Calculations of pH using a number line scale or calculator

The pH for a solution is determined from the definition pH = - log[H _{3}O^{1+}]. A simple graphic relationship between the hydronium ion concentration and pH is shown here. The top row gives the concentration [H_{3}O^{1+}] (also written as H^{+}ion ) and the second line gives the matching pH . This is limited only to the whole numbered exponents of 10.

Table shows acidic pH in red and basic in blue.

Note that at 25^{o}C the product [H^{+}] x [OH^{-}] always must equal 1 x 10^{-14}

[H^{+}]

=10

^{0}10

^{-1}10

^{-2}10

^{-3}10

^{-4}10

^{-5}10

^{-6}10

^{-7}10

^{-8}10

^{-9}10

^{-10}10

^{-11}10

^{-12}10

^{-13}10

^{-14}10

^{-15}

[OH^{-}]

=10

^{-14}10

^{-13}10

^{-12}10

^{-11}10

^{-10}10

^{-9}10

^{-8}10

^{-7}10

^{-6}10

^{-5}10

^{-4}10

^{-3}10

^{-2}10

^{-1}10

^{0}10

^{1}

Kw

=10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}10

^{-14}

pH

=.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

EXAMPLES of pH determinations

Example 1What is the pH of a 0.01 M HCl(aq)? Hydrochloric acid, HCl(aq), is a strong acid. The molarity of a strong acid is the same as the molarity of the hydronium ion because strong acids are 100% ionized. The ion concentrations equal the original acid concentration. [H_{3}O^{1+}] = 1.0 x 10^{-2}; The number scale above can be used to find the pH. The answer is pH = "2".Alternately the pH can be figured using a calculator.

1. pH = -log[H

_{3}O^{1+}];2. pH = -log 1 x 10

^{-2}3. Enter the number 0.01 or 1 x 10

^{-2 }.4, Depress the calculator log function. The display should show -2.

5. Multiply the -2 by a minus 1 . The final answer is "2". This is an acidic solution.

Example 2What is the pH of a 0.001 M HNO_{3}(aq) solution. Nitric acid, HNO_{3}(aq), is a strong acid, this means the acid dissociates 100%. This gives the hydronium ion and nitrate ion concentrations as the molarity of the acid.1. [H

_{3}O^{1+}] = [ NO_{3 }^{1-}] = 1.0 x 10^{-3}mols/ liter.2. The number scale above can be used to find the pH. The answer is pH = "3".

3. Alternately using the equations for the pH definition

pH = -log[H

_{3}O^{1+}] ; pH = -log 1 x 10^{-3}; pH = 3

Example 3What is the pH for a 0.10 M NaOH solution?1. Sodium hydroxide is a strong base.

2. The Na

^{1+}and OH^{1-}concentrations equal the original NaOH concentration.3. [Na

^{1+}] = [ OH^{1- }] = 0.10 M = 1 x 10^{-1 }M.4. The number scale above can be used to find the pH.

5. Look for [ OH

^{1- }] = 1 x 10^{-1 }M . The table gives the [H_{3}O^{1+}] = 1 x 10^{-13 }M .6. This means pH = "13". This is a BASIC solution.

Dr. Walt Volland all rights reserved -1997-2005 revised April 29, 2005