Dynamic Equilibrium and the Equilibrium Constant Kc

1. From Static to Dynamic: The Nature of Chemical Equilibrium

Many Year 12 students arrive with a mental model of equilibrium borrowed from physics — a balance scale sitting perfectly still. This picture is fundamentally wrong for chemistry. Chemical equilibrium is a dynamic process, and understanding that dynamism is the conceptual foundation for everything else in this module.

Consider a reversible reaction sealed inside a closed container:

aA + bB ⇌ cC + dD

In an open system, reactants might escape or products might be removed, so the reaction simply runs to completion. In a closed system, however, products accumulate. As product concentration rises, the reverse reaction begins to compete. Eventually, the rate of the forward reaction equals the rate of the reverse reaction. At that moment, equilibrium is established.

Two types of equilibrium are important to distinguish:

• Static equilibrium — a system at rest, with no ongoing processes. A book sitting on a table is in static equilibrium. No chemical reactions are occurring, and concentrations are unchanging because nothing is happening at all.
• Dynamic equilibrium — a system where opposing processes continue at equal rates. Reactants are still forming products, and products are still re-forming reactants, but the net change in concentration is zero because both rates are identical.

A classic macroscopic analogy: imagine a crowded escalator where people walk up at exactly the same rate that others walk down. The total number of people on each floor appears constant — yet individuals are constantly moving. That constant, two-directional motion at the particle level is the hallmark of dynamic equilibrium.

Key observable features of dynamic equilibrium:

• Constant macroscopic properties — temperature, pressure, and concentrations appear unchanged over time.
• Continues only in a closed system — open systems cannot maintain equilibrium because products or reactants escape.
• Reached from either direction — the same equilibrium state is reached whether you start with pure reactants, pure products, or a mixture of both (at the same temperature).
• The forward and reverse rates are equal, but not necessarily zero.

2. Deriving the Equilibrium Constant Expression K_c

The equilibrium constant expression is not arbitrary — it emerges directly from the kinetics of elementary reactions. Here is the derivation path the NSW HSC expects you to understand (not just memorise).

Consider the general homogeneous equilibrium (all species in the same phase, typically aqueous or gaseous):

aA(aq) + bB(aq) ⇌ cC(aq) + dD(aq)

Using collision theory, the rate of the forward reaction is proportional to the frequency of effective collisions between A and B:

r_forward = k_f[A]^a[B]^b

Similarly, the rate of the reverse reaction:

r_reverse = k_r[C]^c[D]^d

At dynamic equilibrium, these two rates are equal:

k_f[A]^a[B]^b = k_r[C]^c[D]^d

Rearranging by dividing both sides by k_r[A]^a[B]^b:

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

This ratio of rate constants is itself a constant (at constant temperature) — and that ratio is what we call the equilibrium constant K_c. The subscript c denotes that concentrations (in mol L⁻¹) are used.

The formal expression:

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

Critical writing rules for HSC:

• Square brackets [ ] always denote equilibrium concentrations in mol L⁻¹.
• Products always go in the numerator; reactants in the denominator.
• Each concentration is raised to the power of its stoichiometric coefficient in the balanced equation.
• Pure solids and pure liquids are omitted — their concentrations are defined as 1 (constant) and are incorporated into the K_c value itself.
• K_c is dimensionless in rigorous thermodynamics, but at HSC level you may see it expressed with units or without — follow your teacher's convention and be consistent.