pH

[Jon_in_london]

Ph is on a scale of 0-14 yes?
pH can be defined as -log[H+] or as 14-log10[OH-] yes?

So what of 2M HCl or 15M NaOH?

[JamesM]

Originally posted by Jon_in_london
Ph is on a scale of 0-14 yes?

No, as you have noted below, the pH of 2M HCl is -0.31. You're probably thinking about the range of pH indicator paper?


pH can be defined as -log[H+] or as 14-log10[OH-] yes?

Strictly speaking, it's the -log10 of the activity not the concentration, but the first equation you give is pretty much right.

[JamesM]

Actually, a brief googling on the subject brings up a wide variety of websites devoted to the pH scale, all of them repeating the assertion that 0 is the lowest pH possible, and all of them asserting that it should be calculated by taking the -ve log10 of the concentration of H30+, which is surely only correct for solutions with an insanely low concentration of ions in.

How strange. I'm stumped - maybe they're assuming that the concentration is 1.0M (although that wouldn't justify using concentrations rather than activities). I would go back and read Sorenson's original paper, but I suspect it isn't in English.

[pgwenthold]

Originally posted by JamesM


Strictly speaking, it's the -log10 of the activity not the concentration, but the first equation you give is pretty much right.

This is an important distinction, and the one that solves the problem:

activity is approximately the concentration for dilute solutions. Thus, for dilute solutions, you can use pH = - log [H3O+]

However, as the concentration gets greater, the relationship between activity and concentration breaks down. In fact, the activity of a pure substance is 1 (because u = u* + RT ln a, where u is the chemical potential, u* is the chemical potential of the pure material, and a is the activity).

Thus, the activity of pure H3O+ is 1, such that the pH is = 0. Unlike concentration, the ativity is never greater than 1.

[JamesM]

Originally posted by pgwenthold

Unlike concentration, the ativity is never greater than 1.

I'm not sure that's true. It's true that in solution, solvent activity approaches the mole fraction as the mole fraction approaches one, but there's no reason why activities greater than unity shouldn't exist.

According to the copy of Atkins' Physical Chemistry (4th edition) I have here, the hydrogen ion activity of 2M HCl(aq) is 2.02.