Revise Entropy change, ΔS for Cambridge 9701 (23.3)

Entropy, symbolised by $S$, is a thermodynamic quantity that measures the degree of randomness or disorder in a system. A system with high entropy has its particles and energy spread out in many different ways (many microstates), whereas a system with low entropy is highly ordered and has few possible arrangements. The standard entropy of a substance, $S^\circ$, is its entropy content per mole under standard conditions (298 K and 100 kPa). Its units are joules per Kelvin per mole ($J K^{-1} mol^{-1}$).

The entropy change, $ΔS$, is the difference between the entropy of the final state and the initial state. We can often predict its sign without calculation. A process that increases disorder has a positive $ΔS$, while a process that increases order has a negative $ΔS$.

For any chemical reaction, the standard entropy change ($ΔS^\circ_{reaction}$) can be calculated quantitatively using the standard molar entropies ($S^\circ$) of the reactants and products, which are found in data booklets. Remember that unlike standard enthalpies of formation, the standard entropies of elements are not zero.

$\Delta S^\circ_{reaction} = \Sigma S^\circ(\text{products}) - \Sigma S^\circ(\text{reactants})$

Where Σ (sigma) means 'the sum of'. You must multiply the $S^\circ$ value for each substance by its stoichiometric coefficient in the balanced equation.

Entropy change is a key component in determining whether a reaction is spontaneous (or 'feasible'). The Second Law of Thermodynamics states that for a process to be spontaneous, the total entropy of the universe (system + surroundings) must increase. This is combined with enthalpy into a single, powerful equation for Gibbs Free Energy, $ΔG = ΔH - TΔS$, which we will explore in the next topic. A large, positive $ΔS$ can make a reaction feasible even if it is endothermic ($ΔH > 0$), especially at high temperatures where the '$TΔS$' term becomes dominant.