system
Given the following post, respond as if you're commenting on Reddit:
human
What does the pOH tell you about a solution where there is no hydroxide?

Okay, it was hard to make a title for this one, but I'll try to clarify here!

If we have the following reaction:
HCl + H2O → H3O^+ + Cl^-

                                         ↖ Strong acid, no equilibrium.

Let's say the pH for this solution is 1.7. 

Using Kw(10^(-14) molars^2 ) = [OH^- ] * [H3O^+ ]


log([H3O^+ ] * [OH^- ]) = log[10^-14 ]


log[H3O^+ ] + log[OH^- ] = log[10^-14 ]


-log[H3O^+ ] - log[OH^- ] = - log[10^-14 ]


pH + pOH = 14


I would imagine that pH + pOH = 14 is valid for the reaction above. But is this where I am wrong? If not, I continue. 


Since the pH is 1.7 we could calculate that the pOH is 12.3. Using this we could calculate the concentration of hydroxide in the water (10^(-12.3)). But this makes no sense since there is no known concentration of hydroxide in this solution. Where am I thinking wrong?
gpt
As long as you are working with an aqueous solution, the Kw expression is valid.  In another solvent, that wouldn't be true.  

However, in the expression above, your determination of the concentration of hydroxide is correct.  Even if there is a lot of H^+ around, that doesn't mean there can't also be OH^- around.  Pure[ish] water has a concentration of 55 M H2O.  There's plenty of room for both H^+ and OH^- at any attainable concentration of either of those ions in solution.