Potassium hydrogen phthalate (molar mass = 204.2 g/mol)is one of the most commonly used acids for standardizing solutions containing bases.KHP is a monoprotic weak acid with K_a = 3.91 × 10^-6.Calculate the pH of the solution that results when 0.40 g of KHP is dissolved in enough water to produce 25.0 mL of solution.

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First, calculate the molarity of KHP in the solution: $ \frac{0.40 \, \text{g}}{204.2 \, \text{g/mol}} = 0.00196 \, \text{mol} $, and when dissolved in 25.0 mL (or 0.025 L) of water, the molarity is $ \frac{0.00196 \, \text{mol}}{0.025 \, \text{L}} = 0.0784 \, \text{M} $.Given that KHP is a weak acid with $ K_a = 3.91 \times 10^{-6} $, we can use the acid dissociation constant to find the pH. For a weak acid $ HA $, the dissociation is $ HA \rightleftharpoons H^+ + A^- $, and at equilibrium, $ K_a = \frac{[H^+][A^-]}{[HA]} $. Assuming $ x $ is the concentration of $ H^+ $ (and $ A^- $ since they are produced in a 1:1 ratio), and $ 0.0784 - x $ is the concentration of $ HA $ at equilibrium, we can set up the equation $ 3.91 \times 10^{-6} = \frac{x^2}{0.0784 - x} $.Given the small $ K_a $ value, we can approximate $ 0.0784 - x \approx 0.0784 $ to simplify the calculation, leading to $ x^2 = 3.91 \times 10^{-6} \times 0.0784 $. Solving for $ x $, which is the $ [H^+] $, we find $ x \approx 7.0 \times 10^{-4} $. The pH is then $ -\log(7.0 \times 10^{-4}) $, which is approximately 3.26.

Potassium Hydrogen Phthalate (Molar Mass = 204