Concept:The acid dissociation constant (\( \text{K}_a \)) is a measure of acid strength. The "smallest dissociation constant" implies the
weakest acid. Acidity increases with highly electronegative substituents (Fluorine > Bromine) and their proximity to the carboxyl group (\( \alpha \)-position > \( \beta \)-position).
Solution:- To find the weakest acid, we want the weakest halogen placed furthest away from the \( -\text{COOH} \) group to minimize the electron-withdrawing inductive (\( -I \)) effect.
- Option A: Fluorine on the \( \alpha \)-carbon (Very Strong).
- Option D: Bromine on the \( \alpha \)-carbon (Strong).
- Option B: Fluorine on the \( \beta \)-carbon (Moderate).
- Option C: Bromine on the \( \beta \)-carbon. Bromine is less electronegative than Fluorine, and it is located far away on the \( \beta \)-carbon. This exerts the weakest \( -I \) effect, yielding the least stable anion and thus the smallest \( \text{K}_a \).
Why other options are incorrect:All other options feature either a more electronegative halogen (F) or a closer proximity (\( \alpha \)-position), both of which result in a larger dissociation constant.
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