equilibrium

1. Equilibrium

2. Introduction:
The equilibrium of a system is a condition in which the properties
(temperature, pressure, concentration) of the system do not change
with time. Equilibrium always involves two opposing process. When the
two opposing process occur with the same rate, then the system has
come to the point of equilibrium. If the opposing process involve only
the physical changes, then the equilibrium is called physical
equilibrium. On the other hand, if the opposing processes involve
chemical reactions, the equilibrium is known as chemical equilibrium.

3. Physical equilibrium:
1. Liquid-vapour equilibrium: liquid-vapour system in a closed vessel
at constant temperature.
H2O (l) ⇋ H2O (g)
Here the two opposing processes involved are evaporation and
condensation. When the rate of evaporation becomes equal to the
rate of condensation, the equilibrium is reached.

4. 2. Solid-liquid equilibrium:
ice ⇋water
H2O(s) ⇋ H2O(l)
Here two opposing processes involved are melting and freezing.
When the rate of melting become equal to the rate of freezing,
equilibrium is reached.

5. 3. Solid-solution equilibrium:
Sugar(solid) ⇋ Sugar(solution)
If we go on dissolving solid sugar in water, then the solution
becomes saturated. Here the two opposing processes involved are
dissolution and precipitation. When the rate of dissolution becomes
equal to the rate of precipitation, equilibrium is reached.

6. Chemical equilibrium:
When blue vitriol is heated, it loses its water of crystallization and changes to
white, anhydrous copper sulphate is formed. This reaction is forward
reaction.
CuSO4.5H2O (s) → CuSO4(s) + 5H2O (l)
When water is added to anhydrous copper sulphate the reaction is reversed.
This is called the backward reaction
CuSO4(s) + 5H2O → CuSO4.5H2O(s)
We can show these two reactions in the same equation by using two arrows
CuSO4.5H2O (s) ⇋ CuSO4(s) + 5H2O (l)
The reaction in which the products can react to reform the original reactants
is called a reversible reaction.

7. In many chemical reactions the reactants are not used up completely.
Some products are formed but the maximum theoretical yield is not
obtained. A mixture of products and reactants is formed. The products
react together to re-form reactants at the same time as the reactants
are forming products. This type of reversible reaction is called
equilibrium reaction.
For example, consider the reaction between H2 and I2 carried out in a
closed vessel at 400oc.
H2 + I2 ⇋ 2HI
Molecules of HI are breaking down to H2 and I2 at the same rate as
hydrogen and iodine molecules are reacting together to form HI.

8. Characteristics of equilibrium:
• It is dynamic i.e. the forward reaction and backward reactions occur
at the same rate.
• The concentrations of reactants and products remain constant at
equilibrium.
• Equilibrium requires a closed system.

9. Chemical equilibrium
The equilibrium setup in the chemical process is called chemical
equilibrium.

10. Concept of chemical equilibrium
Consider the general reversible reaction
A + B ⇌ C + D
In the beginning (at time t=0), the concentration of A and B are
maximum and the concentration of C and D are minimum (equal to 0).
As the reaction proceeds the concentration of A and B are decreasing
with passage of time whereas the concentration of C and D are
increasing. Therefore the rate of forward reaction is decreasing while
the rate of backward reaction goes on increasing.

11. Fig:Rate of reaction vs time for reversible
reaction:

12. Ultimately a stage comes, when the rate of forward reaction becomes
equal to the rate of backward reaction. The reaction is the said to be in
a state of chemical equilibrium. The variation of the reaction rates with
time and ultimately the attainment of chemical equilibrium may be
represented diagrammatically as shown in figure.
At equilibrium
Rate of forward reaction= rate of backward reaction

13. Law of mass action:
Guldberg and Waage, the two Norwegian chemists, in 1864, put
forward a law concerning the dependence of the rate of the reaction
on the concentration of the reactants. This law is known as Law of mass
action. It states as follows:
“The rate at which a substance reacts is proportional to its active
mass and hence the rate of a chemical reaction is proportional to the
product of the active masses of the reactants.”
Here the term active mass means molar concentration i.e. number of
the moles of solute dissolved in a litre of solution.

14. Mathematical expression: Consider the
reaction
A + B → Products
According to law of mass action,
rate at which a substance A reacts ∝ [A]
rate at which a substance B reacts ∝ [B]
Therefore,
rate at which A and B react together ∝ [A][B]=K[A][B]
Where, K is constant of proportionality and is called velocity constant.

