Consider a weak acid, HA. At low pH, ionization is suppressed so that [ HA ] is not affected by pH. The expression
reduces to: some constant = [ H+ ]
[ A- ]
taking logs and rearranging:
log [ A- ] = a constant - log [ H+ ]
A plot of - log [ A- ] versus pH will have a
slope of 1. The same reasoning works for high pH where
[ A- ]
is independent of pH shows that a plot of
-log [ HA ] versus pH
has a slope of -1. Further
analysis along these lines would confirm the slopes of 2 and -2
when additional equilibria come into play.