Are pH and pOH related to each other?

1 Answer
May 7, 2016

Answer:

Absolutely! In water:

#pH + pOH = 14#

Explanation:

We know that water undergoes autoprotolysis:

#2H_2O rightleftharpoons H_3O^+ + HO^-#

This is an equilibrium reaction, measured precisely over a range of temperatures. It is a fact that at #298K#,

#[H_3O^+][HO^-]# #=# #10^(-14)# (#[H_2O]# is treated as a constant!). Now this is a mathematical equation, which I can manipulate, as long as I do the same thing to both sides.

Taking #log_10# of both sides:

#log_10[H_3O^+] + log_10[HO^-] # #=# #-14#

On rearrangement,

#14# #=# #-log_10[H_3O^+] - log_10[HO^-] #

But by definition, #-log_10[H_3O^+] = pH#, and # log_10[HO^-] =pOH#.

So #pH + pOH = 14#