pH Scale and Calculations
Chapter 14
pH Scale
• We use this scale to measure the strength
of an acid or base.
• pH is defined as the –log[H+]
• pH can use the concentration of
hydronium ions or hydrogen ions.
7
Acid
0
Base
pH Scale
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 515
14
pH of Common Substances
Timberlake, Chemistry 7th Edition, page 335
Ionization of Water
Occasionally, in water, a H+ is transferred
between H2O molecules
..
..
H:O: +
:O:H
..
H
..
H
water molecules
..
H:O:H +
..
..
+
:O:H..
H
hydronium
ion (+)
LecturePLUS Timberlake
hydroxide
ion (-)
5
Pure Water is Neutral
Pure water contains small, but equal
amounts of ions: H3O+ and OH-
H2O + H2O
H 3O +
OH-
H3O+
+
OH-
hydronium hydroxide
ion
ion
1 x 10-7 M 1 x 10-7 M
6
Ion Product of Water Kw
Kw
=
[ H3O+ ] [ OH- ]
=
[ 1 x 10-7 ][ 1 x 10-7 ]
=
1 x 10-14
7
pH of Common Substance
More acidic
More basic
pH
NaOH, 0.1 M
Household bleach
Household ammonia
Lime water
Milk of magnesia
Borax
Baking soda
Egg white, seawater
Human blood, tears
Milk
Saliva
Rain
Black coffee
Banana
Tomatoes
Wine
Cola, vinegar
Lemon juice
Gastric juice
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
[H1+]
[OH1-]
1 x 10-14
1 x 10-13
1 x 10-12
1 x 10-11
1 x 10-10
1 x 10-9
1 x 10-8
1 x 10-7
1 x 10-6
1 x 10-5
1 x 10-4
1 x 10-3
1 x 10-2
1 x 10-1
1 x 100
1 x 10-0
1 x 10-1
1 x 10-2
1 x 10-3
1 x 10-4
1 x 10-5
1 x 10-6
1 x 10-7
1 x 10-8
1 x 10-9
1 x 10-10
1 x 10-11
1 x 10-12
1 x 10-13
1 x 10-14
pOH
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Acid – Base Concentrations
concentration (moles/L)
10-1
pH = 3
pH = 11
OH-
H3O+
pH = 7
10-7
H3O+
OH-
OH-
H3O+
10-14
Timberlake, Chemistry 7th Edition, page 332
[H3O+] > [OH-]
[H3O+] = [OH-]
acidic
solution
neutral
solution
[H3O+] < [OH-]
basic
solution
pH
pH = -log [H+]
Kelter, Carr, Scott, Chemistry A World of Choices 1999, page 285
Self-Ionization Of Water
• Even the purest of water conducts electricity. This
is due to the fact that water self-ionizes, that is, it
creates a small amount of H3O+ and OH-.
H2O + H2O  H3O+ + OHKw = [H3O+][OH-]
• Kw - ion product of water
Kw = 1.0 x 10-14 at 25 oC
• This equilibrium constant is very important because
it applies to all aqueous solutions - acids, bases,
salts, and non-electrolytes - not just to pure water.
Self ionization reaction of water:
O
H
H
+ H
O
O
H
H
+
H + O
H

2 H2O  H3O  OH


K w  [H3O ] [OH ]  10
-14
Kw
[H 3O ] 
[OH-]

H

(at 25C)
pH and pOH
• pH = - log[H3O+]
pOH = - log[OH-]
[H3O+] = 10-pH
[OH-] = 10-pOH
• pKw = pH + pOH = 14.00
• neutral solution: [H3O+] = [OH-] = 10 –7 M pH = 7.0
acidic solution: [H3O+] > 10-7 M
pH < 7.0
[H3O+] < 10-7 M
pH > 7.0
basic solution:
Learning Check pH
A. The [H3O+] of tomato juice is 1 x 10-4 M.
What is the pH of the solution?
1) - 4
2)
4
3)
8
B. The [OH-] of an ammonia solution is
1 x 10-3 M. What is the pH of the solution?
1)
3
2)
11
LecturePLUS Timberlake
3)
-11
14
Solution pH4
A. pH = - log [ 1 x 10-4] = -(- 4) = 4
B. [H3O+] = 1 x 10-11
pH = - log [ 1 x 10- 11] = -(- 11) = 11
LecturePLUS Timberlake
15
Learning Check pH5
The pH of a soap is 10. What is the
[H3O+] of the soap solution?
1) 1 x 10 - 4 M
2) 1 x 1010 M
3) 1 x 10 - 10 M
LecturePLUS Timberlake
16
Solution pH5
The pH of a soap is 10. What is the
[H3O+] of the soap solution?
[H3O+]
= 1 x 10-pH M
= 1 x 10-10 M
LecturePLUS Timberlake
17
pH on the Calculator
[H3O+] is 4.5 x 10-6 M
pH = -log(4.5 x10-6 )
= 5.35
18
Learning Check pH6
A soap solution has a [H3O+] = 2 x 10-8 M.
What is the pH of the solution?
1) 8
2) 7.7
3) 6
LecturePLUS Timberlake
19
Solution pH6
A soap solution has a [H3O+] = 2.0 x
10-8 M. What is the pH of the solution?
B) = 7.7
20
Calculating pH from pOH
• The concentration of [OH–] in a cleaning
product was found to be 10–3 mol L–1.
• Find the pH of the solution.
Practise
• (a) A 0.01 mol L–1 solution of HNO3 is
prepared. Calculate the pH of the
• solution.
• (b) A 0.005 mol L–1 solution of H2SO4 is
prepared. Assuming complete
• ionisation, calculate the pH of the solution.
Sample Problem:
Calculating the pH of a dilution
• 50 mL of a solution of HCl of pH 2 is
diluted so that the new pH is 5. What
• volume of water was added?