Chemical Equilibrium,
Free Energy and
Equilibrium
By
Engr. Asadullah Memon
B.E (Petroleum & Natural Gas)
The Concept of Equilibrium
Chemical equilibrium occurs when a reaction
and its reverse reaction proceed at the same
rate.
The Concept of Equilibrium
• As a system approaches
equilibrium, both the
forward and reverse
reactions are occurring.
• At equilibrium, the
forward and reverse
reactions are proceeding at
the same rate.
A System at Equilibrium
Once equilibrium is
achieved, the amount
of each reactant and
product remains
constant.
Depicting Equilibrium
In a system at equilibrium, both the forward
and reverse reactions are being carried out;
as a result, we write its equation with a
double arrow
N2O4 (g)
2 NO2 (g)
The Equilibrium Constant
• Forward reaction:
N2O4 (g)  2 NO2 (g)
• Rate law:
Rate = kf [N2O4]
The Equilibrium Constant
• Reverse reaction:
2 NO2 (g)  N2O4 (g)
• Rate law:
Rate = kr [NO2]2
The Equilibrium Constant
• Therefore, at equilibrium
Ratef = Rater
kf [N2O4] = kr [NO2]2
• Rewriting this, it becomes
kf
kr
[NO2]2
=
[N2O4]
The Equilibrium Constant
The ratio of the rate constants is a constant
at that temperature, and the expression
becomes
Keq =
kf
kr
[NO2]2
=
[N2O4]
The Equilibrium Constant
• To generalize this expression, consider the
reaction
aA + bB
cC + dD
• The equilibrium expression for this reaction
would be
[C]c[D]d
Kc =
[A]a[B]b
Equilibrium Constants
2 A + 3 B  C + 4 D
Ke = [C][D]4/[A]2[B]3
The Equilibrium Constant
Because pressure is proportional to molar
concentration (n/V) for gases in a closed
system, the equilibrium expression can also
be written
(PC)c (PD)d
Kp =
(PA)a (PB)b
Chemical Equilibrium
The state of a reversible reaction when the
two opposing reaction occur at the same rate
and the concentrations of reactants and
products do not change with time.
The rate of the forward reaction diminishes with time, while that of the
backward reaction increases, until they are equal.
A large K means the reaction lies far to the right at equilibrium.
Fig. Progress of a chemical reaction.
©Gary Christian, Analytical Chemistry,
6th Ed. (Wiley)
Chemical Equilibrium
• Review of Principles.
• Chemical reactions are never “complete”
• Chemical reactions proceed to a state where ratio
of products to reactants is constant
• NH3 + HOH  NH4+ + OH• [NH4+][OH-]/[NH3][HOH] = Kb
• If Kb << 1 (little ionization)
• H2SO4 + HOH  H3O+ + HSO4• [H3O+][HSO4-] / [H2SO4][HOH] = Ka
• If Ka >> 1 (mostly ionized)
Chemical Equilibrium
• Equilibrium
–
–
–
–
is not reached instantaneously
can be approached from either direction
is a dynamic state
amounts of reactants/products can be changed
by “mass action”
– (adding/ deleting products/reactants)
– HCO3- + H+  CO2(g) + HOH
– Ke = [CO2][HOH]/[HCO3-][H+]
Relationship between Kc and Kp
• From the ideal gas law we know that
PV = nRT
• Rearranging it, we get
n
P=
RT
V
Relationship between Kc and Kp
Plugging this into the expression for Kp for
each substance, the relationship between Kc
and Kp becomes
Kp = Kc (RT)n
Where
n = (moles of gaseous product) − (moles of gaseous reactant)
Equilibrium Can Be Reached from
Either Direction
As you can see, the ratio of [NO2]2 to [N2O4] remains
constant at this temperature no matter what the initial
concentrations of NO2 and N2O4 are.
Equilibrium Can Be Reached from
Either Direction
This is the data from the
last two trials from the
table on the previous
slide.
Equilibrium Can Be Reached from
Either Direction
It does not matter whether we start with N2 and H2
or whether we start with NH3. We will have the
same proportions of all three substances at
equilibrium.
What Does the Value of K Mean?
• If K >> 1, the reaction is
product-favored; product
predominates at
equilibrium.
What Does the Value of K Mean?
• If K >> 1, the reaction is
product-favored; product
predominates at
equilibrium.
