Concept:The Henderson-Hasselbalch equation defines the relationship between the pH of a buffer, the \( \text{pKa} \) of the weak acid, and the concentrations of the acid and its conjugate base.
Formula:$$ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) $$
Solution:- The standard form of the equation has a positive logarithm of Base over Acid.
- By logarithmic properties, \( +\log(x/y) = -\log(y/x) \).
- Applying this: \( +\log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) = -\log \left( \frac{[\text{Acid}]}{[\text{Base}]} \right) \).
- Substituting this back gives \( \text{pH} = \text{pK}_a - \log \left( \frac{[\text{Acid}]}{[\text{Base}]} \right) \).
Why other options are incorrect:Option A has a positive sign but inverted ratio. Option B applies a negative sign incorrectly to the standard ratio. Option D algebraically fails when rearranging the standard formula.
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