Question

The term “Ka for the ammonium ion” describes
the equilibrium constant for which of
the following reactions?
1. NH3 + H2O ⇀↽ NH4
+ + OH−
2. NH+
4 + OH− ⇀↽ NH3 + H2O
3. NH3 + H3O
+ ⇀↽ NH+
4 + H2O
4. NH+
4 + H2O ⇀↽ NH3 + H3O
+
5. The term is misleading, because the ammonium
ion is not an acid.
6. NH4Cl(solid) + H2O ⇀↽ NH+
4 + Cl−

Answer 1

The way you have displayed the answers I can't tell what is what. Here is the Ka equation for the NH4^+.

NH4^+ + H2O ==> NH3 + H3O^+
Except for the missing charge on H3O^+, #4 appears the closest.

Answer 2

Yes, the answer is:
4) NH+4 + H2O ⇀↽ NH3 + H3O^+