ionization of water and equations

1. Ionization of water
shahnawaz Rayeen
B.tech Biotechnology
Mangalayatan university

2. Self Ionisation of Water
Water undergoes Self Ionisation
H2O(l) ⇄ H+
(aq) + OH-
(aq)
or
H2O(l) + H2O(l) ⇄ H3O+
(aq) + OH
-
(aq)
The concentration of H+ ions and OH- ions
is extremely small.
Because the equilibrium lies very much on the left hand
side.

3. Glossary
Ionisation
Ionic Product
pH
Logarithm
Kw
Indicator
pH scale
Strong/weak acids
Strong/Weak bases
pH Curve
End-Point
Dissociation Constant

4. Ionic Product of Water
H2O(l) ⇄ H+
(aq) + OH-
(aq)
Kc =
In the above expression, the value of [H2O] may be taken as having a
constant value because the degree of ionisation is so small.
Kc =
Kc [H2O] = [H+] [OH-]
Both Kc and [H2O] are constant values so
Kw = Kc [H2O] = [H+] [OH-]
Kw = [H+] [OH-] is the ionic product of water

5. Kw is temperature dependent
T (°C) Kw (mol2/litre2)
0 0.114 x 10-14
10 0.293 x 10-14
20 0.681 x 10-14
25 1.008 x 10-14
30 1.471 x 10-14
40 2.916 x 10-14
50 5.476 x 10-14
Kw of pure water decreases as the temperature increases

6. Acid–Base Concentrations in Solutions

7. Acid–Base Concentrations in Solutions
OH-
H+
OH-
OH-
H+
H+
[H+] = [OH-]
[H+] > [OH-] [H+] < [OH-]
acidic
solution
neutral
solution
basic
solution
concentration
(moles/L)
10-14
10-7
10-1

8. pH Scale
Soren Sorensen
(1868 - 1939)
The pH scale was invented by the Danish chemist
Soren Sorensen to measure the acidity of beer in a
brewery. The pH scale measured the concentration of
hydrogen ions in solution. The more hydrogen ions,
the stronger the acid.

9. The pH Scale
Neutral Weak
Alkali
Strong
Alkali
Weak
Acid
Strong
Acid
7 8 9 10 11 12 13
3 4 5 6
2 14
1 7 8 9 10 11 12 13
3 4 5 6
2 14
1 9 10 11 12
3 4 5 6
2
1

10. pH Scale
The quantity of hydrogen ions in
solution can affect the color of
certain dyes found in nature. These
dyes can be used as indicators to
test for acids and alkalis. An
indicator such as litmus (obtained
from lichen) is red in acid. If base is
slowly added, the litmus will turn
blue when the acid has been
neutralized, at about 6-7 on the pH
scale. Other indicators will change
color at different pH’s. A
combination of indicators is used to
make a universal indicator.

11. Measuring pH
 Universal Indicator Paper
 Universal Indicator Solution
 pH meter

12. Measuring pH
pH can be measured in several ways
 Usually it is measured with a coloured acid-base
indicator or a pH meter
 Coloured indicators are a crude measure of pH, but
are useful in certain applications
 pH meters are more accurate, but they must be
calibrated prior to use with a solution of known pH

13. Limitations of pH Scale
The pH scale ranges from 0 to 14
Values outside this range are possible but do not
tend to be accurate because even strong acids and
bases do not dissociate completely in highly
concentrated solutions.
pH is confined to dilute aqueous solutions

14. pH
At 250C
Kw = 1 x 10-14 mol2/litre2
[H+ ] x [OH- ] = 1 x 10-14 mol2/litre2
This equilibrium constant is very important because it
applies to all aqueous solutions - acids, bases, salts,
and non-electrolytes - not just to pure water.

15. pH
For H2O(l) ⇄ H+
(aq) + OH-
(aq)
→ [H+ ] = [OH- ]
[H+ ] x [OH- ] = 1 x 10-14 = [1 x 10-7 ] x [1 x 10-7 ]
[H+ ] of water is at 250C is 1 x 10-7 mol/litre
Replacing [H+ ] with pH to indicate acidity of solutions
pH 7 replaces [H+ ] of 1 x 10-7 mol/litre
where pH = - Log10 [H+ ]

16. pH is temperature dependent
T (°C) pH
0 7.12
10 7.06
20 7.02
25 7
30 6.99
40 6.97
pH of pure water decreases as the temperature increases
A word of warning!
If the pH falls as temperature increases, does this mean that water
becomes more acidic at higher temperatures? NO!
Remember a solution is acidic if there is an excess of hydrogen ions over hydroxide ions.
In the case of pure water, there are always the same number of hydrogen ions and
hydroxide ions. This means that the water is always neutral - even if its pH change

17. Students should be able to:
•define pH
•describe the use of the pH scale as a measure of the degree of
acidity/alkalinity
•discuss the limitations of the pH scale
•explain self-ionisation of water
•write an expression for Kw

18. Acid – Base Concentrations and pH
pH = 3
pH = 7
pH = 11
OH-
H+
OH-
OH-
H+
H+
[H3O+] = [OH-]
[H3O+] > [OH-] [H3O+] < [OH-]
acidic
solution
neutral
solution
basic
solution
concentration
(moles/L)
10-14
10-7
10-1

19.  pH describes both [H+ ] and [OH- ]
0 Acidic [H+ ] = 100 [OH- ] =10-14
pH = 0 pOH = 14
7 Neutral [H+ ] = 10-7 [OH- ] =10-7
pH = 7 pOH = 7
14 Basic [H+ ] = 10-14 [OH- ] = 100
pH = 14 pOH = 0

20. 

