The Ionization Reaction of Benzoic Acid

Oct 13, 2025 by miodeya.com 5 views

Introduction

Benzoic acid, $HC_7H_5O_2$ , is a weak organic acid that is commonly used in various applications, including food preservation and pharmaceuticals. In this article, we will explore the concept of percent ionization and calculate the percent ionization of a 0.20 M solution of benzoic acid with a $K_a$ of $6.5 \times 10^{-5}$ .

What is Percent Ionization?

Percent ionization is a measure of the extent to which a weak acid or base dissociates in a solution. It is defined as the ratio of the concentration of the ionized species to the initial concentration of the acid or base. In the case of benzoic acid, percent ionization is the ratio of the concentration of $H_3O^+$ ions to the initial concentration of benzoic acid.

The Ionization Reaction of Benzoic Acid

The ionization reaction of benzoic acid is as follows:

${ HC_7H_5O_2(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + C_7H_5O_2^-(aq) }$

Calculating the Percent Ionization

To calculate the percent ionization of benzoic acid, we can use the following equation:

${ \text{Percent Ionization} = \frac{[\text{H}_3\text{O}^+]}{[\text{HC}_7\text{H}_5\text{O}_2]} \times 100\% }$

We are given that the initial concentration of benzoic acid is 0.20 M and the $K_a$ is $6.5 \times 10^{-5}$ . We can use the $K_a$ expression to calculate the concentration of $H_3O^+$ ions:

${ K_a = \frac{[\text{H}_3\text{O}^+][\text{C}_7\text{H}_5\text{O}_2^-]}{[\text{HC}_7\text{H}_5\text{O}_2]} }$

Since the concentration of benzoic acid is much greater than the concentration of $H_3O^+$ ions, we can assume that the concentration of benzoic acid remains constant. Therefore, we can rewrite the $K_a$ expression as:

${ K_a = \frac{[\text{H}_3\text{O}^+][\text{C}_7\text{H}_5\text{O}_2^-]}{[\text{HC}_7\text{H}_5\text{O}_2]} = \frac{[\text{H}_3\text{O}^+]^2}{[\text{HC}_7\text{H}_5\text{O}_2]} }$

We can now substitute the given values into the equation:

${ 6.5 \times 10^{-5} = \frac{[\text{H}_3\text{O}^+]^2}{0.20} }$

Solving for $[\text{H}_3\text{O}^+]$ , we get:

${ [\text{H}_3\text{O}^+] = \sqrt{6.5 \times 10^{-5} \times 0.20} = 1.3 \times 10^{-3} \text{ M} }$

Now that we have the concentration of $H_3O^+$ ions, we can calculate the percent ionization:

${ \text{Percent Ionization} = \frac{[\text{H}_3\text{O}^+]}{[\text{HC}_7\text{H}_5\text{O}_2]} \times 100\% = \frac{1.3 \times 10^{-3}}{0.20} \times 100\% = 0.65\% }$

Conclusion

In this article, we have calculated the percent ionization of a 0.20 M solution of benzoic acid with a $K_a$ of $6.5 \times 10^{-5}$ . We have shown that the percent ionization is a measure of the extent to which a weak acid or base dissociates in a solution and is defined as the ratio of the concentration of the ionized species to the initial concentration of the acid or base. We have also demonstrated how to calculate the percent ionization using the $K_a$ expression and have found that the percent ionization of benzoic acid is 0.65%.

References

Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
Brown, T. E., LeMay, H. E., Bursten, B. E., & Murphy, C. (2012). Chemistry: The Central Science (13th ed.). Pearson Education.

Q: What is percent ionization?

A: Percent ionization is a measure of the extent to which a weak acid or base dissociates in a solution. It is defined as the ratio of the concentration of the ionized species to the initial concentration of the acid or base.

Q: How is percent ionization calculated?

A: Percent ionization is calculated using the following equation:

${ \text{Percent Ionization} = \frac{[\text{H}_3\text{O}^+]}{[\text{HC}_7\text{H}_5\text{O}_2]} \times 100\% }$

Q: What is the difference between percent ionization and molarity?

A: Percent ionization is a measure of the extent to which a weak acid or base dissociates in a solution, while molarity is a measure of the concentration of a solution. Percent ionization is a ratio of the concentration of the ionized species to the initial concentration of the acid or base, while molarity is a measure of the total concentration of a solution.

Q: How does the $K_a$ value affect percent ionization?

A: The $K_a$ value affects percent ionization by determining the extent to which a weak acid or base dissociates in a solution. A higher $K_a$ value indicates a greater extent of dissociation, while a lower $K_a$ value indicates a lesser extent of dissociation.

Q: Can percent ionization be used to predict the pH of a solution?

A: Yes, percent ionization can be used to predict the pH of a solution. By calculating the percent ionization of a weak acid or base, you can determine the concentration of $H_3O^+$ ions in the solution, which can then be used to calculate the pH of the solution.

Q: What are some common applications of percent ionization?

A: Percent ionization has several common applications in chemistry, including:

Determining the pH of a solution
Calculating the concentration of $H_3O^+$ ions in a solution
Predicting the behavior of weak acids and bases in a solution
Understanding the effects of pH on chemical reactions

Q: How can I calculate percent ionization using a calculator?

A: To calculate percent ionization using a calculator, you can use the following steps:

Enter the concentration of the acid or base (in M)
Enter the $K_a$ value
Calculate the concentration of $H_3O^+$ ions using the $K_a$ expression
Calculate the percent ionization using the equation above

Q: What are some common mistakes to avoid when calculating percent ionization?

A: Some common mistakes to avoid when calculating percent ionization include:

Failing to account for the initial concentration of the acid or base
Failing to use the correct $K_a$ value
Failing to calculate the concentration of $H_3O^+$ ions correctly
Failing to use the correct equation for percent ionization

Conclusion

In this article, we have answered some frequently asked questions about percent ionization, including what it is, how it is calculated, and how it is used in chemistry. We have also provided some common applications of percent ionization and some tips for calculating it using a calculator. By understanding percent ionization, you can gain a deeper understanding of the behavior of weak acids and bases in a solution and make more accurate predictions about the pH of a solution.

References

Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
Brown, T. E., LeMay, H. E., Bursten, B. E., & Murphy, C. (2012). Chemistry: The Central Science (13th ed.). Pearson Education.