Chemical Equilibrium
Introduction
1.)
Equilibria govern diverse phenomena

2.)
Protein folding, acid rain action on minerals to aqueous reactions
Chemical equilibrium applies to reactions that can occur in both directions:



reactants are constantly forming products and vice-versa
At the beginning of the reaction, the rate that the reactants are changing into the
products is higher than the rate that the products are changing into the reactants.
When the net change of the products and reactants is zero the reaction has
reached equilibrium.
Then, system continually exchanges
products
and reactants,
maintaining
First, system
reacheswhile
equilibrium
equilibrium distribution.
Reactants
Product
At equilibrium the amount of reactants and products are constant,
but not necessarily equal
Chemical Equilibrium
Equilibrium Constant
1.) The relative concentration of products and reactants at equilibrium is a
constant.
2.) Equilibrium constant (K):

For a general chemical reaction
Equilibrium constant:
K
c
d
[C ] [ D]
[ A]a [ B]b
Where:
- small superscript letters are the stoichiometry coefficients
- [A] concentration chemical species A relative to standard state
Chemical Equilibrium
Equilibrium Constant
2.) Equilibrium constant (K):


A reaction is favored when K > 1
K has no units, dimensionless
- Concentration of solutes should be expressed as moles per liter (M).
- Concentrations of gases should be expressed in bars.
►
►
express gas as Pgas, emphasize pressure instead of concentration
1 bar = 105 Pa; 1 atm = 1.01325 bar
- Concentrations of pure solids, pure liquids and solvents are omitted
► are unity
► standard
state is the pure liquid or solid
3.) Manipulating Equilibrium Constants
Consider the following reaction:
[ H  ][ A ]
K1 
[ HA]
Reversing the reaction results in a reciprocal equilibrium reaction:
K '1 
[ HA]


[ H ][ A ]
 1 / K1
Chemical Equilibrium
Equilibrium Constant
3.) Manipulating Equilibrium Constants
If two reactions are added, the new K is the product of the two individual K values:
K1
K2
K3
[ H  ][ A ]
K1 
[ HA]
K2 
[CH  ]
[ H  ][C ]
[ A ][CH  ]
K3 
[ HA][C ]
[ H  ][ A ] [CH  ] [ A ][CH  ]
K 3  K1K 2 



[ HA]
[ HA][C ]
[ H ][C ]
Chemical Equilibrium
Equilibrium Constant
3.) Manipulating Equilibrium Constants

Example:
Given the reactions and equilibrium constants:
Kw= 1.0 x 10-14
KNH3= 1.8 x 10-5
Find the equilibrium constant for the reaction:
Solution:
K1= Kw
K2=1/KNH3
K3=Kw*1/KNH3=5.6x10-10
Chemical Equilibrium
Equilibrium and Thermodynamics
1.) Equilibrium constant derived from the thermodynamics of a chemical
reaction.

deals with the relationships and conversions between heat and other forms of
energy
2.) Enthalpy

DH – is the heat absorbed or released when the reaction takes place under
constant applied pressure
DH = Hproducts – Hreactants


Standard enthalpy change (DHo) –
all reactants and products are
in their standard state.
DHo – negative  heat released
- Exothermic
- Solution gets hot

DHo – positive  heat absorbed
- Endothermic
- Solution gets cold
Chemical Equilibrium
Equilibrium and Thermodynamics
3.) Entropy


Measure of a substances “disorder”
Greater disorder  Greater Entropy
- Relative disorder: Gas > Liquid > solid
DS = Sproducts – Sreactants

DSo – change in entropy when all species are in standard state.
- positive
product more disorder
- negative 
product less disorder
DSo = +76.4 J/(K.mol) at 25oC
More disorder for aqueous ions than solid
Chemical Equilibrium
Equilibrium and Thermodynamics
3.) Entropy

Increase in temperature results in an increase in Entropy (S)

Increase occurs for all products and reactants

Primarily concerned with DS, which is only weakly temperature dependent
- generally treat DS and DH as temperature independent
Chemical Equilibrium
Equilibrium and Thermodynamics
4.) Free Energy

