Chemical Equilibrium

In basic chemistry, reactions are classified into two thermodynamic categories based on their directionality: irreversible and reversible. Irreversible reactions proceed in a single direction until the limiting reagent is entirely consumed. Reversible reactions, conversely, occur in both the forward direction (reactants turning into products) and the reverse direction (products reforming the original reactants) simultaneously.

Definition of Chemical Equilibrium

Chemical equilibrium represents the specific state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction (Ferner & Aronson, 2015; Narayan et al., 2020). Once a system reaches this equilibrium state under a given set of conditions, the macroscopic properties—such as the concentrations of both reactants and products, pressure, temperature, and color intensity—remain constant over time (Arpy et al., 2024).

The Dynamic Nature of Equilibrium

A common misconception is that a reaction stops entirely when it reaches equilibrium. In reality, chemical equilibrium is fundamentally dynamic (Marumure, 2020). The forward and reverse reactions continue to take place at exactly the same speed (Ferner & Aronson, 2015). Because chemical bonds are continuously broken and formed at equal rates, there is no net change in the overall concentration of the chemical species involved.

The Law of Mass Action and the Equilibrium Constant

The foundational quantitative mathematical description of a system at equilibrium is provided by the Law of Mass Action, which was originally formulated by Norwegian scientists Cato Guldberg and Peter Waage in 1864 (Ferner & Aronson, 2015).

Statement of the Law

The Law of Mass Action states that at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the active masses (or molar concentrations) of the reacting substances, with each concentration term raised to a power equal to its stoichiometric coefficient in the balanced chemical equation (Ferner & Aronson, 2015; Yamamoto & Kano, 2022).

Derivation of the Equilibrium Constant (K_c)

Consider a simple, single-step reversible homogeneous chemical reaction:

According to the Law of Mass Action, the velocities of the forward and reverse reactions are expressed as: Where k_f and k_b represent the forward and reverse rate constants, respectively (Narayan et al., 2020; Yamamoto & Kano, 2022). At the point of dynamic chemical equilibrium, the two rates balance exactly (v_f = v_b), yielding the following relation (Narayan et al., 2020; Yamamoto & Kano, 2022): The term K_c is known as the Equilibrium Constant expressed in terms of molar concentrations (Yamamoto & Kano, 2022).

Mathematical Forms of the Equilibrium Constant

Depending on the physical state of the reactants and products, the equilibrium constant can be expressed using different units and physical parameters.

Equilibrium Constant in Terms of Partial Pressures (K_p)

For reactions taking place entirely in the gas phase, it is far more practical to monitor partial pressures rather than molar concentrations (Yamamoto & Kano, 2022). The equilibrium constant is then expressed as K_p:

Relationship Between K_p and K_c

By applying the Ideal Gas Law (PV = nRT → P = n/VRT = CRT), a direct algebraic connection can be established between K_p and K_c (Eblin, 1966):

• R: Universal gas constant (0.0821 L atm mol^-1 K^-1).
• T: Absolute temperature measured in Kelvin.
• Δ n_g: The difference between the total number of moles of gaseous products and gaseous reactants:
  Δ n_g = (c + d)_gas – (a + b)_gas

Three Distinct Thermodynamic Scenarios for Δ n_g

Value of Δng​	Mathematical Relationship	Real-World Chemical Example
Δ ng = 0	Kp = Kc	H2(g) + I2(g) ⇌ 2HI(g)
Δ ng > 0	Kp > Kc	PCl5(g) ⇌ PCl3(g) + Cl2(g)
Δ ng < 0	Kp < Kc	N2(g) + 3H2(g) ⇌ 2NH3(g)

Key Characteristics of the Equilibrium Constant (K)

The equilibrium constant possesses unique properties that govern how a chemical system responds to changes.

• Temperature Dependence: The numerical value of the equilibrium constant is completely independent of individual concentrations, pressure, volume, or the presence of a catalyst (Arpy et al., 2024; Eblin, 1966). It changes only with a change in the temperature of the system (Arpy et al., 2024; Eblin, 1966).
• Directional Reciprocal: If the equilibrium constant for a forward reaction is K, the equilibrium constant for the reverse reaction becomes its reciprocal (1/K).
• Stoichiometric Scaling: If the entire balanced chemical equation is multiplied by a factor of n, the new equilibrium constant becomes Kⁿ.
• Pure Solids and Liquids: The active mass (concentration) of any pure solid or pure liquid is always taken as unity ($1$) because its density remains constant regardless of the total amount present. They are omitted from the final K_c or K_p expressions.

