Strong acids dissociate completely. What does it mean? If a strong acid is put into water, it will break completely into H+ and whatever it left (for example HCl --> H+ and Cl-). So if I start with 3 moles of HCl , it will break and give 3 moles of H+ and 3 moles of Cl-.
A weak acid, on the other hand, dissociates only partially. For example, if I start out with 3 moles of acetic acid, only 0.002 moles of it will break down and create H+.
How can you distinguish between strong and weak acids?
Just memorize the strong ones and if your acid is not strong, it must be weak.
Strong acids: hydrochloric acid (HCl), hydroiodic acid (HI), hydrobromic acid (HBr), perchloric acid (HClO4), nitric acid (HNO3) and sulphuric acid (H2SO4).
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