CHEMICAL EQUILIBRIUM:
REVERSIBLE REACTIONS:
“Those reactions in which the products formed also combine together to form the reactants under the similar conditions are termed as the reversible reactions or incomplete reactions”.
Chemical equilibrium: It is the state that occurs in reversible or incomplete reactions.
A state in reversible processes at which some observable properties like concentration, presuure acquire constancy, is called the state of equilibrium or dyamic euilibrum.
At equilibrium, the two opposing procees occure simultaneously at the same raate and in opposite diections.This is alo called dynamic equilibrium.
Consider a general reaction: aA + bB
⇄
cC + dD -------------(1)
Rate of the forward reaction (r
1
) = k
1
[A] a
Rate of the backward reaction (r
2
) = k
2
[C] c
At equilibrium
r
1
= r
2
k
1
[A] a [B] b = k
2
[C] c [D] d
[C] c
[D] d
or k
1
/k
2
= -------------
[A] a
[B] b
[C] c
[D] d
or K c
= ------------
[A] a
[B] b
[B]
[D] d b
-------------(2)
K c
is the equilibrium constant for the general reaction (1)
Equation (2) is known as Law of Chemical equilibrium
In case of gaseous systems, the equilibrium constant Kp is related with Kc as
Kp = Kc (RT)
∆ n
Where,
∆ n = n
2
– n
1

n n
1
2
= number of moles of reactants
= number of mole of the products
The reaction quotient,Q
[C] c
[D] d
(Reaction Qutient) = ------------ -------------------(3)
[A] a
[B] b
The reaction quotient can be used to predict the direction in which a reaction will proceed from a given set of initial conditions.
Where, [A], [B], [C], [D] are initial molar concentrations or partial pressures instead of equilibrium conditions.
If Q = Kc, the system is already in equilibrium
If Q > Kc, the reaction proceeds in the backward direction
If Q < Kc , the reaction proceeds in the forward direction
According to this principle,
“If a system in equilibrium is subjected to a change in temperature, concentration or pressure, then the equilibrium shifts in such a direction so as to undo the effect of the change imposed”.
Illustration: Consider the formation of ammonia by Heber’s Process
N
2
(g) + 3 H
2
⇄
2 NH
3
; ∆H = - 92.7 kJmol -1
Observations: The above reaction is reversible and exothermic
The reaction proceeds with a decrease in volume in the forward direction
Conclusion: a) Effect of concentration : On increasing the concentration of the reactants the equilibrium is shifted in the forward direction where the reactants are consumed and vice versa. b) Effect of temperature: On increasing the temperature the equilibrium shifts in the backward direction where the heat is absorbed and vice versa.

c) Effect of concentration: On increasing the concentration of the reactants the equilibrium shifts in the forward direction where reactants are consumed up and vice versa.
Thus in general,
 Thus according to the Le-Chatelier’s Principle, the equilibrium will shift in that direction where the stress is relived on the system.
 Equilibrium shifts in the forward direction means that more of the products are formed. Conversely the shifting of the equilibrium in the backward direction means that more of the reactants are formed.
 This principle gives a qualitative idea of an equilibrium system's response to changes in reaction conditions.i.e. If a dynamic equilibrium is disturbed by changing any one of the conditions ,the equilibrium moves to counteract the change .
sp
Consider partially soluble salts in solution (i.e. a saturated solution).
Such salts also dissociate in solution to some extent. K sp
gives the measure of the extent of dissociation of a salt in solution.
Higher the value of K sp
of a salt greater is its solubility.
The equilibrium constants for saturated solution and solid formation (precipitate) are called solubility product, K sp
.
If the solution is not saturated, no precipitate will form. In this case, the product of molar concentration is called the ion product or ionic product, Q sp
.
e.g. Consider solubility of a partially soluble salt (A x
B y
) in water.
A x
B y
(s) + aq
⇄
xA y+
+ y B x-
The equilibrium constant at a given temperature is
[A y+
] x
[B x-
] y
K = --------------
[A x
B y
(s)]

or K sp
= [A y+
] x
[B x-
] y ∵
[[A x
B y
(s)] = constant
The value of K sp is constant at a constant temperature.
e.g. The value for the K sp
of silver chloride, however, is about
1.8 x 10 -10 .This very small value indicates the very low solubility of
AgCl.
NOTE:
Q sp
< K sp
Unsaturated solution
Q sp
= K sp
Saturate solution
Q sp
> K sp
Oversaturated solution
K sp
is a special case of general term ionic product O sp
 Solubility product constants are used to describe saturated solutions of ionic compounds of relatively low solubility.

A saturated solution is in a state of dynamic equilibrium between the dissolved, dissociated, ionic compound and the undissolved solid.
Example:
The K sp
for AgCl is 1.8x10
-10 M 2 . What is the molar solubility of AgCl in pure water?
Solution
Let x be the molar solubility, then
AgCl = Ag
+
+ Cl
x x x = (1.8x10
-10 M 2 ) 1/2
= 1.3x10
-5
M
Discussion
The solubility product, K sp
is a more suitable indicator than the usual solubility term of g per 100 mL of solvent or moles per unit volume of solvent.

In case of AgCl, when the cation concentration is not the same as the anion concentration ([Ag
+
] =/= [Cl
-
]) solubility of AgCl can not be defined in terms of moles per L. In this case, the system can be divided into three zones. The condition [Ag
+
] [Cl
-
] = K sp
, is represented by a line which divides the plane into two zones.
When [Ag + ] [Cl ] < K sp
, no precipitate will be formed.
When [Ag
+
] [Cl
-
] > K sp
, a precipitate will be formed.
When AgCl and NaCl dissolve in a solution, both salts give Cl
-
ions. The effect of
[Cl
-
] on the solubility of AgCl is called the common ion effect.
[Ag
+
]
Q sp
> K sp
Q sp
<K sp
Q sp
= K sp
[Cl
-
]
Learn:
 K c
is the constant for molar concentrations
 K p
is the constant for partial pressures
 K sp
is the constant for molar concentrations with no denominator
 K a is the acid dissociation constant for weak acids
 K b
is the base dissociation constant for weak bases.
 K w is the ionization constant of pure water at 25 o
C (1x10
-14
)