Introduction to Equilibria

The state of the system in which its observable properties like temperature, pressure, and composition do not change with time at all conditions is known as equilibrium. In equilibrium condition, two opposing process remains at the same rate at all conditions. There are two types of equilibrium

a) Physical equilibrium

b) Chemical equilibrium

a) Physical equilibrium

An equilibrium that exists in the different phase of the same substance is called physical equilibrium. Some of its examples are

i) Solid - liquid equilibrium

ii) Liquid-vapor equilibrium

iii) solid-vaporinformato

iv) Solid aqueous equilibrium

v) Gas- solution equilibrium

Chemical equilibrium

An equilibrium that exists between reactants and products in a reversible reaction is called chemical equilibrium. Depending upon the phase, chemical equilibrium is homogeneous or heterogeneous.

Reversible and irreversible reaction

A reaction in which reactant gives product and also product converts into reaction under similar condition is called reversible reaction

A reaction in which reactant gives product but product does not convert to form reactant is known as the irreversible reaction.

State of Dynamic equilibrium

A chemical reaction, in equilibrium condition does not stop but it continuously changes in forward and backward reaction. At initial period, the concentration of reactants is maximum and after a certain time interval, the concentration of reactant becomes equal to the concentration of the product.

At an equilibrium condition, where is theconcentration of reactant is equal to the concentration of product per unit time is called state of dynamic equilibrium. At this point, rate of forward reaction is equal to the rate of backward reaction as shown below

Law of Mass Action

It states " at constant temperature and pressure, rate at which reaction proceeds are proportional to the concentration and overall rate of reaction is proportional to the product of concentration raised to the power equal to their stoichiometric coefficients in a balanced chemical reaction"

Let us consider a reversible reaction

where, a,b,c,d are stoichiometric coefficients of A, B, C and D respectively

According to law of mass action,

Rate of forward reaction ( R_f)∝ [A]^a [B]^b

∴R_f = k_f [A]^a[B]^b ----(i)

Rate of backward reaction ( R_b)∝ [C]^c[D]^d

∴ R_b = k_b [C]^c[D]^d ----(ii)

where R_f and R_b are the rates of reaction for forward and backward

and k_f and k_b are the equilibrium constants for forward and backward reaction

At equilibrium condition,

k_f [A]^a[B]^b= k_b [C]^c[D]^d

or, \( \frac {k_f}{k_b}\) = \( \frac{[C]^a\:\:[D]^b}{[A]^a\:\:[B]^b}\)

or, K_eq or k_c =\( \frac{[C]^a\:\:[D]^b}{[A]^a\:\:[B]^b}\) ------(iii)

where k_eq is the equilibrium constant for forward and backward reaction

From equation (iii), equilibrium constant can be defined as the ratio of product of molar concentration of product to the product of molar concnetration of reactants with each term expressed into powers equal to their corresponding stoichiometric coefficients in a balanced chemical reaction

If the equilibrium constant is existing in gaseous phase, it is convenient to write the equilibrium constant in terms of partial pressure as

k_p = \( \frac{P_C^c\:P_D^d}{P_A^a\:P_B^b}\) ---(iv)

Relation between k_p and k_c

Consider a reversible reaction in gaseous state

or, K_eq or k_c =\( \frac{[C]^a\:\:[D]^b}{[A]^a\:\:[B]^b}\) --(i)

k_p = \( \frac{P_C^c\:P_D^d}{P_A^a\:P_B^b}\)---(ii)

Assuming that the gas behaves ideally,

P_iV = n_i RT

or,P_i = \( \frac{n_i}{V}\) RT

or, P_i = [ i ] RT

Putting this value in equation (ii)

Characteristics of equilibrium constant

1. It is a constant for a given reaction at constant temperature

2) Its value does not depend on concentration of reacting species

3) Its value is unaffected by the use of catalyst

4) The equilibrium constant for forward reaction is reciprocal of equilibrium constant for backward reaction

i.e. K_forward = \( \frac {1}{K_{backward}}\)

Physical significance of equilibrium constant

1) The value of equilibrium constant is of great practical importance in determining the extent of reaction and yield of produce formed.

2) If k > > 1 , the reaction is largely favored in forward direction which means the product yield is high

3) If k≅ 1, the reaction is largely favored in both direction, which means the formation of product is intermediate

3) If k < < 1, the reaction is largely favored in backward direction i.e. the yield of product is low

Le Chatelier's principle

The effect of change of temperature, pressure, and concentration on equilibrium is quantitatively explained by a law called Le Chatelier's principle.

It states " If a system in equilibrium is subjected to change in temperature, pressure or concentration then the equilibrium will shift in a direction so as to undo the effect the change"

i) Effect of temperature in equilibrium

According to this principle, an increase in temperature will shift the equilibrium in a direction that absorbs heat. On the other hand, decrease in temperature will shift the equilibrium in the direction that evolves heat.

ii) Effect of pressure

According to this principle, an increase in pressure will shift the equilibrium involving gas species in a direction that leads to decrease in the number of moles. On the other hand, decrease in pressure will shift the equilibrium that leads to increasing in a number of moles.

iii) Effect of concentration

An increase in the concentration of reactant will shift the reaction forward and decrease in concentration of reactants will shift the reaction backward.

iv) Effect of catalyst

A catalyst has no effect on equilibrium position

v) Effect of inert gas

If any gas is increased in equilibrium, then the equilibrium will shift in a direction that leads to decrease in the number of moles if the pressure is kept constant