1) 2K(s) + 2H₂O(l)→ 2KOH(aq) + H₂(g)
This is a single replacement reaction where K reacts with H₂O , displaces the H⁺ ion in water and combines with OH⁻ to form a base.
2) 2Bi(NO₃)₃(aq) + 3H₂S(g)→ Bi₂S₃(s) + 6HNO₃(aq)
This is a double displacement reaction where the ions are exchanged and form new compounds. Since ions are exchanged between 2 compounds its called double displacement.
3) 2HNO₃(aq) + Ba(OH)₂ → Ba(NO₃)₂(aq) + 2H₂O(l)
This is an acid base reaction where nitric acid and barium hydroxide react to form the respective salt and water