The acidity of a solution can be described by its concentration of H⁺. One way to express this concentration is in pH units, which stands for the Power of the Hydrogen ion concentration. pH is defined as

pH = -log₁₀[H⁺]

By the definition of pH, more acidic solutions will have a lower pH. If the pH of a solution is below 7, it is an acid, if it is above 7, it is basic. Why 7? Because water autoionizes: the concentration of H⁺ in pure water is 1.0*10^-7 M, and thus the pH of pure water is -log(10^-7) = 7.

Example 1: Lemon juice has a H⁺ concentration of about 6.3*10^-3 M, depending on the lemon. What is the pH of lemon juice?

Solution: The pH is the -log₁₀ of the hydrogen ion concentration, so

pH = -log₁₀(6.3*10^-3) = 2.2

Example 2: The pH of household vinegar is about 3.0. What is the hydrogen ion concentration of vingear?

Solution: Set up the equation as usual, then take the inverse log (10^x on your calculator) of both sides to eliminate the log

pH = -log₁₀([H⁺])

3.0 = -log₁₀([H⁺])

-3.0 = log₁₀([H⁺])

10^-3 = 10^{log₁₀([H+])} = [H⁺]

[H⁺] = 10^-3 M

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