Question

What determines the strength of an arrhenius base? give one example each of an aqueous solution of a strong base and an aqueous solution of a weak base?

Answer 1

The strength of an Arrhenius base determines percentage of ionization of base and the number of OH⁻ ions formed. 
Strong base completely ionize in water and gives a lot of hydroxide ions (OH⁻), for example sodium hydroxide: NaOH(aq) → Na⁺(aq) + OH⁻(aq).
Weak  base partially ionize in water and gives a few hydroxide ions (OH⁻), for example ammonia: NH₃ + H₂O(l) ⇄ NH₄⁺(aq) + OH⁻(aq).