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As HCl is a strong acid, it will stay dissociated as H+ and Cl- (an acid is stronger the more likely it dissociates and releases a H+). On the other hand, as HF is a weak acid, it will more likely go back into HF as it does not like to be in its dissociated form of H+ and F-.
HCL when disassociated it does so completely which makes it a strong acid because it won't go back with the H+ and therefore is able to donate the proton. On the other hand, HF will disassociate but not completely and therefore will go back with H+ making a weak acid because it is harder to take away the proton from it.
Strong acids completely dissociate. HCl would completely dissociate into H+ and Cl- ions and therefore won't be able to turn back into HCl while HF is a weaker acid, so it doesn't completely dissociate. Since HF doesn't completely dissociate, F- has the ability to pick up a proton/hydrogen and become HF
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