Chem: Calculate volume given molarity and pH

[Winning]

Homework Statement

What volume of solution is needed to dissolve 1.0 mol of a strong base such as KOH to make a solution whose pH is 12.5?

Homework Equations

$$KOH_{(s)} \rightarrow K^{+}_{(aq)} + OH^{-}_{(aq)}$$

$$pH = -log[H_{3}O^{+}]$$

The Attempt at a Solution

I'm not going to bother with the pretty print here... sorry

12.5 = -log[H3O+]
[H3O+] = 10^-12.5
[H3O+] = 3.2 x 10^-13 mol/L

[OH-] = 10^-14/(3.2 x 10^-13) M
[OH-] = 3.1 x 10^-2 M

1.0 mol * 1 L / (3.1 x 10^-2) mol = 32 L

ans: 32 L

I feel like I'm wrong... help please.

 

[Borek]

I feel like I'm wrong...

You feel wrong.