Systems at constant temperature and pressure have a tendency toward
lower enthalpy and higher entropy

Chemical reaction is favored if:
- DH is negative  heat given off
and
- DS is positive  more disorder

Chemical reaction is not favored if:
- DH is positive and DS is negative

Gibbs Free Energy (DG): determines if a reaction is favored or not when both
DH and DS are positive or negative
- A reaction is favored if DG is negative
Free energy:
where T is temperature (Kelvin)
DG = DH -TDS
Chemical Equilibrium
Equilibrium and Thermodynamics
4.) Free Energy

Example:
Is the following reaction favored at 25oC?
DHo = -74.85 x 103 J/mol
DSo = -130.4 J/K.mol
Free energy:
DG = DH –TDS = (-74.85x103 J/mol) – (298.15K)(-130.4 J/K.mol)
DG = -35.97 kJ/mol  DG negative  reaction favored
Favorable influence of enthalpy is greater than unfavorable influence of entropy
Chemical Equilibrium
Equilibrium and Thermodynamics
5.) Free Energy and Equilibrium


Relate Equilibrium constant to the energetics (DH & DS) of a reaction
Equilibrium constant depends on DG:
K e
o
D
G

RT
where
R (gas constant) = 8.314472 J/(K.mol)
T = temperature in kelvins


The more negative DG  larger equilibrium constant
Example:
DG = -35.97
K e
 DG
o
3
.
RT  e  ( 35.97 x 10 J / mol )( 8.314472J /( K mol )( 298.15 K )  2.00 x 10 6
Because K is very large, HCl is very soluble in water and nearly completely ionized
Chemical Equilibrium
Equilibrium and Thermodynamics
5.) Free Energy and Equilibrium

If DGo is negative or K >1 the reaction is spontaneous
-

Reaction occurs by just combining the reactants
If DGo is positive or K < 1, the reaction is not spontaneous
Reaction requires external energy or process to proceed
Gas flows towards a vacuum.
spontaneous
A vacuum does not naturally form.
nonspontaneous
Chemical Equilibrium
Le Châtelier’s Principal
1.) What Happens When a System at Equilibrium is Perturbed?

Change concentration, temperature, pressure or add other chemicals

Equilibrium is re-established
-
-
Reaction accommodates the change in products, reactants, temperature,
pressure, etc.
Rates of forward and reverse reactions re-equilibrate
Chemical Equilibrium
Le Châtelier’s Principal
1.) What Happens When a System at Equilibrium is Perturbed?

Le Châtelier’s Principal:
-
the direction in which the system proceeds back to equilibrium is such that
the change is partially offset.
Consider this reaction:
At equilibrium:
Add excess CO(g):
To return to equilibrium
(balance), some (not all)
CO and H2 are converted
to CH3OH
If all added CO was converted to CH3OH, then reaction
would be unbalanced by the amount of product
Chemical Equilibrium
Le Châtelier’s Principal
2.) Example:
Consider this reaction:
K
[ Br - ][Cr2O72- ][ H  ]8
[ BrO3- ][Cr 3 ]2
 1  10 11 at 25 o C
At one equilibrium state:
[H  ]  5.0 M [Cr2O72- ]  0.10 M [Cr 3 ]  0.0030 M
[Br  ]  1.0 M [BrO 3- ]  0.043 M
Chemical Equilibrium
Le Châtelier’s Principal
2.) Example:
What happens when:
[Cr2O72- ] increased from 0.10 M to 0.20 M
According to Le Châtelier’s Principal, reaction should go back to left to
off-set dichormate on right:
Use reaction quotient (Q), Same form of equilibrium equation, but not at
equilibrium:
Q
[ Br - ][Cr2O72- ][ H  ]8
[ BrO3- ][Cr 3 ]2

1.0 0.20 5.0 8

0.0430.0030 2
 2  10 11  K
Chemical Equilibrium
Le Châtelier’s Principal
2.) Example:
Because Q > K, the reaction must go to the left to decrease numerator and
increase denominator.
Continues until Q = K:
1. If the reaction is at equilibrium and products are added (or reactants
removed), the reaction goes to the left
2. If the reaction is at equilibrium and reactants are added ( or products
removed), the reaction goes to the right
Chemical Equilibrium
Le Châtelier’s Principal
3.) Affect of Temperature on Equilibrium
Combine Gibbs free energy and Equilibrium Equations:
K e
o
D
G


