Understanding the pH Calculation for Weak Acid and Strong Acid Mixtures

The pH of an aqueous solution is a measure of its acidity or basicity, and it is defined as the negative logarithm (base 10) of the hydronium ion concentration:

General pH Calculation

pH -log10[H3O ]

For determining the pH of a mixture containing weak and strong acids, it's crucial to understand the roles each acid plays in the solution. A strong acid completely dissociates in water, while a weak acid partially dissociates, meaning that only a fraction of the acid molecules donate a proton to water.

Strong Acid Contribution

For a strong acid, such as hydrochloric acid (HCl), the dissociation is quantitatively to the right, meaning that the acid almost completely ionizes:

Equilibrium Reaction for Strong Acid

HX (aq) H2O (l) ? H3O X-

The concentration of 3O O > ions in the solution is directly proportional to the concentration of the strong acid. Therefore, the pH of a strong acid solution can be directly calculated:

Calculation for Strong Acids

pH -log10[H3O ]

Example:

For a 10-3 M HCl solution, 3O O > 10-3 M, and thus the pH 3.

Weak Acid Contribution

With a weak acid, the dissociation is less pronounced. The equilibrium lies to the left, indicating that the acid doesn't fully ionize:

Equilibrium Reaction for Weak Acid

HX (aq) H2O (l) ? H3O X-

To calculate the 3O O > concentration in a solution with a weak acid, the equilibrium expression needs to be solved:

Equilibrium Expression for Weak Acid

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

Example:

Let's consider acetic acid (CH3COOH) with a Ka of 1.8 x 10-5. If we mix 0.5 M of HCl and 0.5 M of CH3COOH in equal volumes, the strong acid HCl would be the major supplier of hydrogen ions:

Mixed Solution Calculation

The 3O O > concentration from HCl 1 M (since HCl is a strong acid).

Ka for CH3COOH 1.8 x 10-5 [H ][CH3COO-] / [CH3COOH]

Assuming the 3O O > concentration from acetic acid is negligible compared to the strong acid, we can simplify the equation:

1.8 x 10-5 0.5 M[CH3COO-] / 0.5 M

[CH3COO-] 1.8 x 10-5 M

Thus, the presence of the strong acid HCl suppresses the dissociation of acetic acid, resulting in a very small amount of acetate ion and hydrogen ions.

Calculating the pH Approximatively

When a strong acid and a weak acid are mixed, the pH can be approximated by considering the dominant contribution of the strong acid. If the strong acid is present in a significantly higher concentration, its contribution to the 3O O > concentration will outweigh that of the weak acid:

Approximation Method

pH ≈ -log10[H (from strong acid)]

Example:

In the case of equal volumes of 1 M HCl and 1 M CH3COOH, the pH would be approximately 1, considering the strong acid's contribution is dominant.

Conclusion

The pH of a mixture containing a weak acid and a strong acid can be calculated by considering the dominant source of hydrogen ions, typically the strong acid. This approach simplifies the problem and provides a practical way to estimate the pH in many experimental scenarios.