• If K << 1, the reaction is
reactant-favored; reactant
predominates at
equilibrium.
Manipulating Equilibrium
Constants
The equilibrium constant of a reaction in the
reverse reaction is the reciprocal of the
equilibrium constant of the forward
reaction.
N2O4 (g)
2 NO2 (g)
[NO2]2
2 NO2 (g) Kc = [N O ] = 0.212 at 100C
2 4
[N2O4]
1
K
=
N2O4 (g)
=
c
[NO2]2
0.212
= 4.72 at 100C
Heterogeneous Equilibrium
The Concentrations of Solids and Liquids
Are Essentially Constant
Both can be obtained by dividing the
density of the substance by its molar
mass—and both of these are constants at
constant temperature.
The Concentrations of Solids and
Liquids Are Essentially Constant
Therefore, the concentrations of solids and
liquids do not appear in the equilibrium
expression
PbCl2 (s)
Pb2+ (aq) + 2 Cl−(aq)
Kc = [Pb2+] [Cl−]2
Le Châtelier’s Principle
It Stated that “When a stress is applied on a
system in equilibrium, the system tends to
adjust itself so as to reduce the stress”
“If a system at equilibrium is disturbed by a
change in temperature, pressure, or the
concentration of one of the components, the
system will shift its equilibrium position so as
to counteract the effect of the disturbance or
minimize the stress.”
Le Châtelier’s Principle
There are three ways in which the stress can be caused on a
chemical equilibrium:
(a) Changing the concentration of a reactant or product.
(b) Changing the pressure (or volume) of the system.
(c) Changing the temperature.
Thus, this principal stated that,
“if a change in concentration, pressure, or temperature is
caused to a chemical reaction in equilibrium, the equilibrium
will shift to the right ot the left so as minimize the change”
Gibbs Free Energy & Equilibrium Constant
• G = H – TS but H = E + PV
– G = Gibbs Free Energy H = Enthalpy
– T = Temperature S = Entropy
– E = Internal Energy P = Pressure V = Volume
• G = E + PV – TS but E = q – w
G = q – w + PV - TS
Derivative
dG = dq - dw + (PdV + VdP) – (TdS – SdT)
dG = dq - dw + (PdV + VdP) – (TdS – SdT)
Let’s Simplify by imposing some conditions
on the reaction.
a)
b)
c)
Constant Temperature: dT = 0  SdT = 0
Reversible Reaction: dq = TdS
Expansion work only: dw = PdV
Then all terms except one cancel
dG = VdP
Now consider 1mole of an ideal gas V = RT/P
dG = RTdP/P
Now lets integrate:
dG = RTdP/P
Result:
G2-G1 = RTln(P2/P1)
Make state 1 = standard state
G – Go = RTln(P/Po) but Po = 1 atm
Activity is defined: a = P/Po
G = Go + RTln(a)
This equation is called Van’t Hoff reaction
Isotherm.
General Expressions:
rR + sS  tT + uU
Each Free Energy Term Expressed in Terms of
Activity




tGT = tGTo + RT ln aT
uGU= uGUo + RT ln aU
rGR = rGRo + RT ln aR
sGS = sGSo + RT ln aS
G = Go + RT ln (aTt aUuaRr aSs)
G = Go + RT ln (aTt aUu/aRr aSs)
At Equilibrium: G = 0
Reaction quotient Q = (aTt aUu/aRr aSs) = Ko
Where Ko is the thermodynamic equilibrium constant
0 = Go + RT ln Ko
Go = - RT ln Ko
Where Go is indicate whether forward or reverse is spontaneous.
ln Ko = - Go/RT
Ko = e(- G /RT)
o
CASES
Case 1: If Go is negative, Log k must be positive and reaction
proceeds spontaneous in the forward reaction.
Case 2: If Go is Positive, Log k must be negative and reaction
proceeds spontaneous in the Reverse reaction.
Case 3: If Go is Zero, Log k must be unity and reaction is at
equilibrium.
Ionic Equilibria
The Ostwald’s Dilution Law:
Wilhelm Ostwald’s dilution law is a relationship between the dissociation constant
(Kp/Kc) and the degree of dissociation of a weak electrolyte (acids, bases).
The fraction of the amount of the electrolyte in solution present as free ions is called the
Degree of Dissociation.
