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In the Bronsted-Lowry model of acids and bases, an acid is defined as a substance that donates a proton (H+ ion). The strength of an acid is determined by its ability to donate a proton. A strong acid is an acid that completely dissociates in water to produce H+ ions and the conjugate base. A weak acid is an acid that does not completely dissociate in water.
Both hydrochloric acid (HCl) and perchloric acid (HClO4) are strong acids that completely dissociate in water. Thus, both of these acids will give the same concentration of hydronium ions in water (assuming the same initial concentrations). Therefore, they are considered to be equally strong acids in aqueous solution.