Question

What is difference between a pH of 8 and a pH of 12 in terms of H+ concentration?

Answer 1

Here's what I got.

Explanation:

The pH of a solution is simply a measure of the concentration of hydrogen ions, `"H"^(+)`, which you'll often see referred to as hydronium cations, `"H"_3"O"^(+)`.

More specifically, the pH of the solution is calculated using the negative log base `10` of the concentration of the hydronium cations.

`color(blue)(|bar(ul(color(white)(a/a)"pH" = - log(["H"_3"O"^(+)])color(white)(a/a)|)))`

Now, we use the negative log base `10` because the concentration of hydronium cations is usually significantly smaller than `1`.

As you know, every increase in the value of a log function corresponds to one order of magnitude. For example, you have

`log(10) = 1`

`log(10 * 10) = log(10) + log(10) = 1 + 1 = 2`

`log(10 * 10^2) = log(10) + log(10^2) = 1 + 2 = 3`

and so on. In your case, the difference between a pH of `8` and a pH of `12` corresponds to a difference of four units of magnitude between the concentration of hydronium cations in the two solutions.

Keep in mind, however, that because you're dealing with numbers that are smaller than `1`, and thus with negative logs, that the solution with a higher pH will actually have a lower concentration of hydronium cations.

More specifically, you have

`"pH"_1 = - log(["H"_3"O"^(+)]_1) = 8`

This is equivalent to

`["H"_3"O"^(+)]_1 = 10^(-"pH"_1) = 10^(-8)"M"`

Similarly, you have

`"pH"_2 = - log(["H"_3"O"^(+)]_2) = 12`

This is equivalent to

`["H"_3"O"^(+)]_2 = 10^(-"pH"_2) = 10^(-12)"M"`

As you can see, the first solution has a concentration of hydronium cations that is

`(10^(-8)color(red)(cancel(color(black)("M"))))/(10^(-12)color(red)(cancel(color(black)("M")))) = 10^color(red)(4)`

times higher than the concentration of hydronium cations of the second solution. This corresponds to the fact that you have

`"pH"_2 - "pH"_1 = 12 - 8 = color(red)(4)`

Simply put, a solution that has a pH that is `color(red)(4)` units lower than the pH of a second solution will have a concentration of hydronium cations that `10^color(red)(4)` times higher than that of the second solution.

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