21. pH of Common Substances
Acidic Neutral Basic

22. 14 1 x 10-14 1 x 10-0 0
13 1 x 10-13 1 x 10-1 1
12 1 x 10-12 1 x 10-2 2
11 1 x 10-11 1 x 10-3 3
10 1 x 10-10 1 x 10-4 4
9 1 x 10-9 1 x 10-5 5
8 1 x 10-8 1 x 10-6 6
6 1 x 10-6 1 x 10-8 8
5 1 x 10-5 1 x 10-9 9
4 1 x 10-4 1 x 10-10 10
3 1 x 10-3 1 x 10-11 11
2 1 x 10-2 1 x 10-12 12
1 1 x 10-1 1 x 10-13 13
0 1 x 100 1 x 10-14 14
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
More
basic
More
acidic pH [H+] [OH-] pOH
7 1 x 10-7 1 x 10-7 7

23. Calculations and practice
pH = – log10[H+]
• You will need to memorize the following:
pOH = – log10[OH–]
[H+] = 10–pH
[OH–] = 10–pOH
pH + pOH = 14

24. pH Calculations
pH
pOH
[H+]
[OH-]
pH + pOH = 14
pH = -log10[H+]
[H+] = 10-pH
pOH = -log10[OH-]
[OH-] = 10-pOH
[H+] [OH-] = 1 x10-14

25. pH for Strong Acids
 Strong acids dissociate completely in solution
 Strong alkalis (bases) also dissociate completely in
solution.
 It is easy to calculate the pH of strong acids and strong bases; you
only need to know the concentration.

26. pH Exercises
a) pH of 0.02M HCl
pH = – log10 [H+]
= – log10 [0.020]
= 1.6989
= 1.70
b) pH of 0.0050M NaOH
pOH = – log10 [OH–]
= – log10 [0.0050]
= 2.3
pH = 14 – pOH
= 14 – 2.3
=11.7
c) pH of solution where [H +]
is 7.2x10-8M
pH = – log10 [H+]
= – log10 [7.2x10-8]
= 7.14
(slightly basic)

27. pH of dilute aqueous solutions of strong acids
monoprotic
diprotic
HA(aq) H1+(aq) + A1-(aq)
0.3 M 0.3 M 0.3 M
pH = - log10 [H+]
pH = - log10[0.3M]
pH = 0.48
e.g. HCl, HNO3
H2A(aq) 2 H1+(aq) + A2-(aq)
0.3 M 0.6 M 0.3 M
pH = - log10[H+]
pH = - log10[0.6M]
pH = 0.78
e.g. H2SO4
pH = ?

28. pH = - log [H+]
pH = 4.6
pH = - log10 [H+]
4.6 = - log10 [H+]
- 4.6 = log10[H+]
- 4.6 = antilog [H+]
Given:
2nd log
10x
antilog
multiply both sides by -1
substitute pH value in equation
take antilog of both sides
determine the [hydrogen ion]
choose proper equation
[H+] = 2.51x10-5 M
You can check your answer by working backwards.
pH = - log10[H+]
pH = - log10[2.51x10-5 M]
pH = 4.6

29. Most substances that are acidic in water are actually weak acids.
Because weak acids dissociate only partially in aqueous solution,
an equilibrium is formed between the acid and its ions.
The ionization equilibrium is given by:
HX(aq) H+(aq) + X-(aq)
where X- is the conjugate base.

30. pH calculations for Weak Acids and Weak Bases
For Weak Acids
pH = -Log10
For Weak Bases
pOH = Log10
pH = 14 - pOH

31. Calculating pH - weak acids
A weak acid, HA, dissociates as follows HA(aq) H+
(aq) + A¯(aq) (1)
Applying the Equilibrium Law Ka = [H+
(aq)] [A¯(aq)] mol dm-3 (2)
[HA(aq)]
The ions are formed in equal amounts, so [H+
(aq)] = [A¯(aq)]
therefore Ka = [H+
(aq)]2 (3)
[HA(aq)]
Rearranging (3) gives [H+
(aq)]2 = [HA(aq)] Ka
therefore [H+
(aq)] = [HA(aq)] Ka
A weak acid is one which only partially dissociates in aqueous solution

32. pH of solutions of weak concentrations
Weak Acid
pH of a 1M solution of ethanoic acid with a Ka value of 1.8 x 10-5
pH = -Log10
pH = -Log10
pH = 2.3723

33. pH of solutions of weak concentrations
Weak Base
pH of a 0.2M solution of ammonia with a Kb value of 1.8 x 10-5
pOH = -log10
pOH = -log10
pOH = 2.7319
pH = 14 – 2.7319
pH = 11.2681

34. Theory of Acid Base Indicators
Acid-base titration indicators are quite often weak acids.
For the indicator HIn
The equilibrium can be simply expressed as
HIn(aq, colour 1) H+
(aq) + In-
(aq, colour 2)
The un-ionised form (HIn) is a different colour to the anionic
form (In¯).

