4. HOMOGENEOUS EQUILIBRIA

HOMOGENEOUS EQUILIBRIUM

Homogeneous equilibrium is more straightforward and less complex when compared to Heterogeneous equilibrium. The most common examples are reactions that involve components in the gaseous state or solution reactions.

e.g.: Reaction of Nitrogen and Hydrogen to form Ammonia (Haber’s process)

N₂(g)+ 3H₂(g) ⇔ 2NH₃(g) 

The Esterification reaction between an alcohol and an organic acid is the best example of a liquid phase homogeneous reaction.

CH₃COOH(l) + CH₃CH₂OH(l) ⇔ CH₃COOCH₂CH₃(l) +H₂O(l) 

The equilibrium constant is a number that expresses the relationship between the concentration of products and the reactants in an equilibrium reaction at a given temperature. It is expressed as ‘Kc’. To derive the expression of K_c, let us consider the homogenous equilibrium equation, 

aA + bB ⇔ cC + dD

Note that the products of the reaction are always written on the right side and the reactants are on the left side. The Equilibrium constant K_c for this reaction would consist of a ratio where the products with their coefficient as exponent forms the numerator and similarly the reactants form the denominator.

Example: Let us write the Equilibrium Constant expression K_c for the Haber’s process of Ammonia production

N₂(g)+ 3H₂(g) ⇔ 2NH₃(g) 

 K_c is written as: 

Note that for components that have only one molecule such as for N₂, the exponential power of 1 need not be written. The concentration of only the gaseous and aqueous components in the reactions are taken into account. 

Equilibrium Constant in Gaseous Systems

For an equilibrium reaction that involves gases, equilibrium constants should be expressed in terms of partial pressure. Thus the ideal gas equation is taken into account.

pV = nRT ……(Ideal gas equation)

→ p = n/V x RT

p → Pressure in Pa

n → Number of moles of gas 

V → Volume in cu.m

T → Temperature in K

Here n/V expresses the concentration in moles/m³

Thus, p = c RT

Where c is the concentration in moles/lit

We can also write,

p = [gas] RT

Therefore, at a constant temperature, the pressure of a gas is directly proportional to its concentration.

Consider the reaction

aA + bB ⇔ cC + dD

K_c is written as,

In terms of partial pressure, K_p is written as

( as p = [gas] RT)

 

On substitution, we get the relation between K_c and K_p

Where,  Δn → (number of moles of gaseous products) - (number of moles of gaseous reactants)