Use the born-haber cycle to calculate the lattice energy of kcl. (δhsub for potassium is 89.0 kj/mol, ie1 for potassium is 419 kj/mol, ea1 for chlorine is −349 kj/mol, the bond energy of cl2 is 243 kj/mol, δh∘f for kcl is −436.5 kj/mol .)
Answers
Given data:
Sublimation of K
K(s) ↔ K(g) ΔH(sub) = 89.0 kj/mol
Ionization energy for K
K(s) → K⁺ + e⁻ IE(K) = 419 Kj/mol
Electron affinity for Cl
Cl(g) + e⁻ → Cl⁻ EA(Cl) = -349 kj/mol
Bond energy for Cl₂
1/2Cl₂ (g) → Cl Bond energy = 243/2 = 121.5 kj/mol
Formation of KCl
K(s) + 1/2Cl₂(g) → KCl(s) ΔHf = -436.5 kJ/mol
To determine:
Lattice energy of KCl
K⁺(g) + Cl⁻(g) → KCl (s) U(KCl) = ?
Explanation:
The enthalpy of formation of KCl can be expressed in terms of the sum of all the above processes, i.e.
ΔHf(KCl) = U(KCl) + ΔH(sub) + IE(K) + 1/2 BE(Cl₂) + EA(Cl)
therefore:
U(KCl) = ΔHf(KCl) - [ΔH(sub) + IE(K) + 1/2 BE(Cl₂) + EA(Cl)]
= -436.5 - [89 + 419 + 243/2 -349] = -717 kJ/mol
Ans: the lattice energy of KCl = -717 kj/mol
Final answer:
The lattice energy of KCl is calculated using the Born-Haber cycle by considering the energies of several steps including the sublimation of potassium, ionization of potassium, dissociation of Cl bond, electron affinity of Cl, and formation of KCl. The given values are plugged into a formula resulting in a lattice energy of -718 kJ/mol.
Explanation:
To calculate the lattice energy of KCl using the Born-Haber cycle, we need to follow several thermochemical steps. The steps include, first sublimation of potassium, the ionization of potassium, bond dissociation enthalpy to produce Cl, the electron affinity of Cl, and formation of KCl (s). Combining energy changes associated with all these steps would give us energy change for the formation of KCl from individual K and Cl2, it is called as enthalpy of formation (ΔH°f) for KCl.
Using the given values for each step, we use the formula: ΔH°f = ΔHsub + IE1 + 1/2* DCl2 - EA1 + lattice energy.
Substituting the given values, -436.5 = 89 + 419 + 1/2*243 -349 + lattice energy. Solving gives the lattice energy as -718 kJ/mol.
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