# Electrochemistry and Corrosion

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```					Chemical Equilibria

Professor Brian Kinsella
The Law of Mass Action
• A+B↔C+D
• The velocity at which A and B react is
proportional to their concentrations
• ν1 = k1 x [A] x [B]
• ν2 = k2 x [C] x [D]
• At equilibrium the velocities of the forward
and reverse reaction will be equal and ν1 = ν2
• k1 x [A] x [B] = k2 x [C] x [D]
The Law of Mass Action
• Or
C D  k1   K
A B k2
• K = The equilibrium constant for the reaction
at a given temperature
• For a reversible reaction the equation may be
generalised
The Law of Mass Action
aA  bB  cC  dD

KC 
C  D 
a     d

 A B 
a    b

• (X) indicates the concentration of the reactants and
products, but to be strictly correct it is the activity of
reactants and products that should be used.
Activity and Activity Coefficient
• For a binary electrolyte
• AB ↔ A+ + B-
a A  a B 
Ka                   and K a  the true or
a AB
thermodynamic dissociati on constant

• activity = (concentration) x (activity coefficient)
• Thus at any molar concentration
Activity and Activity Coefficient

Ka   
A B   f
    
A
 f B
AB              f AB
• This is the rigorously correct expression for the law of
mass action as applied to weak electrolytes.
• The activity coefficient varies with concentration and
ionic strength (IS). For ions it varies with the valency
and is the same for all dilute solutions having the
same ionic strength.
• An increase in IS causes the activity coefficient and
activity to decrease.
Calculation of Ionic Strength
I  0.5 ci zi
2

• The ionic strength for 0.1 M HNO3 and 0.2M Ba(NO3)2
= 0.5{(0.1 x 12 + 0.1 x 12)HNO3 + (0.2 x 22 + 0.2 x 2 x 12)}
= 0.5{0.2 + (0.8 + 0.4)} = 0.5{0.2 + 1.2} = 0.7
• The activity coefficient of unionised molecules do not
differ considerably from unity.
• For weak electrolytes, the ionic concentration and
ionic strength is small and the error introduced by
neglecting activity for concentration is small, i.e.,
assuming no other salts in solution.
Acid Base Equilibria in Water
• CH3COOH + H2O ↔ H3O+ + CH3COOH-
• Applying the law of mass action we have

K
CH COO H 
3
    

CH 3COOH 
• K is the equilibrium constant at a particular
concentration also known as the dissociation
constant and ionisation constant.
Acid Base Equilibria in Water
• If one mole of electrolyte is dissolved in V litres of
solution. V = 1/c, where c = concentration in
moles/litre.
• If the degree of dissociation at equilibrium = α
• The amount of unionized electrolyte = 1- α/V
moles/litre.
     2
 c       2
K          or
1   V 1   
• This is also know as Ostwald’s dilution law
Acid Base Equilibria in Water
• To be strictly correct
 2c f H  f A    
K     
1     f HA
As the solution
c x 104   α           K x 105
becomes more dilute,
1.873     0.264       1.78      the degree of
38.86     0.066       1.83      dissociation increases.
At infinite dilution the
68.71     0.050       1.84      weak acid or base
112.2     0.040       1.84      would be totally
dissociated.
Strengths of Acids and Bases
• Bronsted acids and bases
A1-B1 and A2-B2 are conjugate
A1  B2  A 2  B1
acid base pairs
K
A2 B1             K depends on temperature
A1 B2             and the nature of the solvent
It is usual to refer to acid base
A  H 2 O  B  H 3O    strength of the solvent

K'
BH 3O           In water the acid-base pair is
A H 2O          H3O+-H2O

BH  
The conc. of water equals
55.5 moles/litre
Ka
A 
Strengths of Acids and Bases
If A is an anion acid
•   H2PO4-   + H2O ↔            HPO42-      +   H3O+   such as H2PO4- i.e. the

HPO H 
second dissociation
2                         constant for

H PO 
4
Ka                             
phosphoric acid
2            4
If A is a cation acid, e.g.
• NH4+ + H2O ↔ NH3 + H3O+                              ammonium ion.
[NH3] = total conc. of


NH 3 H                                ammonia i.e. free NH3
Ka
NH 4
                               plus NH4OH
The H2O is a base
since it is accepting a
H+
Strengths of Acids and Bases
• NH3 + H2O ↔ NH4+       For a Bronsted base,
again leaving out H2O

Kb   
NH OH 
4
       In this case the H2O is an
acid since it is donating a
NH 3        proton (H+)

