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.

Ionisation

Ionic Product

pH

Logarithm

Kw

Indicator

pH scale

Strong/weak acids

Strong/Weak bases

pH Curve

End-Point

Dissociation Constant

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

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

Acid–Base Concentrations in Solutions

Acid–Base Concentrations in Solutions

OH-

H+OH-

OH-H+

H+

[H+] = [OH-] [H+] > [OH-] [H+] < [OH-]

acidicsolution

neutralsolution

basicsolution

co

nc

en

trat

ion

(m

ole

s/L

)

10-14

10-7

10-1

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.

Neutral Weak Alkali

Strong Alkali

Weak Acid

Strong Acid

7 8 9 10 11 12 133 4 5 62 141 7 8 9 10 11 12 133 4 5 62 141 9 10 11 123 4 5 621

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.

Measuring pHUniversal Indicator Paper

Universal Indicator Solution

pH meter

Measuring pHMeasuring 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

Limitations of pH ScaleThe 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

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.

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+ ]

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 increasesA 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

•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

Acid – Base Concentrations and pH

pH = 3

pH = 7

pH = 11

OH-

H+OH-

OH-H+

H+

[H3O+] = [OH-] [H3O+] > [OH-] [H3O+] < [OH-]

acidicsolution

neutralsolution

basicsolution

co

nc

en

trat

ion

(m

ole

s/L

)

10-14

10-7

10-1

pH describes both [H+ ] and [OH- ]

0 Acidic [H+ ] = 100 [OH- ] =10-14

pH = 0 pOH = 14

Neutral [H+ ] = 10-7 [OH- ] =10-7

pH = 7 pOH = 7

Basic [H+ ] = 10-14 [OH- ] = 100

pH = 14 pOH = 0

pH of Common Substances

Acidic Neutral Basic

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 MHousehold bleachHousehold ammonia

Lime waterMilk of magnesia

Borax

Baking sodaEgg white, seawaterHuman blood, tearsMilkSalivaRain

Black coffeeBananaTomatoesWineCola, vinegarLemon juice

Gastric juice

Mor

e ba

sic

Mor

e ac

idic

pH [H+] [OH-] pOH

7 1 x 10-7 1 x 10-7 7

Calculations and practiceCalculations and practice

pH = – log10[H+]

• You will need to memorize the following:

pOH = – log10[OH–]

[H+] = 10–pH

[OH–] = 10–pOH

pH + pOH = 14

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

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 concentrationonly need to know the concentration.

Strong acids are so named because they react completely with water, leaving no undissociated molecules in solution.

pH ExercisespH Exercisesa) 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)

monoproticmonoprotic

diproticdiprotic

HA(aq) H1+(aq) + A1-(aq)

0.3 M 0.3 M 0.3 M

pH = - log10 [H+]

pH = - log10[0.3M]

pH = 0.48e.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 = 0.78e.g. H2SO4

pH = ?

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

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.

For Weak Acids

pH = -Log10

For Weak Bases

pOH = Log10

pH = 14 - pOH

Calculating pH - Calculating pH - weak acidsweak 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

pH of solutions of weak concentrationsWeak 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

pH of solutions of weak concentrationsWeak 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

Theory of Acid Base IndicatorsAcid-base titration indicators are quite often weak acids.

For the indicator HInThe 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¯).

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+].

Theory of Acid Base IndicatorsApplying 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-]

Theory of Acid Base IndicatorsSummary In acidic solution

HIn(aq) H+(aq) + In¯(aq)

In alkaline solution

Theory of Acid Base IndicatorsAcid-base titration indicators are also often weak bases.

For the indicator MOHThe equilibrium can be simply expressed as

MOH(aq, colour 1) OH-(aq) + M+

(aq, colour 2)

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-].

Theory of Acid Base IndicatorsApplying 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+]

Acid Base Titration CurvesStrong Acid – Strong Base Strong Acid – Weak Base

Weak Acid – Strong Base

25 cm3 of 0.1 mol dm-3 acid is titrated with 0.1 mol dm-3 alkaline solution.

Weak Acid – Weak Base

Choice of Indicator for TitrationIndicator 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

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

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

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

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

indicator pH range

litmus 5 - 8

methyl orange 3.1 - 4.4

phenolphthalein 8.3 - 10.0

Colour Changes and pH ranges

Methyl Orange

Phenolphthalein

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

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