Le Chatelier’s Principle

Formulated by Henri Le Chatelier, this core principle predicts how a chemical system at equilibrium responds to an external disturbance or stressor (Arpy et al., 2024; Novak, 2017).

Statement of the Principle

If a chemical system at equilibrium is subjected to a change in concentration, temperature, or total pressure, the system will shift its equilibrium position in a direction that counteracts, minimizes, or neutralizes the effect of that applied disturbance (Arpy et al., 2024; Novak, 2017).

1. Effect of Concentration Changes

• Adding a Substance: Increasing the concentration of a reactant drives the system to consume those reactants, shifting the equilibrium in the forward direction to produce more products.
• Removing a Substance: Continuously removing a product as it forms forces the system to replace it, continuously shifting the reaction in the forward direction (maximizing product yield).

2. Effect of Pressure Changes

A change in pressure affects only reactions that involve gaseous components where there is a net change in the number of moles (Δ n_g ≠ 0).

• Increasing Pressure: Compressing the system shifts the equilibrium toward the side that has the fewer number of moles of gas, thereby minimizing the pressure increase.
• Decreasing Pressure: Shifts the equilibrium toward the side with the greater number of moles of gas.

3. Effect of Temperature Changes

The direction of the equilibrium shift depends entirely on whether the reaction is exothermic or endothermic.

• Exothermic Reactions (Δ H = -ve): Heat is evolved as a product. Raising the temperature shifts the equilibrium to the left (reverse direction). Lower temperatures favor product formation.
• Endothermic Reactions (Δ H = +ve): Heat is absorbed as a reactant. Raising the temperature shifts the equilibrium to the right (forward direction).

4. Effect of Adding an Inert Gas

• At Constant Volume: Adding an inert gas (such as Argon or Helium) at constant volume does not change the partial pressures or molar concentrations of the reacting gases. Therefore, there is no shift in the equilibrium position.
• At Constant Pressure: Adding an inert gas increases the total volume of the container. To maintain constant pressure, the system shifts toward the side that occupies a larger volume, meaning the side with the greater number of moles of gas.

5. Effect of a Catalyst

As established in chemical kinetics, a catalyst increases the rate of both the forward and reverse reactions to the exact same extent (Eblin, 1966; Narayan et al., 2020). Consequently, a catalyst does not shift the position of equilibrium and has no effect on the value of K (Eblin, 1966). It merely allows the system to reach the same equilibrium state much faster (Eblin, 1966).

Industrial Optimization via Le Chatelier’s Principle

The following table demonstrates how industrial chemical processes manipulate equilibrium variables to achieve maximum product yields while balancing economic efficiency:

Industrial Synthesis Process	Balanced Chemical Equation	Energetics (ΔH)	Optimal Conditions for Maximum Yield
Haber’s Process (Ammonia Synthesis)	N2(g) + 3H2(g) ⇌ 2NH3(g)	-92.4 kJ/mol (Exothermic)	High Pressure (∼ 200 atm), Low Temperature (∼ 700 K), continuous removal of NH3.
Contact Process (Sulfur Trioxide Synthesis)	$2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)</td> <td>-197 \text{ kJ/mol}(Exothermic)</td> <td>High Pressure (1\text{ to }2 \text{ atm}is sufficient), Low Temperature (\sim 673 \text{ K}),V_2O_5catalyst.</td> </tr> <tr> <td><b>Nitric Oxide Synthesis</b> (Birkeland-Eyde Process)</td> <td>N_2(g) + O_2(g) \rightleftharpoons 2NO(g)</td> <td>+180.6 \text{ kJ/mol}(Endothermic)</td> <td>Very High Temperature (\sim 3000 \text{ K}); Pressure change has no effect since\Delta n_g = 0$.

Last Modified: May 25, 2026