Since Kw = [H+][OH-]
Kb  K w K a
A large pKa corresponds
pK   log 10 K       to a weak acid and a
strong base
Strengths of Acids and Bases
For very weak or slightly
   2
K                      ionized electrolytes, the
V 1            relationship can be
reduced since α may be
 2  KV or   KV      neglected in comparison
to unity

1  K1V1  2  K 2V2   For any two weak acids
or bases at a given
1 K1                   dilution V (in litres) we

2 K2                   have
Strengths of Acids and Bases
Acid                   pKa     Acid           pKa
Formic                 3.75    Benzoic        4.21
Acetic                 4.76    Carbonic K1    6.37
Propionic              4.87    Carbonic K1    10.33
Hydrogen Sulphide K1   7.24    Sulphuric K2   1.92
Hydrogen Sulphide K2   14.92   Lactic         3.86
Strengths of Acids and Bases
Base                  pKa     Base                  pKa
Ammonia               9.24    Methylamine           10.64
Ethylamine            10.63   Dimethylamine         10.77
Triethanolamine       7.7     Trimethylamine        9.80
Ethylenediamine K1    7.00    Aniline               4.58
Ethylenediamine K2    10.09   Pyridine              5.17
Data expressed as acidic dissociation constants
The basic dissociation constant may be obtained from the
relationship
pKa (acidic) + pKb (base) = Kw (water) = 10-14 @ 25oC
Strengths of Acids and Bases
• Consider the reactions:
• H2S ↔ HS- + H+
• HS- ↔ S2- + H+
Strengths of Acids and Bases
• E.g.: A saturated aqueous solution of H2S is
approximately 0.1 M.

H HS   9.110
            
8
Both the
H 2 S                               equilibrium
H S   1.2 10
       2
15
equations must be

HS 
satisfied

simultaneously
H   HS  and H S   0.1
                
2

H   HS   9.110  0.1
                               -8

 9.5 10 5
Strengths of Acids and Bases
• By substituting the values for [H+] and [HS-]
into:
•            H S   1.2 1015
    2

HS 


9.5 10  S   1.2 10  9.5 10 
5      2          15         5

S   1.2 10
2          15

Which is the value of K2
Le Chatelier's Principle
• In 1884 the French chemist and engineer Henry-Louis Le
Chatelier proposed one of the central concepts of chemical
equilibria. Le Chatelier's principle can be stated as follows:
• A change in one of the variables that describe a system at
equilibrium produces a shift in the position of the
equilibrium that counteracts the effect of this change.

• If a chemical system at equilibrium experiences a
change in concentration, temperature, volume, or
total pressure, then the equilibrium shifts to counter-
act the imposed change.
Common Ion Effect
• Remember: H2S ↔ HS- + H+
•           HS- ↔ S2- + H+

H HS   9.110
            
8

H 2 S 
H S   1.2 10
       2
15

HS 

H   HS  and H S   0.1
                
2

H   HS   9.110  0.1
                               -8

 9.5 10 5
Common Ion Effect
• The concentration of an ion in solution may be increased
by the addition of another compound that produces the
same ion on dissociation.
• E.g. The S2- ion conc. by addition of 0.25 M HCl
9.110 8  H 2 S  9.110 8  0.1
HS         H   

0.25
      
HS   3.6 10 8
1.2 10  HS  1.2 10  3.6 10
S  
15                 15         8
2

H 

0.25
S   1.7 10 Thus by addition of 0,25 M H
2         22                               +the sulphide
concentration is reduced from 1 x 10-15 to
1.7 x 10-22
Common Ion Effect
• Consider the equilibrium reaction of acetic
acid
• CH3COOH ↔ CH3COO- + H+
Common Ion Effect
• Effect of addition of 0.1 moles NaAc (8.2 g) to 1000
mL of 0.1 M HAc. Consider the acetic acid first.

