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Question

Use the following data to calculate the lattice energy of caesium oxide.
Enthalpy of formation of caesium oxide =233 kJ/mol
Enthalpy of sublimation of Cs=+78 kJ/mol
First ionization energy of Cs=+375 kJ/mol
Enthalpy of dissociation of O2 (g)=494 kJ/mol
First electron affinity of O=141 kJ/mol
Second electron affinity of O=+845 kJ/mol

A
2090 kJ/mol
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B
2090 kJ/mol
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C
2290 kJ/mol
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D
2390 kJ/mol
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Solution

The correct option is A 2090 kJ/mol
Given,
2Cs(s)2Cs(g) ; ΔSubHo=(+78×2) kJ/mol
2Cs (g)2Cs+ ; IE=(2×+375) kJ/mol
12O2 (g)O (g) ; ΔOOHo=(494×12) kJ/mol
O +e1O1; EA1=141 kJ/mol
O1+e1O2;EA2=+845 kJ/mol
2Cs+(g)+O2 (g)Cs2O (s); ΔH0=233 kJ/mol
Since it is impossible to determine lattice enthalpies directly by experiment, we use an indirect method where we construct an enthalpy diagram called a Born-Haber Cycle .
Let us now calculate the lattice enthalpy of Cs2O(s) by following steps given below :
ΔfH0=ΔSubHo+IE+ΔOOHo+EA1+EA2+ΔlatticeHo
233=2(78)+2(375)+4942141+845+ΔlatticeHo
ΔlatticeHo=2090 kJ/mol
the lattice energy of caesium oxide is 2090 kJ/mol

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