TQ Chemistry

Uses in Chemistry

Logarithms can be used in the classroom to calculate the concentration of ions present using either the pH or the pOH of an aqueous solution.
The pH is the measure of the concentration of Hydrogen ions present in an aqueous solution
The pOH is a measure of the concentration of HydrOxide ions present.
Background

As the pH decreases, the concentration of hydrogen ions increases, so the solution becomes more acidic.
As the pH increases, the concentration of hydroxide ions increases, making the solution more alkaline.

                   pH                [ H+(aq)]
            mol per litre


                  15
                  14
                  13
                  12
                  11
                  10
                   9
                   8
                     1x10^-15
                1x10^-14
                1x10^-13
                1x10^-12
                1x10^-11
                1x10^-10
                1x10^-9
                1x10^-8

                   7                 1x10^-7

                     6
                   5
                   4
                   3
                   2
                   1
                   0
                  -1                    1x10^-6
                1x10^-5
                1x10^-4
                1x10^-3
                1x10^-2
                1x10^-1
                1x10⁰
                1x10¹

NOTE: the pH is equivalent to the power the ten is raised to.
Using the logarithms
By applying the formulas pH = -log10[ H⁺ (aq)] and pOH = -log10[ OH^- (aq)], the concentrations can be calculated.
Example:
pH = 3              pH = -log10[ H⁺ (aq)]
                            3 = -log10[ H⁺ (aq)]          so therefore the H⁺ concentration
                           -3 = log10[ H⁺ (aq)]           is 1x10^-3 which by comparing it
                        10^-3= [ H⁺ (aq)]                  with the table is correct!
Other useful formulae

[H⁺ (aq)] = 1x10^-7 moll^-1 = [OH^- (aq)] in an neutral solution

pH + pOH = 14

[H⁺ (aq)] = 10^-pH

A brief history of John Napier               Rules of Logarithms                     Examples of Logarithms
                                     Answers to Examples                    Uses of Logarithms

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pH	[ H+(aq)] mol per litre
15 14 13 12 11 10 9 8	1x10^-15 1x10^-14 1x10^-13 1x10^-12 1x10^-11 1x10^-10 1x10^-9 1x10^-8
7	1x10^-7
6 5 4 3 2 1 0 -1	1x10^-6 1x10^-5 1x10^-4 1x10^-3 1x10^-2 1x10^-1 1x10⁰ 1x10¹