Calculate the pH of 75.0 mL of a 0.10 M of phosphorous acid, H₃PO₃, when 80.0 mL of 0.15 M NaOH are added. K_a1 = 5.0 × 10⁻², K_a2 = 2.0 × 10⁻⁷.

• A. 7.12
• B. 1.35
• C. 6.88
• D. 12.65

Answer: (C)

Verified step by step guidance

1. Determine the initial moles of H3PO3 and NaOH. Use the formula \( \text{moles} = \text{concentration} \times \text{volume} \). Calculate the moles of H3PO3 using \( 0.10 \text{ M} \times 75.0 \text{ mL} \) and the moles of NaOH using \( 0.15 \text{ M} \times 80.0 \text{ mL} \).
2. Identify the reaction between H3PO3 and NaOH. Phosphorous acid is a diprotic acid, meaning it can donate two protons. The first reaction will be \( \text{H}_3\text{PO}_3 + \text{NaOH} \rightarrow \text{NaH}_2\text{PO}_3 + \text{H}_2\text{O} \).
3. Calculate the moles of NaOH that react with H3PO3. Since NaOH is a strong base, it will react completely with the available H3PO3. Subtract the moles of NaOH from the moles of H3PO3 to find the remaining moles of H3PO3 after the first reaction.
4. Consider the second dissociation of H3PO3. The remaining H3PO3 will undergo a second reaction: \( \text{NaH}_2\text{PO}_3 + \text{NaOH} \rightarrow \text{Na}_2\text{HPO}_3 + \text{H}_2\text{O} \). Use the remaining moles of NaOH to determine the extent of this reaction.
5. Calculate the pH of the resulting solution. Use the Henderson-Hasselbalch equation for the buffer solution formed after the reactions: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). Use the appropriate \( \text{pKa} \) value for the dominant species in the solution.