22- Enthalpy and Entropy

The enthalpy change when 1 mole of a solid ionic compound is formed from its gaseous ions under standard conditions. Always exothermic (ΔH < 0).

Because it’s impossible to directly combine gaseous ions in the lab to form a solid lattice. Instead, we use Hess’s Law with measurable enthalpy changes.

Atomisation of Na(s) → Na(g) Atomisation of ½Cl₂(g) → Cl(g) Ionisation of Na(g) → Na⁺(g) + e⁻ Electron affinity: Cl(g) + e⁻ → Cl⁻(g) Lattice formation: Na⁺(g) + Cl⁻(g) → NaCl(s)

First EA: O(g) + e⁻ → O⁻(g), exothermic (–141 kJ/mol) Second EA: O⁻(g) + e⁻ → O²⁻(g), endothermic (+790 kJ/mol) → Adding e⁻ to a negative ion requires energy (repulsion).

The hydration enthalpy is the enthalpy change when 1 mole of gaseous ions dissolve in sufficient water to give an infinitely dilute solution. Hydration enthalpies are always negative. The enthalpy of solution is then equal to the enthalpy of hydration minus the lattice energy Ionic solid → gaseous ions → aqueous ions

Higher charge → stronger attraction → more exothermic LE Smaller ions → closer together → more exothermic LE

A measure of disorder or energy dispersal in a system. Units: J K⁻¹ mol⁻¹ Gases > liquids > solids in entropy.

a) Negative (gas → liquid = more order) b) Positive (solid → solid + gas = more disorder)

ΔS° = ΣS°(products) – ΣS°(reactants) Use data book values in J K⁻¹ mol⁻¹

ΔG = ΔH – TΔS ΔG < 0 → reaction is feasible (spontaneous) T must be in Kelvin Ensure units match: ΔH in kJ/mol, ΔS in kJ/K/mol

Always feasible: ΔH < 0 and ΔS > 0 Never feasible: ΔH > 0 and ΔS < 0 Temp-dependent: ΔH < 0, ΔS < 0 → feasible at low T ΔH > 0, ΔS > 0 → feasible at high T

High activation energy → slow rate (e.g., H₂O₂ decomposition). ΔG predicts thermodynamic feasibility, not speed.

ΔG = 16 – (298 × 0.077) = 16 – 22.9 = –6.9 kJ/mol → Yes, feasible (endothermic but entropy-driven).

Set ΔG = 0 → T = ΔH / ΔS (Ensure ΔH and ΔS same sign, and units consistent)

Large, irregularly shaped ions (e.g., [EMIM]⁺) can’t pack efficiently into a lattice → low melting point.

Feasible tends to be used to describe reactions which are energetically favourable, so reactions that should go Spontaneous tends to be used to describe reactions that go of their own accord

Definition: The enthalpy change when 1 mole of a compound is formed from its elements in their standard states under standard conditions (298 K, 100 kPa). Exo/Endo: Usually exothermic (e.g., ΔₐH°(NaCl) = –411 kJ mol⁻¹), but can be endothermic for unstable compounds.

Symbol: ΔₗₑH° or ΔₗₐₜH° Definition: The enthalpy change when 1 mole of a solid ionic compound is formed from its gaseous ions under standard conditions. Exo/Endo: Always exothermic (e.g., ΔₗₑH°(NaCl) = –788 kJ mol⁻¹).

Symbol: ΔₐₜH° Definition: The enthalpy change when 1 mole of gaseous atoms is formed from an element in its standard state under standard conditions. Exo/Endo: Always endothermic (bonds broken). E.g., Na(s) → Na(g), ΔₐₜH° = +108 kJ mol⁻¹ E.g., ½Cl₂(g) → Cl(g), ΔₐₜH° = +121 kJ mol⁻¹

Symbol: IE₁ or ΔᵢₑH° Definition: The enthalpy change to remove 1 mole of electrons from 1 mole of gaseous atoms to form 1 mole of gaseous 1+ ions. Exo/Endo: Always endothermic (e.g., Na(g) → Na⁺(g) + e⁻, Δ = +496 kJ mol⁻¹)

Symbol: IE₂, IE₃, etc. Definition: Energy to remove further electrons from gaseous ions (e.g., Mg⁺(g) → Mg²⁺(g) + e⁻). Exo/Endo: Always endothermic (and larger than previous IE).

Symbol: EA₁ or ΔₑₐH° Definition: The enthalpy change when 1 mole of electrons is added to 1 mole of gaseous atoms to form 1 mole of gaseous 1– ions. Exo/Endo: Usually exothermic (e.g., Cl(g) + e⁻ → Cl⁻(g), Δ = –346 kJ mol⁻¹)

Symbol: EA₂, etc. Definition: Adding an electron to a negative ion (e.g., O⁻(g) + e⁻ → O²⁻(g)). Exo/Endo: Always endothermic due to repulsion (e.g., EA₂(O) = +790 kJ mol⁻¹)

Symbol: ΔₛₒₗH° Definition: The enthalpy change when 1 mole of solute dissolves in excess water to form an infinitely dilute solution. Exo/Endo: Can be exothermic (e.g., NaOH) or endothermic (e.g., KCl, Δ = +16 kJ mol⁻¹)