So #pOH# is the basic counterpart of #pH# #(=-log_10[H_3O^+])#.
This derives from the autoprotolysis reaction in water:
#2H_2O(l) rightleftharpoons H_3O^+ + HO^-#
This equilibrium has been carefully measured, and at #298K# we write,
#K_w=[HO^-][H_3O^+]# #=# #10^-14#.
We can take #log_10# of both sides to give:
#log_10K_w# #=# #log_10[HO^-] + log_10[H_3O^+]# #=# #log_10{10^-14}#
#log_10K_w# #=# #log_10[HO^-] + log_10[H_3O^+]# #=# #-14# (because by definition, #log_a(a^b)=b#. On rearrangement:
#14=-log_10[HO^-] - log_10[H_3O^+]#
And, again by definition,
#pH + pOH =14#
The autoprotolysis of water is a bond breaking reaction. How would you predict #K_w# to evolve at elevated temperature? What would this mean with respect to #pH# and #pOH#?
