Which of the following correctly represents the Henderson-Hasselbalch equation for a solution of propanoic acid (C2H5COOH) and its conjugate base (C2H5COO^-)?

• A. pH = pKa - log([C2H5COOH]/[C2H5COO^-])
• B. pH = pKa - log([C2H5COO^-]/[C2H5COOH])
• C. pH = pKa + log([C2H5COOH]/[C2H5COO^-])
• D. pH = pKa + log([C2H5COO^-]/[C2H5COOH])

Answer: (D)

Verified step by step guidance

1. Recall that the Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of its conjugate base and acid.
2. The general form of the Henderson-Hasselbalch equation is: \(\mathrm{pH} = \mathrm{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)\), where \([\text{A}^-]\) is the concentration of the conjugate base and \([\text{HA}]\) is the concentration of the acid.
3. Identify the acid and conjugate base in this problem: propanoic acid is \(\mathrm{C_2H_5COOH}\) (acid, HA) and its conjugate base is \(\mathrm{C_2H_5COO^-}\) (A\(^-\)).
4. Substitute the species into the equation: \(\mathrm{pH} = \mathrm{p}K_a + \log \left( \frac{[\mathrm{C_2H_5COO^-}]}{[\mathrm{C_2H_5COOH}]} \right)\).
5. Compare this form to the options given and confirm that the correct representation has the conjugate base concentration in the numerator and the acid concentration in the denominator, with a positive sign before the logarithm.