acid. In this case, we assumed that the concentration of benzoic acid is negligible compared to the concentration of sodium benzoate. However, in reality, the concentration of benzoic acid may not be negligible, and the Henderson-Hasselbalch equation may not be accurate.

Future Directions

In future studies, it would be interesting to explore the effects of varying the concentration of benzoic acid on the pH of the solution. Additionally, it would be useful to investigate the effects of temperature on the pH of the solution.

References

[1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
[2] Brown, T. E., & LeMay, H. E. (2011). Chemistry: The Central Science. Pearson Education.

Appendix

Derivation of the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation can be derived from the equilibrium constant expression for the dissociation of a weak acid:

Ka = [H+][A-]/[HA]

Rearranging this equation, we get:

[H+] = Ka * [HA]/[A-]

Taking the negative logarithm of both sides, we get:

pH = -log[H+] = -log(Ka * [HA]/[A-]) = -log(Ka) + log([A-]/[HA]) = pKa + log([A-]/[HA])

Introduction

In our previous article, we explored how to calculate the pH of a 0.54 M solution of sodium benzoate (NaC6H5CO2) at 25°C, given that benzoic acid (HC6H5CO2) is a weak acid with a pKa of 4.20. In this article, we will answer some frequently asked questions about calculating pH in weak acid solutions.

Q: What is the Henderson-Hasselbalch equation?

A: The Henderson-Hasselbalch equation is a mathematical formula that allows us to calculate the pH of a weak acid solution. It is given by:

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

where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

Q: What is the pKa of a weak acid?

A: The pKa of a weak acid is a measure of its strength. It is defined as the negative logarithm of the dissociation constant of the acid:

pKa = -log(Ka)

Q: How do I choose the correct pKa value for my weak acid?

A: The pKa value you choose will depend on the specific weak acid you are working with. You can find the pKa value for a particular weak acid in a reference book or online database.

Q: What is the difference between a strong acid and a weak acid?

A: A strong acid is an acid that completely dissociates in water, producing a high concentration of hydrogen ions. A weak acid, on the other hand, only partially dissociates in water, producing a lower concentration of hydrogen ions.

Q: Can I use the Henderson-Hasselbalch equation to calculate the pH of a strong acid solution?

A: No, the Henderson-Hasselbalch equation is only applicable to weak acid solutions. For strong acid solutions, you can use the equation:

pH = -log[H+]

Q: What is the significance of the pH value?

A: The pH value is a measure of the concentration of hydrogen ions in a solution. A pH value of 7 is neutral, while a pH value less than 7 is acidic and a pH value greater than 7 is basic.

Q: Can I use the Henderson-Hasselbalch equation to calculate the pH of a buffer solution?

A: Yes, the Henderson-Hasselbalch equation can be used to calculate the pH of a buffer solution. A buffer solution is a solution that resists changes in pH when an acid or base is added to it.

Q: What is the relationship between pH and pKa?

A: The pH and pKa values are related by the Henderson-Hasselbalch equation:

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

This equation shows that the pH of a weak acid solution is dependent on the pKa value of the acid and the ratio of the concentrations of the conjugate base and the weak acid.

Conclusion

In this article, we have answered some frequently asked questions about calculating pH in weak acid solutions. We have discussed the Henderson-Hasselbalch equation, the pKa value, and the significance of the pH value. We have also explored the relationship between pH and pKa.

References

[1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
[2] Brown, T. E., & LeMay, H. E. (2011). Chemistry: The Central Science. Pearson Education.

Appendix

Derivation of the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation can be derived from the equilibrium constant expression for the dissociation of a weak acid:

Ka = [H+][A-]/[HA]

Rearranging this equation, we get:

[H+] = Ka * [HA]/[A-]

Taking the negative logarithm of both sides, we get:

pH = -log[H+] = -log(Ka * [HA]/[A-]) = -log(Ka) + log([A-]/[HA]) = pKa + log([A-]/[HA])

This is the Henderson-Hasselbalch equation, which we used to calculate the pH of the sodium benzoate solution.