Now before starting a pH calculation, we have to understand something about concentration of hydronium and hydroxide in solution. Or even in just normal water. Now here’s the thing, if water actually collides with water an exchange of atoms can actually take place according to collision theory and what can happen is that one water molecule can lose a proton to another. So one can act as an acid and the other is a base and form hydronium hydroxide in solution. It would form equal concentrations of them and so therefore they would kind of cancel out in terms of their reactivity and we would have a neutral solution still. But water does breakdown into ions, and water does have hydronium and hydroxide in it.
And because this is an equilibrium, the concentrations of these two at any one time will vary accordingly to always give us a constant? So what is that constant when real? In 25 degrees Celsius in real conditions, the concentration of hydronium or hydroxide in water is 1.00 x 10-7 moles/liter. It’s not a very high concentration, but it’s actually quite significant. So if we’re going to write an expression for this reaction, remember we don’t include liquids in the expression, so the K value just equals the concentration of hydronium times hydroxide over one. Or we call it the KW, and that equals these two concentrations multiplied together to give us the equilibrium constant of 1.00 x 10-14.
So here’s the thing, if I said to you, you know what the concentration of hydronium in solution actually goes up to 10-6, remember that’s higher than 10-7, what will be the concentration of the hydroxide be in solution? Well it would have to be 10-8. Six and eight still equals to 14. But do you get it? The idea is now we’ve got more hydronium than hydroxide, the solution is now an acid because it has a greater concentration of the acidic molecule. They both still equal this equilibrium constant of 1.00 x 10-14. So you can now be asked a myriad of questions or at least this next one.
So break that question down, understand that you’ve got the hydroxide ion concentration and you're looking for hydronium. You’ve got this formula memorized now. The KW equals the hydronium times the hydroxide concentration. So if you're solving for hydronium you're going to take hydroxide divide it into each side to get hydronium equals KW over hydroxide—manipulation of that formula. Plug your numbers in 1.00 x 10-14 is the KW, you’ve got to know that. There is your concentration of hydroxide there and so your answer is 4.3 x 10-9.
Now you're going to say, “It looks like I just saw something here.” 10-9 and 16 equals negative 15. Yeah, but 2.3 x 4.3 equals ten. Ten times 10-15, is the same as 1.00 x 10-14. It all works out, that’s good. And because the concentration of the hydroxide is greater than the hydronium, this solution is a base. But the thing is, do you always have to kind of do this mental gymnastics to be able to figure out the solutions in acid or base? Now Soren Sorensen comes up with a pH formula about 100 years ago and now that is the standard by which we compare acidity. And here’s how we do it.