Final answer:
To find the pH of a 0.33 M nitrous acid solution, we calculate the concentration of H⁺ ions using the given Ka value and the initial acid concentration. We find that the pH of the solution is approximately 1.96.
Step-by-step explanation:
To calculate the pH of a 0.33 M solution of nitrous acid (HNO2) with a given Ka of 4.0 × 10⁻⁴, we need to set up the dissociation equation for the weak acid:
HNO2 (aq) → H⁺ (aq) + NO2⁻ (aq)
At equilibrium, the concentrations of the products and reactants are related by the acid dissociation constant (Ka):
Ka = [H⁺][NO2⁻] / [HNO2]
Assuming x is the amount of HNO2 that dissociates, the concentration of H⁺ and NO2⁻ will both be x and the concentration of undissociated HNO2 will be 0.33 - x. Since HNO2 is a weak acid, x will be much smaller than 0.33 and can be ignored, simplifying the equation to:
Ka = x² / 0.33
Solving for x gives:
x = √(Ka × 0.33) = √(4.0 × 10⁻⁴ × 0.33) ≈ 1.1 × 10⁻²
The concentration of H⁺ (which is the same as [H3O⁺]) is approximately 1.1 × 10⁻² M. To find the pH, we take the negative logarithm:
pH = -log([H⁺]) = -log(1.1 × 10⁻²) ≈ 1.96
Thus, the pH of the 0.33 M HNO2 solution is approximately 1.96.