Calculating the pH of a 0.023M HCl Solution: A Comprehensive Guide

Hydrochloric acid (HCl) is a strong acid that ionizes completely in water to form hydronium ions (H3O ) and chloride ions (Cl-). Understanding the pH of an HCl solution is crucial for various scientific and industrial applications. In this article, we will guide you through the process of calculating the pH of a 0.023 M HCl solution step by step.

Step-by-Step Calculation of pH

The pH of a solution is defined by the formula:

What is pH?

P

$$pH - log_{10}[H_3O^ ]$$

In this context, the concentration of hydronium ions ([H3O ]) in the solution is the key factor. For hydrochloric acid, which is a strong acid, the ionization process can be represented as:

Solution Equations

Strong Acid Ionization

$$HCl (aq) H_2O rightleftharpoons H_3O^ Cl^-$$

Since HCl is a strong acid, the reaction with water is nearly quantitative. Therefore, the concentration of H3O ions in the solution is essentially equal to the initial concentration of HCl.

Calculation

Given:

Molarity of HCl 0.023 M

Required:

pH - log[H]

Substitute the concentration:

$$pH - log[0.023]$$

To solve this, we calculate:

$$- log[0.023] -[-1.638] 1.64$$

Thus, the pH of a 0.023 M HCl solution is 1.64.

Further Insights into HCl Solutions

As previously mentioned, the dissociation of HCl in water can be expressed as:

$$HCl (aq) H_2O xrightarrow{} H_3O^ Cl^-$$

The concentration of H ions in the solution is equal to the concentration of HCl, which is 0.023 M. Therefore, we can use the formula for pH:

Alternate Calculation Method

Logarithmic Calculation

$$pH - log(0.023) 1.64$$

Both methods yield the same result, confirming the consistency of the pH value for a strong acidic solution.

Related Concepts: [HO-], pOH, and pH Consistency

For a solution with a given concentration of hydronium ions, we can also calculate the hydroxide ion concentration ([HO-]) and pOH using the equation:

$$[HO^-] Kw/[H_3O^ ]$$

Where Kw (ion product of water) is a constant:

$$ Kw [H_3O^ ][HO^-] 10^{-14}$$

For a 0.023 M HCl solution:

$$[HO^-] frac{10^{-14}}{0.023} approx 4.35 times 10^{-13} M$$

The pOH is given by:

$$pOH -log [HO^-] -log(4.35 times 10^{-13}) approx 12.37$$

Since pH pOH 14 for a neutral solution, this confirms our pH calculation:

$$pH pOH 1.64 12.37 14$$

This consistency in pH calculation is a fundamental aspect of acid-base chemistry, particularly in understanding strong acids like HCl.