Chemistry
posted by Jonah .
A tank contains exactly 10^(6)liters of pure water. 1.0*10^(6) moles of HCl (g) is bubbled into this tank. What is the resulting pH?
The answer is 7, but I was only able to deduce that based on the fact that water has a neutral pH, but there's a mathematical way to do it and I'm not sure how to go about it.

I don't know.

HCl is a strong acid meaning that it dissociates 100%; therefore, 1E6 mol/1E6L = 1E12M HCl.
HCl ==> H^ + Cl^
1E12...0.....0
1E12..1E12..1E12
..........HOH ==> H^+ + OH^
I...............1E12....0
C..................x......x
E..............1E12+x....x
(H^+)(OH^) = Kw = 1E14
(1E12+x)(x) = 1E14
Solve the quadratic. I get all of these numbers on the calculator like
9.99995E8
pH = log(H^+) = 7.00000.
With no temperature listed I couldn't look up the correct value for Kw at that particular temperature but I think this will do the trick.