Why is the pH of pure water i.e. neutral 7?

Since it was thought it's cool to have a pH scale of 0 to 14, and pure water in the middle of it. Actually, I'm not 100% sure of the origin, it probably has a greater reason than the one I mentioned.

In pure water, the hydrogen ion (hydroxonium ion) concentration must be equal to the hydroxide ion concentration.

 

[OH-] term in the Kw expression by another [H+].

 

[H+]2 = 1.00 x 10-14

 

Taking the square root of each side gives:

 

[H+] = 1.00 x 10-7 mol dm-3

 

Converting that into pH:

 

pH = - log10 [H+]

 

pH = 7

Ahh yes, the logarithm thing. I knew it had something to do with those, but since I'm going to have my first logarithm lessons (ever) in a week or so, I had no idea it goes that way.

Since it was thought it's cool to have a pH scale of 0 to 14, and pure water in the middle of it.

 

Yeah, but 10M HCl has a pH of -1, and 10M BaOH has a pH of 15, so the scale from 0-14 only works for dilute acids and bases (less than 1M)

Yeah, but the usual scale is 0-14. Of course, there are incredibly strong acids that don't even need to have H+ or OH-.