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

##### 1 Answer

Here's what I got.

#### Explanation:

The **pH** of a solution is simply a measure of the concentration of hydrogen ions,

More specifically, the pH of the solution is calculated using the **negative log base**

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

Now, we use the *negative* log base

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 **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 **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 **units lower** than the pH of a second solution will have a concentration of hydronium cations that **times higher** than that of the second solution.