RT  e
 DH o TDS 
o
D
H

 DS
RT
R
e
e
 DH o
RT  e
DS o

R
Only Enthalpy term is temperature dependent:
K(T )  e
 DH o
RT
RT
Chemical Equilibrium
Le Châtelier’s Principal
3.) Affect of Temperature on Equilibrium
1. Equilibrium constant of an endothermic reaction (DHo = +) increases if
the temperature is raised.
D
DH = +
2. Equilibrium constant of an exothermic reaction (DHo = -)decreases if the
temperature is raised.
D
DH = -
Chemical Equilibrium
Le Châtelier’s Principal
4.)
Thermodynamics vs. Kinetics

Thermodynamics predicts if a reaction will occur
-

determines the state at equilibrium
Thermodynamics does not determine the rate of a reaction
-
Will the reaction occur instantly, in minutes, hours, days or years?
DG = spontaneous
Diamonds
-
Graphite
While reaction is spontaneous, takes millions of years to occur
Chemical Equilibrium
Solubility Product
1.)
Equilibrium constant for the reaction which a solid salt dissolves to give
its constituent ions in solution

Solid omitted from equilibrium constant because it is in a standard state

Example:
K sp  [ Hg 22 ][Cl- ]2  1.2  10 18
Chemical Equilibrium
Solubility Product
1.)
Saturated Solution – contains excess, undissolved solid


Solution contains all the solid capable of dissolving under
the current conditions
Example:
Find [Cu2+] in a solution saturated with Cu4(OH)6(SO4) if [OH-] is
fixed at 1.0x10-6M. Note that Cu4(OH)6(SO4) gives 1 mol of SO42- for
4 mol of Cu2+?
K sp  2.3  10 69
Chemical Equilibrium
Solubility Product
2.)
If an aqueous solution is left in contact with excess solid, the solid will
dissolve until the condition of Ksp is satisfied


Amount of undissolved solid remains constant
Excess solid is required to guarantee ion concentration is consistent with Ksp
3.) If ions are mixed together such that the concentrations exceed Ksp, the
solid will precipitate.
4.) Solubility product only describes part of the solubility of a salt


Only includes dissociated ions
Ignores solubility of solid salt
Chemical Equilibrium
Common ion effect – a salt will be less soluble if one of
its constituent ions is already present in the solution.
Decrease in the solubility of MgF2 by
the addition of NaF
PbCl2 precipitate because the
ion product is greater than Ksp.
Chemical Equilibrium
Common Ion Effect
1.)
Affect of Adding a Second Source of an Ion on Salt Solubility


Equilibrium re-obtained following Le Châtelier’s Principal
Reaction moves away from the added ion
Find [Cu2+] in a solution saturated with Cu4(OH)6(SO4) if [OH-] is
fixed at 1.0x10-6M and 0.10M Na2SO4 is added to the solution.
Chemical Equilibrium
Complex Formation
1.)
High concentration of an ion may redissolve a solid


Ion first causes precipitation
Forms complex ions, consists of two or more simple ions bonded to each other
ppt. formation
Complex forms and
redissolves solid
Chemical Equilibrium
Complex Formation
2.)
Lewis Acids and Bases



M+ acts as a Lewis acid  accepts a pair of electrons
X- acts as a Lewis base  donates a pair of electrons
Bond is a coordinate covalent bond
ligand
Lewis acid
adduct
Lewis base
Chemical Equilibrium
Complex Formation
3.)
Affect on Solubility

Formation of adducts increase solubility
Implies low Pb2+ solubility:

Ksp
K sp  [ Pb2  ][ I - ]2  7.9  10 9
Solubility equation becomes a complex mixture of reactions
- don’t need to use all equations to determine the concentration of any species
Only one concentration of Pb2+ in solution
Concentration of Pb2+ that
satisfies any one of the
equilibria must satisfy all
of the equilibria
All equilibrium conditions are satisfied simultaneously
Chemical Equilibrium
Complex Formation
3.)
Affect on Solubility

