Example: Determination of pH from [H3O+]

What is the pH of a solution whose [H3O+] = 1 X 10-4 M

pH = -log[H3O+]

pH = - log[1 X 10-4]

pH = - [ log 1 + log 10-4 ]

Note: When you multiply numbers you always ADD their log forms

log 1 is always zero

log 10x = x

so log 10-4 = -4

pH = - [ log 1 + log 10-4 ] = - [ 0 + (-4) ] = - [-4 ] = +4

Example: Determination of pH from [H3O+] when coefficient is other than "1"

What is the pH of a solution whose [H3O+] = 2.5 X 10 -5 M

pH = -log[H3O+]

pH = - log[2.5 X 10 -5]

pH = - [ log 2.5 + log 10-5 ]

Note: When you multiply numbers you always ADD their log forms

log 10x = x

so log 10-5 = -5

 

log 2.5 can be determined using a calculator having the log function key:

 

Enter the number in this case 2.5

 

depress the log key

 

Read the display which should be .3979 for this problem

pH = - [.3979 - 5] = 4.6021 or +4.602

Alternately if you can enter a number in scientific notation into your calculator key in 2.5 X 10 -5

depress the log key

Read the display which should be -4.602 for this problem

Multiply by -1 to get + 4.602

Example: Determination of pH from [OH1- ] using defintion pOH and equation pH + pOH = 14

Calculate the pH of a solution that has a [OH1-] = 1 X 10-5 M

Determine pOH = -log[OH1- ] = -log [1 X 10-5 ] = 5

Use the relationship pH + pOH = 14

pH + 5 = 14

pH = 14 -5 = 9

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.