# The Sørensen pH scale and strong acids diltution from pH 1 to pH 4 by 1000 times?

I am reading a chemistry book that makes the following point about Sørensen's pH discovery regarding [H+] being in negative powers of 10:

To dilute a solution from a pH 1 to a pH 4 (just 3 pH units) would require dilution by 10 x 10 x 10 = 1000 times.

I don't understand how this calculation is derived, nor is there any proof available in the book.

Can someone explain how this is the case?

• let $c_1$ be concentration 1, $V_1$ be Volume 1 and so on then $c_1= 10^{-pH}$ and $c_1\times V_1 = c_2\times V_2$ – MaxW Mar 10 '17 at 22:16
• There is nothing even remotely resembling a discovery in this. The power of logarithms was known for centuries by then. – Ivan Neretin Mar 10 '17 at 22:34

The confusion here probably comes from your statement that Sørensen discovered the pH scale for expressing [$\ce{H+}$]. The pH scale is something that he created or defined for convenience. The definition of pH is basically:
$$\mathrm{pH} = -\log[\ce{H^+}]$$
Since this is a (negative) log scale, a pH of 4 has 10 times the $[\ce{H+}]$ as does a pH of 5, and so on. In other words each pH unit represents a factor of 10 change in $[\ce{H+}]$.