Where,
Kp is dissociation constant,
α is degree of dissociation,
c(A-) is concentrations of anions,
c(K+) concentration of cations,
c0 is overall concentration,
c(KA) is concentration of associated electrolyte.
According to the Arrhenius
Theory of Dissociation,
An electrolyte dissociates into ions in the water solutions These ions are in
a state of equilibrium with the undissociated molecules. These equilibrium is
called Ionic equilibrium
Or
The molecules of an electrolyte in solution are constantly splitting up into ions
and the ions are constantly reuniting to form unionized molecules. Therefore,
a dynamic equilibrium exists between ions and unionized molecules of the
electrolyte in solution.
If one mole of electrolyte be dissolved in V litre of the solution then
C = 1/V
Where V is known as the Dilution For the solution. Therefore,
Kc = α2 / (1 - α )V
For weak electrolytes, Put (1 - α ) = 1, Therefore
α = √ Kc.V
Or
α = K’√V
It implies that, the degree of dissociation is proportional to the square root
of the dilution.
For Strong electrolytes,
α2+ αKc-KcV=0
Limitations of Ostwald's dilution law
 The law holds good only for weak electrolytes and fails
completely in the case of strong electrolytes.
 The value of 'α' is determined by conductivity
measurements by applying the formula Λ/Λ∞.
 The cause of failure of Ostwald's dilution law in the case
of strong electrolytes is due to the following factors"
(i) The law is based on the fact that only a portion of the electrolyte is dissociated into
ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are
almost completely ionized at all dilutions and Λ/Λ∞ does not give accurate value of 'α'.
(ii) When concentration of the ions is very high, the presence of charges on the ions
appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be
strictly applied in the case of string electrolytes.
Theory of Strong Electrolytes
(Debye-Huckel Theory)
The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel
as a theoretical explanation for departures from ideality in solutions of
electrolytes.
The main ideas of the theory are given below:
1. The strong electrolyte is completely ionized at all dilutions.
2. Since oppositely charged ions attract each other
3. It suggests that anions and cations are not uniformly distributed in the
solution of an electrolyte but that the cation tend to be found in the
vicinity of anions and vice-versa.
4. Degree in equivalent conductance with increase in concentration is due to
fall in mobilities of the ions to greater inter-ionic effect and vice-versa.
Buffer Solution
 Necessary to main the certain pH of a solution in lab: or Industrial Processes.
 Defined as “A buffer solution is one which maintain its pH fairly constant even
upon the addition of small amounts of acid or base”.
 How to buffer operates.
 Two Types of buffer solution
1.
A weak acid together with a salt of the same acid with the strong base.
These are called Acid Buffers e.g. CH3COOH + CH3COONA.
2.
A weak base and its salt with a strong acid. These are called Basic Buffers
e.g. NH4OH + NH4CL
Acid-Base Indicators
 In a acid base titration the base solution can be added gradually from a burette
into an acid solution contained in a receiver flask. When the amount of the base
added equals the amount of the acid in the flask, the equivalence point ot the
end point is reached.
 The end point of the titration is shown by the colour change of an indicator
previously added to the acid solution in the receiver flask.
 An acid base indicator is an organic dye that signals the end point by a visual
change colour.
 Examples: Phenolpathalein and methyl orange
 Phenolphythalein (Pink in base solution and colourless in acid solution)
 Methyl orange (Colour change from red (in acid) to yellow (in base)).
Acid-Base Indicators
pH range of Indicator
Indicator
Colour Change (Acid- Base)
pH range
Methyl orange
Red – Orange
3.1 - 4.4
Methyl red
Red – yellow
4.4 - 6.0
Litmus
Red – Blue
5.0 - 8.0
Bromothymol blue
Yellow – Blue
6.0 - 7.6
phenolpathalein
Colourless – Pink
8.3 - 10.0
Catalysis
 A substance which alters the rate of a chemical reaction, itself remaining
chemically unchanged at the end of the reaction.
 Catalyst may increase or decrease the arte of the reaction.
 Positive catalyst and Positive catalysis.
 Negative catalyst and Negative catalysis.
 Two types of catalysis:
1. Homogenous catalysis: The catalyst is in the same phase as the reactants
and is evenly distributed throughout.
2. Heterogeneous catalysis: The catalyst is in the different physical phase as
the reactants.