Question

In the Born-Haber cycle of the given reaction, $\text{N}{{\text{a}}_{(s)}}+\frac{1}{2}C{{l}_{2(g)}}\to NaC{{l}_{(s)}}$, the number of endothermic and exothermic stages respectively are:
(A) 2,3
(B) 3,1
(C) 3,2
(D) 2,2

Answer 1

Hint: Formation of sodium chloride involves various stages such as sublimation of sodium metal, ionization of sodium atoms, dissociation of chlorine, formation of chlorine ion, formation of sodium chloride. Sublimation, ionization, dissociation is endothermic and formation of chloride ion and formation of sodium chloride are exothermic.

Complete solution step by step:
- the lattice enthalpy of an ionic compound is the enthalpy change that occurs when one mole of an ionic compound dissociates into its ions in gaseous state.
-Lattice enthalpy cannot be calculated directly so indirect methods can be used by constructing Born Haber cycle.
-First stage is sublimation of sodium atoms; sublimation is a process where solid state is directly converted into gaseous state.
\[N{{a}_{(s)}}\to N{{a}_{(g)}}\text{ }{{\Delta }_{sub}}H=108.4kJ\text{ mo}{{\text{l}}^{-1}}\]
Sublimation of sodium atoms is an endothermic stage.
-Second stage is ionization of sodium atoms, In ionization gaseous atoms of sodium area ionized to sodium ion.
$N{{a}_{(g)}}\to N{{a}^{+}}_{(g)}+{{e}^{-1}}_{(g)}\text{ }{{\Delta }_{i}}H=496kJ\text{ mo}{{\text{l}}^{-1}}$
Ionization of sodium atoms is an endothermic reaction.
-dissociation of chlorine, enthalpy of this reaction is half the bond dissociation enthalpy.
\[\frac{1}{2}C{{l}_{2(g)}}\to C{{l}_{(g)\text{ }}}\frac{1}{2}{{\Delta }_{bond}}H=121kJ\text{ mo}{{\text{l}}^{-1}}\]
Dissociation of chlorine is an endothermic reaction
-Chlorine atoms are converted to chlorine ions by gaining electrons.
$C{{l}_{(g)}}+{{e}^{-1}}_{(g)}\to C{{l}^{-}}_{(g)}\text{ }{{\Delta }_{eg}}H-=348.6kJ\text{ mo}{{\text{l}}^{-1}}$
This reaction is exothermic.
-Formation of sodium chloride, when ions combine to form crystalline solid, energy is released.
\[N{{a}^{+}}_{(g)}+C{{l}^{-}}_{(g)}\to N{{a}^{+}}C{{l}^{-}}_{(s)}\]
Formation of sodium chloride from its ions is an exothermic reaction.
So as Sublimation, ionization, dissociation is endothermic and formation of chloride ion and formation of sodium chloride are exothermic.

In the Born-Haber cycle of the given reaction, $\text{N}{{\text{a}}_{(s)}}+\frac{1}{2}C{{l}_{2(g)}}\to NaC{{l}_{(s)}}$, the number of endothermic and exothermic stages respectively are (C) 3,2.

Note: Born Haber illustrates a sequence of steps in formation of sodium chloride.it is impossible to determine lattice energy directly by experiment so it is indirectly obtained by an enthalpy diagram called Born Haber cycle. When a crystalline ionic compound dissociates in its ions, lattice enthalpy is positive, that is energy is absorbed.