## Calculating pH

The pH of a substance is defined by:

pH = −log[H

^{+}]

where the quantity [H

^{+}] represents the concentration of hydrogen ions, measured in moles per liter, in the substance.

- A substance with a pH < 7 is considered an acid
- A substances with a pH > 7 is considered a base

Example #1:

Find the pH of milk whose concentration of hydrogen ions, [H

^{+}] = 4 x 10

^{-7}moles/liter.

Solution #1:

Using pH = −log[H

pH = −log(4 x 10

pH ≈ −(−6.4)

pH ≈ 6.4

^{+}]:pH = −log(4 x 10

^{-7})pH ≈ −(−6.4)

pH ≈ 6.4

Example #2:

Find the concentration of hydrogen ions, [H

^{+}], for vinegar with a pH = 3.1.Solution #2:

Using pH = −log[H

3.1 = −log[H

Multiplying each side by −1:

−3.1 = log[H

Raising both sides to power of 10:

10

[H

^{+}]:3.1 = −log[H

^{+}]Multiplying each side by −1:

−3.1 = log[H

^{+}]Raising both sides to power of 10:

10

^{−3.1}= [H^{+}][H

^{+}] ≈ 7.94 x 10^{-4}moles/liter