35. Theory of Acid Base Indicators
Applying Le Chatelier's equilibrium principle:
Addition of acid
• favours the formation of more HIn (colour 1)
HIn(aq) H+
(aq) + In-
(aq)
because an increase on the right of [H+]
causes a shift to left
increasing [HIn] (colour 1)
to minimise 'enforced' rise in [H+].

36. Theory of Acid Base Indicators
Applying Le Chatelier's equilibrium principle:
Addition of base
• favours the formation of more In- (colour 2)
HIn(aq) H+
(aq) + In-
(aq)
The increase in [OH-] causes a shift to right
because the reaction
H+
(aq) + OH-
(aq) ==> H2O(l)
Reducing the [H+] on the right
so more HIn ionises to replace the [H+]
and so increasing In- (colour 2)
to minimise 'enforced' rise in [OH-]

37. Theory of Acid Base Indicators
 Summary
 In acidic solution
 HIn(aq) H+
(aq) + In¯(aq)
 In alkaline solution

38. Theory of Acid Base Indicators
Acid-base titration indicators are also often weak bases.
For the indicator MOH
The equilibrium can be simply expressed as
MOH(aq, colour 1) OH-
(aq) + M+
(aq, colour 2)

39. Theory of Acid Base Indicators
Applying Le Chatelier's equilibrium principle:
Addition of base
• favours the formation of more MOH (colour 1)
MOH(aq) M+
(aq) + OH-
(aq)
because an increase on the right of [OH-]
causes a shift to left
increasing [MOH] (colour 1)
to minimise 'enforced' rise in [OH
-].

40. Theory of Acid Base Indicators
Applying Le Chatelier's equilibrium principle:
Addition of acid
• favours the formation of more M+ (colour 2)
MOH(aq) M+
(aq) + OH-
(aq)
The increase in [H+] causes a shift to right
because the reaction
H+
(aq) + OH-
(aq) ==> H2O(l)
Reducing the [OH-] on the right
so more MOH ionises to replace the [OH-]
and so increasing M+ (colour 2)
to minimise 'enforced' rise in [H+]

41. Acid Base Titration Curves
Strong Acid – Strong Base Strong Acid – Weak Base
Weak Acid – Strong Base Weak Acid – Weak Base

42. Choice of Indicator for Titration
 Indicator must have a complete colour change in
the vertical part of the pH titration curve
 Indicator must have a distinct colour change
 Indicator must have a sharp colour change

43. Indicators for Strong Acid Strong Base Titration
Both phenolphthalein
and methyl orange
have a complete
colour change in the
vertical section of the
pH titration curve

44. Indicators for Strong Acid Weak Base Titration
Only methyl orange
has a complete
colour change in the
vertical section of the
pH titration curve
Phenolphthalein has
not a complete colour
change in the vertical
section on the pH
titration curve.
Methyl Orange is
used as indicator for
this titration

45. Indicators for Weak Acid Strong Base Titration
Only phenolphthalein
has a complete
colour change in the
vertical section of the
pH titration curve
Methyl has not a
complete colour
change in the vertical
section on the pH
titration curve.
Phenolphthalein is
used as indicator for
this titration

46. Indicators for Weak Acid Weak Base Titration
Neither phenolphthalein
nor methyl orange have
completely change colour
in the vertical section on
the pH titration curve
No indicator suitable
for this titration
because no vertical
section

47. indicator pH range
litmus 5 - 8
methyl orange 3.1 - 4.4
phenolphthalein 8.3 - 10.0

48. Colour Changes and pH ranges

49. Methyl Orange

50. Phenolphthalein

51. Universal indicator components
Indicator Low pH color Transition pH range High pH color
Thymol blue (first transition) red 1.2–2.8 orange
Methyl Orange red 4.4–6.2 yellow
Bromothymol blue yellow 6.0–7.6 blue
Thymol blue (second transition) yellow 8.0–9.6 blue
Phenolphthalein colourless 8.3–10.0 purple

52. Students should be able to:
• calculate the pH of dilute aqueous solutions of strong acids and bases
• distinguish between the terms weak, strong, concentrated and dilute
in relation to acids and bases
• calculate the pH of weak acids and bases (approximate method of
calculation to be used – assuming that ionisation does not alter the
total concentration of the non-ionised form)
• define acid-base indicator
• explain the theory of acid-base indicators
• justify the selection of an indicator for acid base titrations