what property do all strong acids and strong bases have in common
Both the strong acids and strong bases have the ability to conduct electricity.
When both of them (strong acid and strong base) are dissolved in water, they completely dissociate into corresponding ions (as they are strong species) and make the water more conductive.
Therefore, all strong acids and strong bases have a common property, i.e. the degree of dissociation (in water) = 1 (~100% dissociation).
The general equations for the dissociation of a strong acid and a strong base in water can be shown as follows.
HA(aq) H+ (aq)+ A-(aq).
BOH B+(aq) + OH-(aq).
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