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

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.