H CH COO  

3

 2c
 1.82  10 5  K
CH COOH 
3
1  
• 1–α≈1

  K c  1.82 104  0.0135
• Hence [H+] = 0.00135, [CH3COO-] = 0.00135, and
[CH3COOH] = 0.0986
Common Ion Effect
• The concentration of sodium and acetate ions
produced by addition of the completely dissociated
sodium acetate are:
• [Na+] = 0.1, and [CH3COO-] = 0.1 mole/litre
• The CH3COO- will tend to decrease the ionisation of
the acetic acid, since K is constant, and the acetate
ion conc. derived from it.
• Hence we may write [CH3COO-] = 0.1
• α’ is the new degree of ionisation
• [H+] = α’c = 0.1 α’, and *CH3COOH] = (1 – α’)c = 0.1
since α’ is negligibly small.
Common Ion Effect
• Substituting in the mass-action equation

H CH COO   0.1 '0.1  1.82 10

3

5

CH 3COOH                  0.1
 '  1.8  10  4
H    ' c  1.8 10
                    4

• The addition of 0.1 M NaAc to 0.1M acetic acid has
decreased the degree of ionisation from 1.35 to
0.018%, and the [H+] from 0.00135 to 0.000018
Solubility Product
• For sparingly soluble salts <0.01 M
AB  A   B 
  

S AB  A B       

Aa Bb  aA a   bB b 
  B 
S Aa Bb  A   a a   b b

• AgCl (solid) ↔ Ag+ + Cl-
• The velocity of the reactions depends on temperature
Solubility Product
•   v1 = k1
•   v2 = k2[Ag+][Cl-]
•   At equilibrium k1 = k2[Ag+][Cl-]
•   [Ag+][Cl-] = k1/k2 = SAgCl
•   Again to be strictly correct activities and not
concentrations should be used. At low concentration
the activities are practically equal to concentration.
Solubility Product
[KCl]    [Cl-] x 103 [Ag+] x 108 SAgCl = [Ag+][Cl-] x 1010

0.00670      6.4         1.75               1.12

0.00833      7.9         1.39               1.10

0.01114     10.5         1.07               1.12

0.01669     15.5         0.74               1.14

0.03349     30.3         0.39               1.14
Solubility Product – Inert Electrolyte
• In the presence of moderate concentrations of salts,
the ionic strength will increase. This will, in general
lower the activity coefficient of both ions, and
consequently the ionic concentrations and (and
therefore the solubility) must increase in order to
maintain the solubility product constant.

 
a A  f A A
• E.g. fA+ decreased from 1 – 0.8, the activity will
decrease and the concentration will increase in order
to maintain the correct activity conc.
Solubility Product
• The solubility increases by the addition of
electrolytes with no common ions
Solubility Product – Effect of Acids
• M+ + A- + H+ + Cl- ↔ HA + M+ + Cl-
• If the dissociation constant of the acid HA is small,
the anion A- will be removed from the solution to
form the un-dissociated acid HA. Consequently more
of the solid will pass into solution to replace the
anions removed and this process will continue until
equilibrium is established [M+][A-] = SMA
• Fe2+ + CO32- ↔ Fe2CO3↓
• kSFe2CO3 = [Fe2+][CO32-]
• H2CO3 ↔ H+ + HCO3- K1 = 4.3 x 10-7
Solubility Product – Effect of Acids
• HCO3- ↔ H+ + CO3- K2 = 5.6 x 10-11
• CO32- + H+ → HCO3-
• Also for sparingly soluble sulphates, Ba, Sr and Pb
Ba2+ + SO42- + H+ + Cl- ↔ HSO4- + Ba2+ + Cl-
Since the K2 is comparatively large
HSO4- ↔ H+ + SO42- (pKa = 1.92), the effect of
addition of a strong acid is relatively small.
Complex Ions
• The increase in solubility of a precipitate upon the
addition of excess of the precipitating agent is
frequently due to the formation of a complex ion.
• E.g. the ppt of silver cyanide
• SAgCN = [Ag+][CN-] because the solubility product is
exceeded
• K+ + CN- + Ag+ + NO3- → AgCN↓ + K+ + NO3-
or Ag+ + CN- → AgCN↓
The ppt dissolves on addition of excess potassium
cyanide due to the formation of the complex ion
[Ag(CN)2]-
AgCN (solid) + CN- (excess) ↔ *Ag(CN)2]- a soluble
complex ion. K[Ag(CN)2] a soluble complex salt.
Instability Constants of Complex Ions

Ag CN 
       2
The complex ion
 Ag CN  
 21

 1.0 10          formation renders the
2                                concentration of the
Cu CN 
          4                          silver ion concentration

 CuCN  
4
3
 5.0 10  28    so small that the
solubility product of silver

Cu NH 
2             4                      cyanide is not exceeded.

 CuNH                 4.6 10 14
3                          Also bear in mind that the
2
CN- ion is also in excess.
3 4
Instability Constants of Complex Ions
• Cu2+ + NH4OH ↔ Cu(OH)2↓ + NH4+
• Cu(OH)2 + 4NH4+ → Cu(NH4)42+ + OH-

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