What is the pH of a buffer solution prepared by dissolving 0.250 mol of NaH2PO4 and 0.075 mol of NaOH in enough water to make 1.00 L of solution? (Ka (H2PO4-) = 6.2 X 10^-8) (a) 6.32 (b) 6.83 (c) 7.21 (d) 7.71

Verified step by step guidance

1. Identify the components of the buffer solution: NaH2PO4 (weak acid) and NaOH (strong base).
2. Determine the reaction between NaH2PO4 and NaOH: NaH2PO4 + NaOH -> Na2HPO4 + H2O.
3. Calculate the moles of Na2HPO4 formed and the remaining moles of NaH2PO4 after the reaction.
4. Use the Henderson-Hasselbalch equation: pH = pKa + log([A^-]/[HA]), where [A^-] is the concentration of Na2HPO4 and [HA] is the concentration of NaH2PO4.
5. Calculate the pH using the given Ka value to find pKa: pKa = -log(Ka).

Key Concepts

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, NaH2PO4 acts as the weak acid, while NaOH provides the conjugate base, H2PO4-. Understanding how buffers work is essential for calculating the pH of the solution.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant (Ka), [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is crucial for determining the pH of the buffer solution in the given problem.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, indicating how well it donates protons (H+) to the solution. A lower Ka value signifies a weaker acid. In this question, the provided Ka value for H2PO4- (6.2 x 10^-8) is necessary for calculating the pKa, which is used in the Henderson-Hasselbalch equation to find the pH of the buffer solution.