Final answer:
To find the pH of a solution when 0.500 moles of acetic acid are diluted to 1.00 L, we use the Ka value of 1.8 x 10⁻⁵. An ICE table helps determine the concentration of H⁺ ions at equilibrium, which is used in the pH calculation.
Step-by-step explanation:
To calculate the pH of the resulting solution when 0.500 moles of acetic acid are dissolved in water and diluted to 1.00 L, we need to use the acid ionization constant (Ka) and the initial concentration of the acetic acid. The ionization of acetic acid in water can be represented by the following equation:
CH₃COOH(aq) → CH₃COO⁻(aq) + H⁺(aq)
The Ka value for acetic acid is given as 1.8 x 10⁻⁵. Since we're starting with a 0.500 M solution, we can set up an ICE table to find the concentration of H⁺ ions, which will then allow us to calculate the pH:
- Initial concentrations: [CH₃COOH] = 0.500 M, [CH₃COO⁻] = 0 M, [H⁺] = 0 M
- Change in concentrations: [CH₃COOH] will decrease by x, [CH₃COO⁻] will increase by x, and [H⁺] will increase by x
- Equilibrium concentrations: [CH₃COOH] = 0.500 - x, [CH₃COO⁻] = x, [H⁺] = x
Now we can write the Ka expression for acetic acid:
Ka = ([CH₃COO⁻][H⁺]) / [CH₃COOH]
Since Ka is relatively small, we can assume that the change x will be small and thus [CH₃COOH] ≈ 0.500 M. Plugging the values and solving for x, we have:
Ka = 1.8 x 10⁻⁵ = (x)(x) / 0.500 M
Upon solving for x (which represents [H⁺]), we use the pH formula:
pH = -log([H⁺])
From here, you would perform the arithmetic to find the value of x and then calculate the pH of the solution.