Total concentration is dependent on each individual complex species
Pbtotal  Pb 2   PbI   PbI 2 ( aq )  PbI 3  PbI 42  
Total solubility of lead depends on [I-] and the
solubility of each individual complex formation.
Chemical Equilibrium
Complex Formation
3.)
Affect on Solubility

Example:
Given the following equilibria, calculate the concentration of each zinc-containing
species in a solution saturated with Zn(OH)2(s) and containing [OH-] at a fixed
concentration of 3.2x10-7M.
Zn(OH)2 (s)
Zn(OH)+
Zn(OH)3Zn(OH)42-
Ksp = 3.0x10-16
b1 = 2.5 x104
b3 = 7.2x1015
b4 = 2.8x1015
Chemical Equilibrium
Acids and Bases
1.)
Protic Acids and Bases – transfer of H+ (proton) from one molecule to
another

Hydronium ion (H3O+) – combination of H+ with water (H2O)

Acid – is a substance that increases the concentration of H3O+

Base – is a substance that decreases the concentration of H3O+
- base also causes an increase in the concentration of OH- in aqueous solutions
acid
2.) Brønsted-Lowry – definition does not require the formation of H3O+

Extended to non-aqueous solutions or gas phase

Acid – proton donor

Base – proton acceptor
acid
base
salt
Chemical Equilibrium
Acids and Bases
3.)
Salts – product of an acid-base reaction



4.)
Any ionic solid
Acid and base neutralize each other and form a salt
Most salts with a single positive and negative charge dissociate completely
into ions in water
Conjugate Acids and Bases
Products of acid-base reaction
are also acids and bases
A conjugate acid and its base or a
conjugate base and its acid in an
aqueous system are related to each
other by the gain or loss of H+
Chemical Equilibrium
Acids and Bases
5.)
Autoprotolysis – acts as both an acid and base

Extent of these reactions are very small
water
K w  [ H  ][OH - ]  1.0  10 14
- H3O+ is the conjugate acid of water
- OH- is the conjugate base of water
- Kw is the equilibrium constant for the dissociation of water
Acetic acid
K  3.5  10 15
Chemical Equilibrium
Acids and Bases
6.)
pH – negative logarithm of H+ concentration

Ignores distinction between concentration and activities (discussed later)
pH   log[ H  ]
pH  pOH   log[ K w ]  14.00 at 25 o C



A solution is acidic if [H+] > [OH-]
A solution is basic if [H+] < [OH-]
An aqueous solution has a neutral pH if [H+]=[OH-]
- This occurs when [H+] = [OH-] = 10-7M or pH = 7
Chemical Equilibrium
Acids and Bases
6.)
pH

pH values for some common samples
Chemical Equilibrium
Acids and Bases
6.)
pH

Example:
What is the pH of a solution containing 1x10-6 M H+?
What is [OH-] of a solution containing 1x10-6 M H+?
Chemical Equilibrium
Acids and Bases
7.)
Strengths of Acids and Bases

Depends on whether the compound react nearly completely or partially to
produce H+ or OH-

strong acid or base completely dissociate in aqueous solution
- equilibrium constants are large
- everything else termed weak
Strong  no undissociated HCl or KOH
Chemical Equilibrium
Acids and Bases
7.)
Strengths of Acids and Bases

weak acids react with water by donating a proton
- only partially dissociated in water
- equilibrium constants are called Ka – acid dissociation constant
- Ka is small
Ka
Equivalent
Ka

