Direct Energy, 2018a

210 9.2 Measures of the Ability of Charges to Flow
As an example, let's ndthe pH of a solution with 10 15 ions of H + in 1
L of water.
[
H
+ ] = 1015 ions
1 L
1
·
6.022 · 10 23 ions
mol
(
pH =log
−9 mol
=1.66 · 10
L
(9.12)
)
1
≈ 9
1.66 · 10 −9 (9.13)
Notice that the exponent of [ H +] is -9, andthe pH is 9. Qualitatively, the
pH tells us the negative of the order of magnitude of the amount concentration
of hydrogen ions. The solution in this example is alkaline.
As a relatedexample, let's ndthe pH of a solution with 10 20 ions of
H + in 1 L of water.
[
H
+ ] = 1020 ions
1 L
1
·
6.022 · 10 23 ions
mol
(
pH =log
−4 mol
=1.66 · 10
L
(9.14)
)
1
≈ 4
1.66 · 10 −4 (9.15)
This example has more hydrogen ions in the solution, so it is more acidic.
The pH of 4 tells us that the solution has approximately 10 −4 mol
L
of
hydrogen ions.
How many hydrogen ions are found in a 1 L solution with a pH of 7?
( ) 1
−7 mol
10
L
7=log
[H + ]
[ ] H
+ −7 ions
=10
mol
(9.16)
(9.17)
ions
· 1 L · 6.022 · 1023
mol =6.022 · 1016 ions H + (9.18)
A neutral solution, with a pH of 7, still contains H + ions.