R1.4 Entropy and spontaneityIB Chemistry HL: Revision notes

Entropy, S, is a measure of the dispersal or distribution of matter and/or energy in a system. The more ways the particles and their energy can be arranged, the higher the entropy. Standard entropies, S⦵, are always positive and are given in the data booklet in J K⁻¹ mol⁻¹.

Under the same conditions, S(gas) > S(liquid) > S(solid). Entropy increases when a solid melts, a liquid boils, a solid dissolves, or a reaction produces more moles of gas. It decreases when the number of moles of gas falls (2SO₂ + O₂ → 2SO₃) or when a precipitate forms from ions in solution.

ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants), multiplying each value by its coefficient. Example: N₂ + 3H₂ → 2NH₃: ΔS⦵ = 2(193) − [192 + 3(131)] = −199 J K⁻¹ mol⁻¹. Unlike ΔfH⦵, elements do not have S⦵ = 0.

ΔG⦵ = ΔH⦵ − TΔS⦵, with T in kelvin. Units: ΔH and ΔG in kJ mol⁻¹, ΔS in J K⁻¹ mol⁻¹ — divide ΔS by 1000 before substituting. At constant pressure a change is spontaneous when ΔG is negative.

• ΔH −, ΔS +: spontaneous at all T
• ΔH +, ΔS −: never spontaneous
• ΔH −, ΔS −: spontaneous at low T
• ΔH +, ΔS +: spontaneous at high T

The switch-over happens when ΔG⦵ = 0, so T = ΔH⦵ / ΔS⦵ (ΔS in kJ K⁻¹ mol⁻¹). For CaCO₃ → CaO + CO₂: T = 178 / 0.161 = 1.11 × 10³ K. This assumes ΔH⦵ and ΔS⦵ do not vary with temperature, so the answer is approximate.

For a mixture that is not under standard conditions, ΔG = ΔG⦵ + RT ln Q, where Q is the reaction quotient. As a reaction approaches equilibrium, ΔG becomes less negative and reaches zero at equilibrium, where Q = K. Setting ΔG = 0 gives ΔG⦵ = −RT ln K: a negative ΔG⦵ means K > 1 (products favoured); a positive ΔG⦵ means K < 1. Remember R = 8.31 J K⁻¹ mol⁻¹, so convert ΔG⦵ to J mol⁻¹.