Construct a Born Haber cycle for the formation of calcium oxide showing clearly using equations, the steps of the enthalpy stages involved

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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v
1/2 O₂ (g) --(ΔH₃)--> O (g) --(ΔH₄)--> O²⁻ (g)
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v
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.

Sure! The Born-Haber cycle for the formation of calcium oxide (CaO) involves several steps. Here's a step-by-step breakdown of the stages involved, along with the corresponding equations:

Step 1: Formation of calcium gas
Ca(s) → Ca(g) ΔH1 = sublimation enthalpy of calcium (ΔH1)

Step 2: Ionization of calcium gas
Ca(g) → Ca+(g) + e- ΔH2 = first ionization energy of calcium (ΔH2)

Step 3: Atomization of oxygen gas
1/2O2(g) → O(g) ΔH3 = 1/2 the bond dissociation energy of oxygen (ΔH3)

Step 4: Electron affinity of oxygen atom
O(g) + e- → O-(g) ΔH4 = electron affinity of oxygen (ΔH4)

Step 5: Formation of calcium oxide
Ca+(g) + O-(g) → CaO(s) ΔH5 = lattice energy of calcium oxide (ΔH5)

Now, we can calculate the overall enthalpy change for the formation of calcium oxide by summing up the enthalpies of these individual steps:

ΔHformation = ΔH1 + ΔH2 + ΔH3 + ΔH4 + ΔH5

The overall enthalpy change for the formation of calcium oxide (CaO) can be calculated by substituting the corresponding values for each step.

To construct a Born Haber cycle for the formation of calcium oxide (CaO), we need to consider the various enthalpy changes involved in the formation of the compound. The Born Haber cycle is essentially an energy cycle that depicts the steps in which an ionic compound is formed from its constituent elements.

Here are the steps involved and the corresponding equations:

1. Sublimation of calcium (Ca):
Ca(s) → Ca(g)
ΔH1: sublimation enthalpy of calcium

2. Dissociation of oxygen (O2):
O2(g) → 2O(g)
ΔH2: dissociation enthalpy of oxygen

3. Ionization of calcium (Ca):
Ca(g) → Ca+(g) + e-
ΔH3: first ionization energy of calcium

4. Electron affinity of oxygen (O):
O(g) + e- → O-(g)
ΔH4: electron affinity of oxygen

5. Formation of calcium oxide (CaO):
Ca+(g) + O-(g) → CaO(s)
ΔH5: lattice enthalpy of calcium oxide

The overall enthalpy change (ΔHf) for the formation of calcium oxide can be calculated as the sum of these enthalpy changes:

ΔHf (CaO) = ΔH1 + ΔH2 + ΔH3 + ΔH4 + ΔH5

It is important to note that the sublimation enthalpy (ΔH1) and dissociation enthalpy (ΔH2) can be experimental values obtained from reference sources. The ionization energy (ΔH3) and electron affinity (ΔH4) can also be obtained from reference tables. The lattice enthalpy (ΔH5) can be calculated using Born-Haber cycle principles and various energy terms, such as the electrostatic potential energy and the Madelung constant for calcium oxide.

By constructing and analyzing this Born Haber cycle, we can not only determine the enthalpy change for the formation of calcium oxide but also understand the individual steps and energy changes involved in the process.