Calculate [H₃O⁺] and [OH^–] for each solution at 25 °C. a. pH = 8.55

Verified step by step guidance

1. Identify the relationship between pH and [H3O+]. Use the formula: \([H_3O^+] = 10^{-pH}\).
2. Substitute the given pH value into the formula to find \([H_3O^+]\).
3. Use the relationship between [H3O+] and [OH-] at 25 °C, which is given by the ion product of water: \(K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}\).
4. Rearrange the equation to solve for \([OH^-]\): \([OH^-] = \frac{K_w}{[H_3O^+]}\).
5. Substitute the calculated \([H_3O^+]\) into the equation to find \([OH^-]\).

Key Concepts

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is considered neutral, while values below 7 indicate acidity and values above 7 indicate basicity. The pH is logarithmically related to the concentration of hydrogen ions, [H+], in the solution, where lower pH values correspond to higher [H+] concentrations.

Hydronium Ion Concentration

The concentration of hydronium ions, [H3O+], in a solution can be calculated from the pH using the formula [H3O+] = 10^(-pH). This relationship shows that as pH increases, the concentration of hydronium ions decreases, indicating a more basic solution. For a pH of 8.55, this calculation is essential to determine the exact concentration of hydronium ions present.

Water Ion Product

At 25 °C, the product of the concentrations of hydronium ions and hydroxide ions, [H3O+][OH-], is constant and equal to 1.0 x 10^-14, known as the water ion product (Kw). This relationship allows for the calculation of hydroxide ion concentration, [OH-], using the formula [OH-] = Kw / [H3O+]. Understanding this concept is crucial for determining the balance between hydronium and hydroxide ions in a solution.