Calculations of pH using a number line scale or calculator
| The pH for a solution is determined from the definition pH = - log[H3O1+]. A simple graphic relationship between the hydronium ion concentration and pH is shown here. The top row gives the concentration [H3O1+] (also written as H+ ion ) and the second line gives the matching pH . This is limited only to the whole numbered exponents of 10. |
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Table shows acidic pH in red and basic in blue. Note that at 25oC the product [H+] x [OH-] always must equal 1 x 10-14 |
|
[H+] |
= |
100 |
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 |
100 |
101 |
|
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 1 What 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. [H3O1+] = 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[H3O1+]; 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 2 What is the pH of a 0.001 M HNO3(aq) solution. Nitric acid, HNO3(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. [H3O1+] = [ NO3 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[H3O1+] ; pH = -log 1 x 10-3 ; pH = 3 Example 3 What is the pH for a 0.10 M NaOH solution? 1. Sodium hydroxide is a strong base. 2. The Na1+ and OH1- concentrations equal the original NaOH concentration. 3. [Na1+] = [ OH1- ] = 0.10 M = 1 x 10-1 M. 4. The number scale above can be used to find the pH. 5. Look for [ OH1- ] = 1 x 10-1 M . The table gives the [H3O1+] = 1 x 10-13 M . 6. This means pH = "13". This is a BASIC solution.
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