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A strong acid completely dissociates when put in water, where the H+ is ionized in the water. A weak acid does not completely ionize in water. Only a small amount of the molecule becomes aqueous in the water. Only a small amount of H+ is ionized.
If you are asking how we know, there is a tendency for acids made with elements on the far right side of the periodic table to be strong acids because of their high electronegativity. But we know them mostly from memorizing them!
A way to test the difference in weak acids vs strong acids is by comparing how they react in water. Weak acids tend to partially ionize in water, while strong acids tend to completely dissociate. Essentially we are comparing how much H+ is ionized. Another method is just memorizing which acids are which!
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