Final answer:
To calculate the pH of a buffer solution, determine the pKa of the acid component, and then substitute the concentrations of the acid and base into the Henderson-Hasselbalch equation. In this case, the pH of the buffer solution is approximately 12.35.
Step-by-step explanation:
A buffer solution is a solution that resists changes in pH when an acid or base is added. To calculate the pH of a buffer solution, you need to consider the dissociation of the acid and base components of the buffer. In this case, the acid component is Na₂HPO₄ and the base component is KH₂PO₄.
First, calculate the pKa of the acid component using the given K₂ value, which is 4.2 × 10⁻¹³. The pKa is equal to the negative logarithm of the K₂ value, so the pKa = -log(4.2 × 10⁻¹³) ≈ 12.4.
Next, use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution. The Henderson-Hasselbalch equation is pH = pKa + log([base]/[acid]). In this case, [base] = 0.16 M and [acid] = 0.18 M. Substitute these values into the equation to find the pH:
pH = 12.4 + log(0.16/0.18) = 12.4 - log(0.888) ≈ 12.4 - (-0.051) ≈ 12.35.