A Born-Haber cycle is a thermochemical cycle that represents the series of steps involved in the formation of an ionic compound. In the case of calcium oxide (CaO), the formation is between calcium (Ca) and oxygen (O₂). The Born-Haber cycle involves the following steps:
1. Atomization of calcium: Converting solid calcium into one mole of gaseous calcium atoms.
Ca (s) → Ca (g) ΔH₁ = Enthalpy of atomization of Ca
2. Ionization of calcium: Convert one mole of gaseous calcium atoms into gaseous calcium ions.
Ca (g) → Ca⁺² (g) + 2e⁻ ΔH₂ = Ionization energy of Ca
3. Atomization of O₂: Convert oxygen molecule into one mole of gaseous oxygen atoms.
1/2 O₂ (g) → O (g) ΔH₃ = 1/2 * Enthalpy of atomization of O₂
4. Ionization of O: Remove one mole of electrons from gaseous oxygen atoms, converting them to one mole of negatively charged gaseous oxygen ions.
O (g) + 2e⁻ → O²⁻ (g) ΔH₄ = - Electron affinity of O
5. Lattice formation: Combination of gaseous calcium ions and gaseous oxygen ions to form one mole of solid calcium oxide.
Ca⁺² (g) + O²⁻ (g) → CaO (s) ΔH₅ = - Lattice energy (U)
Now, we can write down the overall reaction for the formation of calcium oxide. The standard enthalpy change of formation ΔHf° for this reaction is the sum of the enthalpies for the individual steps of the cycle.
Ca (s) + 1/2 O₂ (g) → CaO (s) ΔHf° = ΔH₁ + ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅
The Born-Haber cycle for the formation of calcium oxide can be represented as:
Ca (s) --(ΔH₁)--> Ca (g) --(ΔH₂)--> Ca⁺² (g) + 2e⁻
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1/2 O₂ (g) --(ΔH₃)--> O (g) --(ΔH₄)--> O²⁻ (g)
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Ca⁺² (g) + O²⁻ (g) --(ΔH₅)--> CaO (s)
By connecting the initial and final states of the reaction with the enthalpy changes associated with each step, the Born-Haber cycle allows for the calculation of the enthalpy change of formation for calcium oxide or any other ionic compound.
Construct a Born Haber cycle for the formation of calcium oxide showing clearly using equations, the steps of the enthalpy stages involved
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