59. The [H⁺] of 0.1 N acetic acid solution is 1.33 × 10^-3. The pH of the solution (correct to two decimal places) is           .

How to Calculate the pH of a 0.1 N Acetic Acid Solution

In this problem, the hydrogen ion concentration is already provided. Therefore, there is no need to calculate the degree of dissociation or use the acid dissociation constant (K_a). The solution simply requires application of the definition of pH.

Given Data

Hydrogen ion concentration

[H⁺] = 1.33 × 10⁻³ mol L⁻¹

Formula Used

The pH of a solution is defined as

pH = −log[H⁺]

Calculation

Substituting the given hydrogen ion concentration,

pH = −log(1.33 × 10⁻³)

Using the logarithmic identity

log(a × 10^b) = log(a) + b

Therefore,

pH = −(log 1.33 − 3)

Since

log 1.33 = 0.1239

Hence,

pH = −(0.1239 − 3)

pH = 3 − 0.1239

pH = 2.8761

Correct to two decimal places,

pH = 2.88

Why the pH is Less Than 3

Although acetic acid is a weak acid, it still releases hydrogen ions into solution through partial ionization. The given hydrogen ion concentration is greater than 10⁻³ mol L⁻¹, so the pH must be slightly less than 3. This agrees perfectly with the calculated value of 2.88.

Final Answer

pH = 2.88

Correct Answer: 2.88