Using Le Châtelier's Principle vs Collision Theory in Equilibrium

Welcome back to the Science Ready blog! For HSC Chemistry students, Module 5: Equilibrium and Acid Reactions is central to understanding how chemical systems behave. A key concept here is dynamic equilibrium, which describes a state where the forward and reverse reaction rates are equal, and the macroscopic properties of the system remain constant.

But what happens when we disturb this delicate balance? That's where Le Châtelier's Principle and Collision Theory come in. These two powerful tools allow us to predict and explain how changes in temperature, concentration, and volume (or pressure) influence an equilibrium system.

This post breaks down the role of each principle, focusing on the similarities and differences in how they explain the effects of disturbances, as demonstrated in past HSC questions (like the one concerning the cobalt complex equilibrium).

Understanding the Pillars of Equilibrium Explanation

We use two distinct principles to explain changes in equilibrium:

• Le Châtelier's Principle (Predictive Tool): This principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that partially counteracts the imposed change until a new equilibrium is established. It tells us which direction the reaction shifts and the relative change in concentration of reactant and product as a result of the shift. 

• Collision Theory (Mechanistic Explanation): This theory explains why the reaction shifts. It is based on the idea that for a reaction to occur, reactant particles must collide with sufficient energy (greater than the activation energy) and correct orientation. The use of collision theory focuses on changes in reaction rate as a cause for changes in reactant and product concentrations. Collision theory helps explain macroscopic outcomes in terms microscopic changes.

Regardless which principle is used to predict the effect of various factors on an equilibrium, the final outcome should be the same. 

The Effect of Concentration Changes

Changing the concentration of a reactant or product is the most direct way to disturb a system.

1. Le Châtelier's Principle on Concentration

When a reactant's concentration is increased, the system shifts to the product side to consume the added reactant. Conversely, decreasing a reactant's concentration causes the system to shift to produce more of it.

• Example (From the Cobalt Equilibrium):

   

  $$[CoCl_{4}^{2-}](aq) + 6H_{2}O(l) \rightleftharpoons [Co(H_{2}O)_{6}^{2+}](aq) + 4Cl^{-}(aq)$$

  Adding chloride ion would cause the equilibrium to shift to the left (reverse reaction) to consume the added chloride ion. 

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2. Collision Theory on Concentration

Increasing the concentration of a reactant increases the frequency of successful collisions between the reactant particles.

• If the concentration of a reactant increases, the frequency of effective collisions for the forward reaction increases. The forward rate instantly becomes greater than the reverse rate pushing the system towards products. As concentration of products increases, and reactants decrease, the reverse and forward reaction rates will increase and decrease respectively, until they become equal again at a new equilibrium.

• The change in concentration does not affect the activation energy or the inherent reaction pathway for either the forward or reverse reaction. 

The Effect of Temperature Changes

Temperature is unique because it is the only factor that changes the actual value of the equilibrium constant, `K_{eq}`.

1. Le Châtelier's Principle on Temperature

Heating an equilibrium system causes the reaction to proceed in the direction that absorbs heat (the endothermic direction) to counteract the increase in temperature.

• Example (From the Cobalt Equilibrium):

  The system shifts blue when heated, which means the `\text{CoCl}_4^{2-}` (blue) concentration increases. The forward reaction is:

   

  $$\text{CoCl}_{4}^{2-}(aq) + 6\text{H}_{2}\text{O}(l) \rightleftharpoons \text{Co}(\text{H}_{2}\text{O})_{6}^{2+}(aq) + 4\text{Cl}^{-}(aq)$$

   

  Since heating favors the reverse (pink-producing) reaction, the reverse reaction must be endothermic (`\Delta H_{\text{reverse}} > 0`). Therefore, the `\text{CoCl}_4^{2-}` (blue-producing) forward reaction must be exothermic (`\Delta H_{\text{forward}} < 0`).

  • When the solution is cooled, the system shifts to release heat, favouring the exothermic direction (the forward reaction in the provided question).

  • This shift to the right consumes the blue complex and produces the pink complex, resulting in a pink colour and an increase in `K_{eq}` (due to increased product/reactant ratio).

    
    

2. Collision Theory on Temperature

Increasing the temperature increases the kinetic energy of all particles. This has two effects:

1. Increases Collision Frequency: All collisions (both effective and non-effective) become more frequent.

2. Increases Fraction of Successful Collisions: A greater proportion of collisions will meet or exceed the activation energy.

Crucially, temperature increases the rate of both the forward and reverse reactions, but the increase is greater for the reaction with the larger activation energy (endothermic reaction).