Collision theory and dynamic equilibrium

What you’ll learn

• Explain rate changes using collision frequency and activation energy.
• Interpret temperature and catalyst effects using energy distributions.
• Predict qualitative shifts of equilibrium and industrial compromises.

Understand the idea

A successful collision requires sufficient energy and a suitable orientation. Higher concentration or gas pressure increases collision frequency; greater exposed solid area offers more reaction sites. Raising temperature increases the fraction of particles above the activation-energy threshold, usually producing a much larger rate effect than the modest change in collision frequency alone.

A Maxwell–Boltzmann distribution shows how molecular energies vary. At higher temperature, the peak lowers and shifts and the high-energy tail becomes more significant while the total area remains the particle count. A catalyst supplies an alternative pathway with lower activation energy; it does not raise the temperature or change the reaction enthalpy.

In a closed reversible system, dynamic equilibrium occurs when forward and reverse rates are equal. Both reactions continue and concentrations remain constant, but the concentrations need not be equal. Changing concentration, pressure or temperature can disturb this balance. Increased pressure favours the side with fewer gaseous moles, and increased temperature favours the endothermic direction.

A catalyst speeds approach to equilibrium in both directions without changing the equilibrium composition at a fixed temperature. Industrial conditions balance conversion, speed, energy demand, separation and equipment costs. An exothermic synthesis may have a better equilibrium yield at low temperature but an impractically slow rate, requiring a compromise.

Key formulae

$$\text{mean rate}=\frac{\Delta\text{product amount}}{\Delta t}$$

$$r_{\mathrm{forward}}=r_{\mathrm{reverse}}\quad\text{at equilibrium}$$

$$\mathrm{N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)}\quad\Delta H<0$$

$$E_{a,\mathrm{catalysed}}<E_{a,\mathrm{uncatalysed}}$$

Worked example

For the exothermic equilibrium $\mathrm{N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)}$, explain the separate effects of increasing pressure and increasing temperature on ammonia yield.

1. There are four gaseous reactant moles for every two gaseous product moles.
2. Increasing pressure favours the smaller gas amount and shifts equilibrium toward ammonia.
3. Increasing temperature favours the endothermic reverse direction, decreasing equilibrium ammonia yield.

Answer: Higher pressure increases equilibrium yield; higher temperature decreases it.