Final answer:
To calculate the pH of a 0.204 M maleic acid solution, we consider the first dissociation constant (Ka1) and the initial concentration, ignoring Ka2 due to its much smaller value. We find the concentration of the hydronium ions ([H+]), then use the negative logarithm to find the pH.
Step-by-step explanation:
To determine the pH of a 0.204 M maleic acid (H₂C₄H₂O₄) solution, we need to consider only the first dissociation since the Ka1 of maleic acid is significantly larger than its Ka2. Typically, for a diprotic acid like maleic acid, the first dissociation will contribute the most to the hydronium ion concentration in the solution. The second dissociation constant being much smaller means it contributes significantly less and can often be ignored for the initial pH calculation.
For the first dissociation,
H₂C₄H₂O₄ → HC₄H₂O₄⁻ + H⁺
we apply the formula for the ionization of a weak acid:
Ka1 = [H⁺][HC₄H₂O₄⁻]/[H₂C₄H₂O₄].
Assuming [H⁺] = x and [HC₄H₂O₄⁻] = x, the concentration of H₂C₄H₂O₄ will be (0.204 - x). Given Ka1 = 1.20 x 10⁻³, we set up the expression:
1.20 x 10⁻³ = (x)(x)/(0.204 - x).
Because Ka1 is small, we can assume x << 0.204 and simplify the equation to:
1.20 x 10⁻³ = x²/0.204. Solving for x gives us the [H⁺], and then we calculate pH = -log([H⁺]).
Since the second dissociation is much smaller and does not significantly contribute to the [H⁺], we ignore it for this initial approximation. To achieve greater accuracy, especially at higher concentrations, both dissociations would need to be considered in a more complex calculation.