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start by drawing some lewis structures
Yes! A good way to explain this would be to draw resonance structures for both!
The delocalization of the negative across a structures means more stability.
The greater area over which the delocalization is possible, the greater the stabilization. Thus, this is what makes it a stronger acid.
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When you want to compare the strengths of acids, study the relative stability of their conjugate bases.
Firstly to check the acidic strenght of any acid or to compare any acid draw its structure and conjugate base in the above question when you draw the conjugate base of carboxylic acid it is stabilise by 2 resonating structures where as in conjugate base of phenol i.e phenoxide ion has 5 or 6 resonating structures but in carboxylic acid the resonating structure has 2 equilating resonance structures ( i.e dispersal of charge on same atom in resonating structure ) this type of resonance is more stable than normal resonance so i.e why carboxylic acid is more acidic than phenol