Law of Mass Action: Applications, Active Mass, Equilibrium Constant, Important Questions

Just imagine that water is flowing from the upper floor to the lower floor. Will it flow forever? Of course not. The flow will stop when the two levels become equal. This state can be considered as a state of equilibrium. This idea also applies to many chemical reactions and can be explained by the Law of Mass Action.

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Law of Mass Action

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The Law of Mass Action states that the rate of a chemical reaction is proportional to the product of the active masses of the reactants.

Consider a reaction- 

A + B ⇔ C + D

Let the concentration of reactions be [A] and [B]

Rate of reaction ∝ [A] [B]

R ∝ [A] [B]

R = K [A] [B]

Here, K is the rate constant. 

Active Mass

Active Mass means molar concentration. The active mass refers to the number of moles dissolved per litre of the solution.

This law explains the behavior exhibited by solutions in dynamic equilibrium. The law of mass action also states that the ratio between the concentrations of reactants and concentrations of products is constant at the state of equilibrium.

K_c = [C][D] / [A][B]

Also Read: Law of Mass Action in Detail

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Law of Mass Action: Equilibrium Constant

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At the state of chemical equilibrium, the ratio of reactant concentration and product concentration is constant, which can be explained with the help of the equilibrium constant (Kc).

Consider a simple reversible reaction where A & B are the reactants and C & D are the products.

A + B ⇔ C + D

According to the Law of Mass Action,

K_c = [C][D] / [A][B]

Here, 

K_c­ is called the equilibrium constant. 

In this equation, the concentration of A at equilibrium is represented as [A] (similarly for B, C, and D), and the stoichiometric coefficients of the reactants and products are 1. It has been experimentally observed that the equilibrium constant is also dependant on the stoichiometric coefficients of the reactants and products.

Therefore, the law of mass action explains that the equilibrium constant, at a constant temperature, is equal to the product of the concentration of products divided by the product of the concentration o reactant, each raised to the corresponding stoichiometric coefficient.

This is also known as the equilibrium law or the law of chemical equilibrium.

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Law of Mass Action: Representation of Equilibrium Constant

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Equilibrium Constant for the balanced reaction of the following type:

aA + bB ⇔ cC + dD

According to the Law of Mass Action, the equilibrium constant is the value obtained by relating the equilibrium concentration of the products and the reactants. 

For forward reaction, the equilibrium constant can be given by:

K_c = [C]^c[D]^d / [A]^a[B]^b

For reverse reaction, the equilibrium constant can be expressed as the inverse of the forward reaction and can be expressed by:

K’_c = 1/K_c = [A]^a[B]^b / [C]^c[D]^d

If the coefficient of the chemical equations is multiplied by a factor ‘n’ then the equilibrium constant becomes Kcn.

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Law of Mass Action: Relation between K_c, K_p and K_x

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K_p = K_c(RT)^Δng

K_p = K_x. PΔn_g

Where, 

Δn_g = moles of gaseous products - moles of gaseous reactants

K_c = Equilibrium constant expressed in terms of the concentration of the reactants/products

K_p = Constant of partial pressures of reactants and products.

K_x = Mole fraction of reactants and products

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Applications of the Law of Mass Action

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The Law of Mass action applies to semiconductors and, therefore, it has a number of important applications in the fields of electronics and semiconductor physics. It also depicts a relationship between the concentrations of electron holes and free electrons when the semiconductor system is in a state of thermal equilibrium.

The law of mass action also applies to the following fields:

• In semiconductor physics and Sociophysics. 
• In Mathematical ecology
• For the explanation of diffusion in condensed matter
• For solving the model of the spread of disease in mathematical epidemiology
• Ostwald’s Dilution Law for determining the dissociation equilibrium of weak electrolytes

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Law of Mass Action: Things to Remember

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• According to the Law of Mass Action, the rate of a chemical reaction is proportional to the product of the active masses of the reactants.
• Law of Mass Action also states that the ratio between the concentrations of reactants and concentrations of products is constant at the state of equilibrium.

K_c = [C][D] / [A][B]

• The active mass of a substance can be defined as the number of moles dissolved per litre of the solution.
• The relation between K_p, K_c, and K_x can be expressed as:

          K_p = K_c(RT)Δn_g and K_p = K_x. PΔn_g

• The Law of Mass action has various applications in the field of semiconductor physics, Sociophysics, Mathematical ecology and mathematical epidemiology.

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