weak bases react with water by removing a proton
- only partially dissociated in water
- equilibrium constants are called Kb – base dissociation constant
- Kb is small
Kb
Equivalent
[ H  ][ A ]
Ka 
[ HA]
Kb
[ BH  ][OH  ]
Kb 
[ B]
Chemical Equilibrium
Some Common Weak Acids (carboxylic acids)
ACID
FORMULA
Ka
pKa
ACID
FORMULA
Ka
pKa
acetic acid
H(C2H3O2)
1.74 E-5
4.76
hydrocyanic acid
HCN
6.17 E-10
9.21
ascorbic acid (1)
H2(C6H6O6)
7.94 E-5
4.10
hydrofluoric acid
HF
6.31 E-4
3.20
ascorbic acid (2)
(HC6H6O6)-
1.62 E-12
11.79
lactic acid
H(C3H5O3)
8.32 E-4
3.08
boric acid (1)
H3BO3
5.37 E-10
9.27
nitrous acid
HNO2
5.62 E-4
3.25
boric acid (2)
(H2BO3)-
1.8 E-13
12.7
octanoic acid
H(C8H15O2)
1.29 E-4
4.89
boric acid (3)
(HBO3)=
1.6 E-14
13.8
oxalic acid (1)
H2(C204)
5.89 E-2
1.23
butanoic acid
H(C4H7O2)
1.48 E-5
4.83
oxalic acid (2)
(HC2O4)-
6.46 E-5
4.19
carbonic acid (1)
H2CO3
4.47 E-7
6.35
pentanoic acid
H(C5H9O2)
3.31 E-5
4.84
carbonic acid (2)
(HCO3)-
4.68 E-11
10.33
phosphoric acid (1)
H3PO4
6.92 E-3
2.16
chromic acid (1)
H2CrO4
1.82 E-1
0.74
phosphoric acid (2)
(H2PO4)-
6.17 E-8
7.21
chromic acid (2)
(HCrO4)-
3.24 E-7
6.49
phosphoric acid (3)
(HPO4)=
2.09 E-12
12.32
citric acid (1)
H3(C6H5O7)
7.24 E-4
3.14
propanoic acid
H(C3H5O2)
1.38 E-5
4.86
citric acid (2)
(H2C6H5O7)-
1.70 E-5
4.77
sulfuric acid (2)
(HSO4)-
1.05 E-2
1.98
citric acid (3)
(HC6H5O7)=
4.07 E-7
6.39
sulfurous acid (1)
H2SO3
1.41 E-2
1.85
formic acid
H(CHO2)
1.78 E-4
3.75
sulfurous acid (2)
(HSO3)-
6.31 E-8
7.20
heptanoic acid
H(C7H13O2)
1.29 E-5
4.89
uric acid
H(C5H3N4O3)
1.29 E-4
3.89
hexanoic acid
H(C6H11O2)
1.41 E-5
4.84
Chemical Equilibrium
Some Common Weak Acids (Metals cations)
Chemical Equilibrium
Some Common Weak Bases (amines)
BASE

FORMULA
pKb
alanine
C3H5O2NH2
7.41 E-5
4.13
Ammonia
NH3 (NH4OH)
1.78 E-5
4.75
dimethylamine
(CH3)2NH
4.79 E-4
3.32
ethylamine
C2H5NH2
5.01 E-4
3.30
glycine
C2H3O2NH2
6.03 E-5
4.22
hydrazine
N2H4
1.26 E-6
5.90
methylamine
CH3NH2
4.27 E-4
3.37
trimethylamine
(CH3)3N
6.31 E-5
4.20
The Ka or Kb of an acid or base may also be written in terms of “pKa” or “pKb”
pK a   log( K a )

Kb
pK b   log( K b )
As Ka or Kb increase  pKa or pKb decrease
- a strong acid/base has a high Ka or Kb and a low pKa or pkb
Chemical Equilibrium
Acids and Bases
8.)
Polyprotic Acids and Bases – can donate or accept more than one proton

Ka or Kb are sequentially numbered
- Ka1,Ka2,Ka3 Kb1,Kb2,Kb3
Chemical Equilibrium
Acids and Bases
8.)
Relationship Between Ka and Kb
[ H  ][ A ]
Ka 
[ HA]
Kb 
[ HA][OH  ]
[ A ]
K w  Ka  Kb
[ H  ][ A ] [ HA][OH  ]


 [ H  ][OH  ]
[ HA]
[ A ]
K w  Ka  Kb
Chemical Equilibrium
Acids and Bases
8.)
Relationship Between Ka and Kb

Example:
Write the Kb reaction of CN-. Given that the Ka value for
HCN is 6.2x10-10, calculate Kb for CN-.