What is the stronger base: ammonia or ethoxide ion?

Ethoxide ion is the stronger base.

Ammonia is a weak base:

##"NH"_3 + "H"_2"O" ⇌ "NH"_4^+ + "OH"^"-"; K_"b" = 1.8 × 10^"-5"##

Ethanol is a very weak acid:

##underbrace( "CH"_3"CH"_2"OH")_color(red)("weak acid") + "H"_2"O" ⇌ "H"_3"O" ^+ + underbrace("CH"_3"CH"_2"O"^"-")_color(red)("conjugate base"); K_"a" ≈ 10^"-16"##

Hence, its conjugate base is a strong base.

##"CH"_3"CH"_2"O"^"-" + "H"_2"O" ⇌ "CH"_3"CH"_2"OH" + "OH"^"-"##; ##K_"b" = bb"large"##

Thus, there are three reasons why ethoxide ion is a stronger base than ammonia.

1. It is the conjugate base of a very weak acid.
2. It has a negative charge, whereas ammonia is neutral.
3. It has three lone pairs that can accept a proton, compared with only one lone pair for ammonia.