Homogeneous Equilibria: Equilibrium Constant, Derivation & Examples

Homogeneous equilibrium is where the components involved in a reversible reaction are all in the same phase. To understand this clearly, we need to get a better understanding of what Chemical Equilibrium is and how it is achieved.

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What is Chemical Equilibrium?

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Chemical equilibrium is defined as the state in which the concentration of both the reactants and products do not change with time. The reaction rates of the forward and backward reactions will be equal at this stage and it appears as though the reaction has stopped. But in reality, the reactants and products are being created at the same rate. 

The Chemical equilibrium can be of two types as Homogeneous and Heterogeneous. Homogeneous is where the components are all in the same phase whereas, in a Heterogeneous reaction, the components will be in different phases. 

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Homogeneous Equilibrium

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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.

Example 1: Reaction of Nitrogen and Hydrogen to form Ammonia (Haber’s process)

N₂(g)+ 3H₂(g) ⇔ 2NH₃(g) 

Example 2: 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) 

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What is Equilibrium Constant?

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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. 

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Equilibrium Constant in Gaseous Systems

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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)

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Things To Remember

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• Homogenous equilibrium is where all the components of the reaction are in the same phase.
• The Equilibrium constant Kc establishes the relationship between the concentrations of the reactants and products.
• Only the concentration of gaseous and aqueous components are taken into account for Equilibrium constant expression.
• Partial pressure should be considered for the Equilibrium constant of gaseous systems.

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Sample Questions based on Homogeneous Equilibria

Ques. What is K_c for the following reaction in a state of equilibrium? (2 marks)

Ques. Explain why pure liquids and solids can be ignored while writing the value of equilibrium constants. (2 marks)

Ques. At 450K, K_p = 2.0 x 10¹⁰ bar^-¹ for the equilibrium reaction, 
2SO₂(g)+ O₂(g) ⇔ 2SO₃(g)
What is K_c at this temperature? (2 marks)

Ques. A sample of HI (g) is placed in a flask at a pressure of 0.2 atm. At equilibrium partial pressure of HI (g) is 0.04 atm. What is K_p for the given equilibrium? (2 marks) 
2HI(g) ⇔ H₂(g) + I₂(g)

Ques. K =0.04 atm at 898 K for the equilibrium shown below. What is the equilibrium concentration ok C₂H₆ when it is placed in a flask at 4 atm pressure and allowed to come to equilibrium? (2 marks)
C₂H₆(g) ⇔ C₂H₄(g) + H₂(g)