Concept:The pH of an acidic buffer is dictated by the Henderson-Hasselbalch equation, which relies on the logarithmic ratio of the conjugate base (salt) to the weak acid.
Formula:$$ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Salt}]}{[\text{Acid}]} \right) $$
Solution:- The weak acid concentration (\( \text{CH}_3\text{COOH} \)) is held perfectly constant at 0.1M across all four options.
- Therefore, the pH will increase strictly as the concentration of the conjugate base (\( [\text{Salt}] \)) increases, because the mathematical fraction \( \frac{[\text{Salt}]}{[\text{Acid}]} \) becomes larger.
- Let's analyze the ratios:
- Option A: \( \log(0.01 / 0.1) = \log(0.1) = -1 \)
- Option B: \( \log(0.05 / 0.1) = \log(0.5) = -0.3 \)
- Option C: \( \log(0.10 / 0.1) = \log(1) = 0 \)
- Option D: \( \log(0.15 / 0.1) = \log(1.5) = +0.176 \)
- Option D adds a positive value to the \( \text{pK}_a \), resulting in the mathematically highest pH. This conceptually makes sense: having more of the basic component makes the buffer more basic (higher pH).
Why other options are incorrect:Options A, B, and C have lower concentrations of the conjugate base, leading to lower, more acidic pH values.
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