6.5.3 Energy Cycle Involving Enthalpy of Solution, Lattice Energy and Enthalpy of Hydration

This topic explains the energy cycle that relates enthalpy of solution, lattice energy, and enthalpy of hydration. It shows how these quantities are connected through Hess's Law.

Definition

Energy Cycle: A diagrammatic representation of the energy changes involved in a process, based on Hess's Law.

Enthalpy of Solution (ΔH_solution): The net heat change when one mole of a substance dissolves in a solvent.

Lattice Energy (ΔH_lattice): The energy released when one mole of an ionic solid is formed from its gaseous ions.

Enthalpy of Hydration (ΔH_hydration): The energy released when one mole of gaseous ions is hydrated (surrounded by water molecules).

Main Idea

• Breaking the lattice (reverse of lattice energy) — endothermic.
• Hydrating the ions — exothermic.

The net enthalpy change is the sum of these two steps.

Core Concept

According to Hess's Law:

Δ H_Solution = Δ H_{Reverse lattice} + Δ H_Hydration

• ΔH_Reverse lattice has the same magnitude as ΔH_lattice but opposite sign.
• ΔH_Hydration is determined by adding the ΔH_Hydration of both cations and anions.
• The energy cycle can be represented as:

MX_(s) Δ H_Solution→ M⁺_(aq) + X^-_(aq)

MX_(s) Δ H_{Reverse lattice}→ M⁺_(g) + X^-_(g) Δ H_Hydration→ M⁺_(aq) + X^-_(aq)

Detailed Explanation

The Energy Cycle

- The energy cycle involves three main steps:

• The solid ionic compound (MX) is converted into gaseous ions.
• This is the reverse of lattice energy.
• It is endothermic (energy is absorbed).
• ΔHReverse lattice = −ΔHlattice

• The gaseous ions are surrounded by water molecules.
• This is the enthalpy of hydration.
• It is exothermic (energy is released).
• ΔHHydration = ΔHhyd(cation) + ΔH_hyd(anion)

• The net enthalpy change is the sum of Steps 1 and 2.
• ΔHSolution = ΔHReverse lattice + ΔH_Hydration

Intermediate Level

Energy Cycle for Dissolving

Formula

Δ H_Solution = Δ H_{Reverse lattice} + Δ H_Hydration

Δ H_{Reverse lattice} = -Δ H_lattice

Δ H_Solution = -Δ H_lattice + Δ H_Hydration

Example: NaCl

• ΔH_lattice = −786 kJ/mol
• ΔH_Hydration = −783 kJ/mol

Solution: Δ H_Solution = +786 + (-783) = +3 kJ/mol

Final Answer: +3 kJ/mol (endothermic)

Important Points

• 1. Energy cycle relates ΔHsolution, ΔHlattice, and ΔH_hydration.
• 2. ΔHSolution = ΔHReverse lattice + ΔH_Hydration.
• 3. ΔHReverse lattice = −ΔHlattice.
• 4. ΔH_Hydration = sum of hydration enthalpies of cation and anion.
• 5. ΔHSolution = ΔHHydration − ΔH_lattice.
• 6. Example: NaCl, ΔH_Solution = +3 kJ/mol (endothermic).

Remember

• - Energy cycle: ΔHSolution = ΔHReverse lattice + ΔH_Hydration
• - ΔH_Reverse lattice: −ΔH_lattice
• - ΔH_Hydration: Sum of cation and anion hydration
• - ΔH_Solution = ΔH_Hydration − ΔH_lattice
• - Example: NaCl, ΔH_Solution = +3 kJ/mol

Common Mistakes

• 1. Forgetting the sign of ΔH_Reverse lattice: It is the opposite of ΔH_lattice.
• 2. Forgetting to sum the hydration enthalpies: Both cation and anion contribute.
• 3. Mixing up the formula: ΔHSolution = ΔHHydration − ΔH_lattice.
• 4. Confusing endothermic and exothermic dissolution: Endothermic = absorbs heat; Exothermic = releases heat.

Quick Revision

• Energy cycle relates ΔHsolution, ΔHlattice, and ΔH_hydration.
• ΔHSolution = ΔHReverse lattice + ΔH_Hydration.
• ΔHReverse lattice = −ΔHlattice.
• ΔH_Hydration = sum of hydration enthalpies of cation and anion.
• ΔHSolution = ΔHHydration − ΔH_lattice.
• Example: NaCl, ΔH_Solution = +3 kJ/mol (endothermic).

60-Second Revision

• Energy cycle: ΔHSolution = ΔHReverse lattice + ΔH_Hydration
• ΔH_Reverse lattice: −ΔH_lattice
• ΔH_Hydration: Sum of cation and anion hydration
• ΔH_Solution = ΔH_Hydration − ΔH_lattice
• Example: NaCl, ΔH_Solution = +3 kJ/mol

QUALITY VALIDATION

• Topic: 6.5.3 Energy Cycle Involving Enthalpy of Solution, Lattice Energy, and Enthalpy of Hydration
• Chapter: 6 (Energetics)

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