Calculating the pH of a 0.530 M Solution of Hypochlorous Acid: A Step-by-Step Guide

Hypochlorous acid (HOCl) is a weak acid, and understanding how to calculate its pH in a dilute solution is crucial for various fields including environmental science, water treatment, and biochemistry. In this article, we will walk through the steps to determine the pH of a 0.530 M solution of HOCl, focusing on the principles and calculations involved.

Understanding Hypochlorous Acid and Its Dissociation

Hypochlorous acid (HOCl) is a weak electrolyte that partially dissociates in water as follows:

HOCl ? H? OCl?

The dissociation constant (Ka) for HOCl is approximately 3.5 × 10-8 at 25°C. This value is crucial for determining the pH of the solution.

Setting Up the Equilibrium Expression

To calculate the pH, we need to set up the equilibrium expression for the dissociation of HOCl. The Ka expression is given by:

K_a [H?][OCl?] / [HOCl]

Let x be the concentration of H? and OCl? that dissociate. The concentrations at equilibrium can be expressed as:

[H?] x [OCl?] x [HOCl] 0.530 - x

Solving the Equilibrium Expression

Substituting these values into the Ka expression:

K_a x2 / (0.530 - x)

Given that HOCl is a weak acid, we can assume that x is small compared to 0.530 M. Therefore, we can approximate:

K_a ≈ x2 / 0.530

Substituting the value of Ka:

3.5 × 10-8 x2 / 0.530

Solving for x2:

x2 3.5 × 10-8 × 0.530

x2 ≈ 1.855 × 10-8

x ≈ sqrt{1.855 × 10-8} ≈ 4.31 × 10-5 M

Calculate the pH

Now that we have [H?] x ≈ 4.31 × 10-5 M, we can calculate the pH:

Don't forget, pH -log[H?]

pH -log(4.31 × 10-5) ≈ 4.37

Conclusion

The pH of a 0.530 M solution of HOCl is approximately 4.37.

Additional Resource

For a detailed understanding of how to solve equilibrium problems involving weak acids, you can refer to this article on weak acid calculations, which provides a comprehensive guide and additional examples.

Frequently Asked Questions

What is the difference between a strong and weak acid?

A strong acid, such as hydrochloric acid (HCl), dissociates completely in water, meaning [H?] [A?]. In contrast, a weak acid, like HOCl, only partially dissociates, leading to lower [H?] concentrations in solution.

How does the concentration of a weak acid affect its pH?

The pH of a weak acid solution is influenced by both the dissociation constant (Ka) and the initial concentration of the acid. Higher initial concentrations generally result in higher [H?] and lower pH values, provided the dissociation is significant.

What is the significance of the dissociation constant (K_a) in calculating the pH of a weak acid?

The dissociation constant (Ka) quantifies the extent to which a weak acid dissociates in water. A smaller Ka indicates less dissociation, leading to a higher pH. Conversely, a larger Ka indicates more dissociation, resulting in a lower pH.