15. Again, consider the reaction
2A + 3B → Products
It can be written as
A + A + B+ B+ B → Products
Rate at which first A reacts ∝ [A]
Rate at which second A reacts ∝ [A]
Rate at which A reacts ∝ [A][A]
Similarly rate at which B reacts ∝ [B][B][B]
Therefore, rate of reaction between A and B ∝ A 2 B 3

16. Again consider the general reversible reaction
A + B ⇌ C + D
At equilibrium, suppose the active masses of A, B, C and D are
represented as [A],[B],[C] and [D] respectively,
Applying law of mass action,
Rate at which A and B react together i.e. rate of the forward reaction∝
[A][B]
=Kf[A][B] where Kf is a constant of proportionality and is called
velocity constant for the forward reaction.
Similarly, rate at which C and D react together i.e. rate of the backward
reaction ∝ [C][D]
=Kb[C][D] where Kb is called velocity constant for the backward
reaction

17. At equilibrium,
Rate of forward reaction = rate of backward reaction
Kf[A][B] = Kb[C][D]
C [D]
A [B]
=
Kf
Kb
= K or K c
At constant temperature, as Kf and Kb are constant, therefore
𝐾 𝑓
𝐾 𝑏
= K =Kc
is also constant at constant temperature and is called ‘equilibrium
constant.’

18. Again consider the more general reversible
reaction
aA + bB + ……….. ⇌ xX + yY + ………
Applying law of mass action,
Kc =
𝑋 𝑥
𝑌 𝑌
……..
𝐴 𝑎
𝐵 𝑏
…….
………………………(i)
Where Kc is equilibrium constant. It is constant at constant
temperature.
Thus, product of the molar concentration of the products each raised
to the power equal to its stoichiometric coefficients divided by the
product of the molar concentration of the reactants each raised to the
power equal to its stoichiometric coefficients is constant at constant
temperature which is called equilibrium constant.

19. Relation between Kp and Kc
Consider the general reversible reaction
aA + bB ⇌ xX + yY
If the equilibrium constant for this reaction is expressed in terms of
concentration, we may write
Kc =
X x
Y y
A a
B b
Simply Kc =
CX
x
C Y
y
CA
a
CB
b …………………………….(i)
Where CA, CB,CX and CY represents the molar concentration of A, B, X
and Y respectively.

20. If A, B, X and Y are gaseous, the equilibrium constant for the above
reaction may be expressed in terms of pressure
Kp =
PX
x
P Y
y
PA
a
P B
b…………………..(ii)
If the gases are supposed to be ideal, then we can apply the ideal gas
equation as
PV=nRT
Or, P =
n
V
RT
= CRT (where
n
V
= number of moles per litre
C=n
V
molar concentration)

21. For the gases A, B, X and Y, we may write
PA = CART PB = CBRT
PX = CXRT, and PY = CYRT
Putting the values in equation (ii)
Kp =
CX
RT x
. CY
RT y
CART a
. CBRT b
=…………..in baord

22. Dynamic nature of chemical equilibrium:
When the equilibrium is reached the most important observable
property is that the concentration of each of the reactants and
products becomes constant. For example, in decomposition of CaCO3
in closed vessel at a particular temperature, the amount of CO2
become constant.
Thus when equilibrium is reached, it appears that the reaction has
stopped. However this is not the case. The reaction is still going on in
the forward as well as backward direction but the rate of forward
reaction becomes equal to the rate of backward reaction. In other
words, as much of the reactants react to form the products, the same
amount of products react to give back the reactants in the same time.
Hence the equilibrium is dynamic in nature and not static.

23. Characteristics of equilibrium constant:
1. The equilibrium constant is constant for a particular reaction at a
particular temperature. Its value will not depend upon the
concentrations of reactants taken for the reaction.
2. The value of equilibrium constant does not depend upon the use of
catalyst.
3. The value of equilibrium constant depend upon temperature.
4. The value of equilibrium constant K depends upon the way the
reaction is written. E.g

24. H2 + I2 ⇌ 2HI
K =
HI 2
H2
[I2
]
But if the reaction is reversed
2HI ⇌ H2 + I2
K’ =
H2 [I2]
HI 2 Then K=
1
K′

25. Significance of equilibrium constant:
If the value of equilibrium constant is high then it indicates that the
reaction goes to almost completion in forward reaction. If the value of
equilibrium constant is low then the reaction does not go completion,
and the yield is low.

