Chemical Equilibria

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Chemical Equilibria

• Professor Brian Kinsella

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The Law of Mass Action

• A B ? C D
• The velocity at which A and B react is
  proportional to their concentrations
• ?1 k1 x A x B
• ?2 k2 x C x D
• At equilibrium the velocities of the forward and
  reverse reaction will be equal and ?1 ?2
• k1 x A x B k2 x C x D

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The Law of Mass Action

• Or
• K The equilibrium constant for the reaction at
  a given temperature
• For a reversible reaction the equation may be
  generalised

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The Law of Mass Action

• (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.

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Activity and Activity Coefficient

• For a binary electrolyte
• AB ? A B-
• activity (concentration) x (activity
  coefficient)
• Thus at any molar concentration

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Activity and Activity Coefficient

• 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.

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Calculation of Ionic Strength

• 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)
• 0.50.2 (0.8 0.4) 0.50.2 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.

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Acid Base Equilibria in Water

• CH3COOH H2O ? H3O CH3COOH-
• Applying the law of mass action we have
• K is the equilibrium constant at a particular
  concentration also known as the dissociation
  constant and ionisation constant.

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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 a
• The amount of unionized electrolyte 1- a/V
  moles/litre.
• This is also know as Ostwalds dilution law

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Acid Base Equilibria in Water

• To be strictly correct

As the solution becomes more dilute, the degree
of dissociation increases. At infinite dilution
the weak acid or base would be totally
dissociated.
c x 104 a K x 105
1.873 0.264 1.78
38.86 0.066 1.83
68.71 0.050 1.84
112.2 0.040 1.84
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Strengths of Acids and Bases

• Bronsted acids and bases

• A1-B1 and A2-B2 are conjugate acid base pairs
• K depends on temperature and the nature of the
  solvent
• It is usual to refer to acid base strength of the
  solvent
• In water the acid-base pair is H3O-H2O
• The conc. of water equals 55.5 moles/litre

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Strengths of Acids and Bases
If A is an anion acid such as H2PO4- i.e. the
second dissociation constant for phosphoric acid

• H2PO4- H2O ? HPO42- H3O
• NH4 H2O ? NH3 H3O

If A is a cation acid, e.g. ammonium ion. NH3
total conc. of ammonia i.e. free NH3 plus
NH4OH The H2O is a base since it is accepting a H
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Strengths of Acids and Bases

• NH3 H2O ? NH4

For a Bronsted base, again leaving out H2O In
this case the H2O is an acid since it is donating
a proton (H)
Since Kw HOH- A large pKa corresponds to a
weak acid and a strong base
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Strengths of Acids and Bases
For very weak or slightly ionized electrolytes,
the relationship can be reduced since a may be
neglected in comparison to unity
For any two weak acids or bases at a given
dilution V (in litres) we have
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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
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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 _at_ 25oC
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Strengths of Acids and Bases

• Consider the reactions
• H2S ? HS- H
• HS- ? S2- H

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Strengths of Acids and Bases

• E.g. A saturated aqueous solution of H2S is
  approximately 0.1 M.

Both the equilibrium equations must be satisfied
simultaneously
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Strengths of Acids and Bases

• By substituting the values for H and HS-
  into

Which is the value of K2
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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.

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Common Ion Effect

• Remember H2S ? HS- H
• HS- ? S2- H
  

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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

Thus by addition of 0,25 M H the sulphide
concentration is reduced from 1 x 10-15 to 1.7 x
10-22
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Common Ion Effect

• Consider the equilibrium reaction of acetic acid
• CH3COOH ? CH3COO- H

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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.
• 1 a 1
• Hence H 0.00135, CH3COO- 0.00135, and
• CH3COOH 0.0986

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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
• a is the new degree of ionisation
• H ac 0.1 a, and CH3COOH (1 a)c
  0.1 since a is negligibly small.

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Common Ion Effect

• Substituting in the mass-action equation
• 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

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Solubility Product

• For sparingly soluble salts lt0.01 M
• AgCl (solid) ? Ag Cl-
• The velocity of the reactions depends on
  temperature

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Solubility Product

• v1 k1
• v2 k2AgCl-
• At equilibrium k1 k2AgCl-
• AgCl- 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.

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Solubility Product
KCl Cl- x 103 Ag x 108 SAgCl AgCl- 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
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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.
• 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.

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Solubility Product

• The solubility increases by the addition of
  electrolytes with no common ions

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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 MA- SMA
• Fe2 CO32- ? Fe2CO3?
• kSFe2CO3 Fe2CO32-
• H2CO3 ? H HCO3- K1 4.3 x 10-7

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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.

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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 AgCN- 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. KAg(CN)2 a soluble
  complex salt.

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Instability Constants of Complex Ions
The complex ion formation renders the
concentration of the silver ion concentration so
small that the solubility product of silver
cyanide is not exceeded. Also bear in mind that
the CN- ion is also in excess.
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Instability Constants of Complex Ions

• Cu2 NH4OH ? Cu(OH)2? NH4
• Cu(OH)2 4NH4 ? Cu(NH4)42 OH-