The #"pKa"# is just the negative base 10 logarithm of the #"Ka"#. In other words:
#"pKa" = -log("Ka")#
For example, ammonia has a #"pKa"# of about #36#. A higher #"pKa"# indicates a weaker acid. This is because:
#10^(-"pKa") = "Ka"#
We can see that the #"Ka"#, which is known as the acid dissociation constant, is higher for higher degrees of dissociation, and vice versa. Thus, the lower the #"Ka"#, the weaker the acid.
The lower the #"Ka"#, the higher the #"pKa"# must be for #10^(-"pKa")# to decrease. We can prove that like so:
#"pKa"_("NH"_3) = 36#
#10^(-36) = "Ka"_("NH"_3)#
And then...
#"pKa"_("NH"_4^(+)) = 9.4#
#10^(-9.4) = "Ka"_("NH"_4^(+))#
And of course...
#10^(-36) " << " 10^(-9.4)#
That means ammonium dissociates much more than ammonia does in water (#26.6# orders of magnitude more). In fact, an ammonium hydroxide solution readily equilibrates to be pretty much all ammonia and water.
