Entropy and Spontaneity in Chemical Systems

(a) Entropy as a Measure of Freedom and Natural Changes

Entropy (S) measures the disorder or randomness of a system, related to the freedom of movement of particles.

  • Systems tend to evolve towards a state of maximum entropy (greatest disorder).

  • Second Law of Thermodynamics: In all natural processes, the total entropy of the universe increases.

  • Example: Ice melting into water increases entropy because liquid water has more disorder than solid ice.

(b) Entropy in Different States of Matter

Solids: Particles are closely packed with little movement → low entropy.

Liquids: Particles have more freedom to move than in solids → moderate entropy.

Gases: Particles are widely spaced and move freely → high entropy.

  • General trend: S(gas) > S(liquid) > S(solid)

  • Entropy increases when:

    • A solid changes to a liquid or gas.

    • A liquid changes to a gas.

    • The number of particles increases (e.g., decomposition reactions).

(c) Calculating Entropy Change

  • Entropy change (ΔS) is determined using absolute entropy values:

ΔS = Sfinal − Sinitial

  • If ΔS>0 , the system becomes more disordered.

  • If ΔS<0, the system becomes less disordered.

Example: The reaction N₂O₄(g) → 2NO₂(g) increases entropy because one molecule splits into two.

(d) Gibbs Free Energy Change

Determines whether a reaction is spontaneous or not.

Given by the equation: ΔG=ΔH−TΔS where:

ΔG = Gibbs free energy change (J mol−1)

ΔH = Enthalpy change (J mol−1)

T = Temperature (K)

ΔS = Entropy change (J K−1 mol−1)

  • Conditions for spontaneity:

    • If ΔG <0, the reaction is spontaneous.

    • If ΔG 0>, the reaction is non-spontaneous.

    • If ΔG = 0, the system is at equilibrium.

(e) Spontaneous Reactions and Entropy Effects

Exothermic reactions (ΔH<0) are often spontaneous as they release energy.

Endothermic reactions (ΔH>0) can still be spontaneous if ΔS is positive and large enough to make ΔG<0

Example: Dissolving salts like NaCl in water is endothermic but occurs spontaneously because the increase in entropy outweighs the enthalpy cost.