26. Le-Chatelier’s principle:
The effect of concentration, temperature and pressure on a system in
equilibrium can be predicted with the help of a generalization first
proposed by French chemist Le Chatelier in 1884. After his name, this
generalization is known as Le Chatelier’ principle.
The principle may be stated as, “if a system at equilibrium is subjected
to stress by changing pressure, temperature, or concentration, then
the equilibrium shifts in such a way so as to undo the effect of the
change imposed”

27. Factors affecting equilibrium:
Effect of concentration on equilibrium:
If a system is at equilibrium and the concentration of one of the species
involved in the reaction is increased, the system will readjust so as to
decrease the concentration of that species. Thus, the reaction will
proceed in such a manner so as to consume some of the increased
concentration.

28. To illustrate this, let us consider the reaction,
aA + bB ⇌ cC + dD
At equilibrium, the concentrations of A, B, C and D are constant. If at
equilibrium a small amount of the substance 'A' is added to this
reaction, then according to the Le Chatelier' principle, the equilibrium
shifts in a direction so as to undo the effect of the increased
concentration of 'A'. In other words the reaction proceeds in the
direction, which decreases the concentration of 'A'. Thus, with an
increase in the concentration of any one of the reactants such as 'A',
the equilibrium will shift towards right.
On the other hand, when the concentration of C (or any other product)
is increased, the reaction will shift towards left (reactant side).

31. Effect of temperature on equilibrium:
According to the Le Chatelier's principle, when the temperature or heat
supplied to a system at equilibrium is increased, the system should
move in a direction so that the added heat is absorbed. Thus, an
increase in the temperature of a system at equilibrium, favors an
endothermic reaction i.e., a reaction that proceeds with the absorption
of heat.
Again, a decrease in the temperature of a system at equilibrium, favors
an exothermic reaction i.e., the reaction, which proceeds with the
evolution of heat.
For example in the following,

32. N2(g) + 3H2(g) ⇌ 2 NH3(g) ∆H = -93.6KJ
The reaction is exothermic in the forward direction and endothermic in
the backward direction.
i.e. In above equilibrium, if temperature is increased then
equilibrium will shift towards backward direction yielding more
amount of reactants.
If temperature is decrease then equilibrium will shift towards forward
direction yielding more amount of products.

33. Effect of pressure on equilibrium
Change of pressure has no significant effect on the following
equilibrium.
• The equilibrium involving only solids are not affected by a change of
pressure. Virtually no change in volume results due to change in
pressure in solids
• The equilibrium involving liquids and/or gases, where the number of
molecules before and after the attainment of equilibrium remain the
same, (where Δn = 0), the reactions are not affected by a change of
pressure. For example, in the reactions,

35. However, in gaseous reactions where there is a change in the number
of molecules in going from reactants to products or vice-versa, pressure
plays an important role. For example, the equilibrium in the following
reactions are greatly influenced by any change in the pressure of the
system.

37. In gaseous reaction if the total number of gaseous molecules of the
reactants are different from the total number of molecules of the
product, then the change of pressure will effect the state of
equilibrium.
In above equilibrium 4 moles of reactants combine to give 2 moles of
ammonia. If pressure is increased to this equilibrium, the volume of
the gas will be decreased, and the number of molecules per unit
volume will be increased. Because of this, the equilibrium of the
system will be disturbed, and the system will be under strain. To
minimize this strains more nitrogen and hydrogen will combine so as to
decrease the number of molecules per unit volume. That is formation
of ammonia will be favored by increase in pressure.

38. Effect of catalyst on equilibrium:
Catalyst has no effect upon the equilibrium concentration of the
reactants and products. In fact, a catalyst accelerates the forward and
backward reactions to the same extent and therefore simply helps in
the attainment of the equilibrium state faster.

39. Effect of the inert gas on equilibrium:
• Addition of inert gas at constant volume: when inert gas is added to the
equilibrium system at constant volume, it will cause the increase the total
pressure of the system. But the partial pressure of each of the reactant as
well as product will not be affected and will remain the same. Hence under
these conditions, there will be no effect in equilibrium.
• Addition of inert gas at constant pressure: when inert gas is added to the
equilibrium system at constant pressure, it will result in the increase in
volume. As a consequence of this, the number of moles per unit volume of
various reactants and products will decrease, to counter balance this stress,
the equilibrium will shift to the side where number of moles are decreased.