Law of Mass Action

What is the Law of Mass Action?

The Law of Mass Action explains the relationship between the velocity of a chemical reaction and the molar concentration of the reactants at a particular temperature. Put forward by Norwegian scientists, Peter Wage and Cato Gulberg in 1864, the Law of Mass Action in Chemistry underpins many different types of physiological, biochemical, and pharmacological phenomena. 

Now, let’s define the Law of Mass Action:

The law states that the rate of a chemical reaction at a given temperature and instant is directly proportional to the product of the reactants’ active masses. Here, active mass means the molar concentration of a substance per unit volume of it. The unit of active mass is mol dm-3, and its value is expressed within square brackets.

Mathematical Expression of the Law of Mass Action

Consider a hypothetical reaction:

A + B → Products

As per the Law of Mass Action definition, the rate of reaction ‘R’ is given as:

R ∝ [A] [B]

For any general reaction denoted by aA + bB → Products, the rate of the reaction according to the Law of Mass Action is indicated as:

R ∝ [A]a [B]b

How to Derive the Law of Mass Action?

Consider the following reversible reaction hypothetically:

aA + bB ⇌ cC + dD


According to the Law of Mass Action, the rate of forward reaction will be:

Rf ∝ [A]a [B]b

Therefore, Rf = Kf [A]a [B]b, where Kf is the forward reaction’s rate constant

Similarly, the backward reaction rate will be:

Rb ∝ [C]c [D]d

Or,  Rb= Kb[C]c [D]d, where Kb is the backward reaction’s rate constant

Now, for a reaction to be in chemical equilibrium, 

Rf = Rb

Or, Kf [A]a [B]b = Kb[C]c [D]d

Therefore, Kf / Kb = [C]c [D]d / [A]a [B]b

Or, Kc = [C]c [D]d / [A]a [B]b

The above equation is known as the Mass Law equation, and Kc is termed as the equilibrium constant. 

What is the Equilibrium Constant in the Law of Mass Action Equation?

Kc or the equilibrium constant is expressed as the ratio of the product of the equilibrium concentrations of the products to the product of the equilibrium concentration of the reactants, with each concentration term raised to the individual stoichiometric coefficients of the reactants and the products in the balanced chemical equation. 

Explanation of the Law of Mass Action for a Gaseous System

For gaseous systems, the concentration terms are replaced by partial pressures. To explain the Law of Mass Action for such systems, we consider that the partial pressure of a gas is directly proportional to its concentration at a given temperature.

For the hypothetical reversible equation aA(g) + bB(g) ⇌ cC(g) + dD(g), the equilibrium constant Kp in terms of partial pressures will be:


Kp = [PC]c [PD]d / [PA]a [PB]b

Concentration Quotient versus Equilibrium Constant

The Concentration Quotient (Qc)of a chemical reaction at a given temperature is defined as the ratio of the product of the concentrations of the products to that of the reactants. However, as the system reacts the value of Qc will fluctuate, but the equilibrium concentrations will determine the equilibrium constant Kc.

  • If Qc> Kc, the reaction will be occurring in the backward direction

  • If Qc< Kc, the reaction will be occurring in the forward direction

  • If Qc= Kc, the reaction shall remain in equilibrium


Example of the Law of Mass Action

Consider the reaction 2NO2 ⇌ N2O4

Applying the Law of Mass Action formula, the expression for the equilibrium constant for this reaction is:

Kc = [N2O4] / [NO2]2

Taking the values of [N2O4] = 0.0417 mol L-1 and [NO2] = 0.0165 mol L-1,

Kc = [0.0417] / [0.0165]2 = 153

Applications of the Law of Mass Action

  • Ostwald’s Dilution Law for determining the dissociation equilibrium of weak electrolytes

  • Semiconductor physics 

  • For explaining diffusion in condensed matter

  • For solving the model of disease dissemination in mathematical epidemiology.

FAQ (Frequently Asked Questions)

1. What are the Factors Affecting the Rate of Chemical Reactions?

Ans:

  • Concentration: The reaction rate increases with an increase in the concentration of reactants.

  • Pressure: Pressure influences gaseous reactions. These can be categorised as three types of gaseous reactions:

  • Reactions With an Increase in Volume: For reactions that are accompanied by an increase in volume, a reduction in pressure increases the rate of reaction.

Example: PCl5(g) ⇌ PCl3(g) + Cl2(g)

  • Reactions With a decrease in Volume: For reactions that are accompanied by a reduction in volume, an increase in pressure increases the rate of reaction.

Example: N2(g) + 3H2⇌2NH3 (g) 

  • Reactions with No Change in Volume: Reactions, where volume remains unchanged are independent of changes in pressure.

Example: H2(g) + Cl2⇌2HCl (g) 

  • Temperature: In general, reaction rates increase with an increase in temperature.

  • Catalysts: Catalysts increase the reaction rate.

  • Particle size: Solid reactants in powdered form provide a greater surface area to increase the reaction rate.

2. What is Le Chatelier’s Principle of Chemical Equilibrium?

Ans: Le Chatelier’s principle states that for reactions that are in dynamic equilibria, changes in concentration, pressure, or temperature shifts the position of equilibrium to counteract the change and to establish a new equilibrium state. 

  • Concentration: Increasing the reactant concentration of a system will shift the equilibrium towards the right, forming more products. Conversely, reducing the concentration of the product(s) will also shift the equilibrium towards the right.

  • Pressure: If the volume of a system decreases, or pressure increases, the equilibrium will shift in the direction that involves a lesser number of moles of gas. Similarly, if the pressure decreases and the volume of the system increases, the equilibrium will favour the side that produces more number of moles of gas.

  • Temperature: For endothermic reactions, an increase in temperature will shift the equilibrium to the right. Conversely, for exothermic reactions, increasing the temperature will shift the equilibrium to the left.