Why is pKa of `F-CH_(2)COOH` lower than that of `Cl-CH_(2)COOH`?

Explanation

`pK_(a)` of `FCH_(2)COOH` is lower than that of `ClCH_(2)COOH` implies that `FCH_(2)COOH` is a stronger acid than `ClCH_(2)COOH`. This is due to the following two reasons:
(i) Due to stronger -I-effect of F over Cl, the electron density in the O-H bond in `FCH_(2)COOH` is much lower than in `ClCH_(2)COOH`. as a result, O-H bond in `FCH_(2)COOH` is much weaker than in `ClCH_(2)COOH` and hence `FCH_(2)COOH` loses a proton more easily than `ClCH_(2)COOH` i.e., `FCH_(2)COOH` is a stronger acid than `ClCH_(2)COOH`.
(ii) Due to stronger -I-effect of F over Cl, the dispersal of the -ve charge in `FCH_(2)COO^(-)` occurs more effectively than in `ClCH_(2)COO^(-)`.

In other words, `FCH_(2)COO^(-)` is more stable than `ClCH_(2)COO^(-)` and hence `FCH_(2)COOH` is a stronger acid than `ClCH_(2)COOH`, i.e.., `FCH_(2)COOH` has lower `pK_(a)` than `ClCH_(2)COOH`.