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The lattice enthalpy of an ionic compound is the enthalpy when one mole of an ionic compound present in its gaseous state, dissociates into its ions. It is impossible to determine it directly by experiment. Suggest and explain an indirect method to measure lattice enthalpy of $\mathrm{NaCl}(\mathrm{s})$.
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- $\mathrm{Na}(\mathrm{s})+\frac{1}{2} \mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{Na}^{+}(\mathrm{g})+\mathrm{Cl}^{-}(\mathrm{g})$;
$\Delta_{\text {lattice }} \mathrm{H}^{\circ}$
- Born - Haber Cycle
- Steps to measure lattice enthalpy from Born - Haber cycle
- Sublimation of sodium metal
(1) $\mathrm{Na}(\mathrm{s}) \rightarrow \mathrm{Na}(\mathrm{g}) ; \Delta_{\mathrm{sub}} \mathrm{H}$
(2)Ionisation of sodium atoms
$\mathrm{Na}(\mathrm{g}) \rightarrow \mathrm{Na}^{+}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) ; \Delta_{\mathrm{r}} \mathrm{H}$
i.e., Ionisation enthalpy
(3) Dissociation of chlorine molecule
$\frac{1}{2} \mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{Cl}(\mathrm{g}) ; \frac{1}{2} \Delta_{\text {bond }} \mathrm{H}$
i.e., One-half of bond dissociation enthalpy
(4) $\mathrm{Cl}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{Cl}^{-}(\mathrm{g}) ; \Delta_{\mathrm{eg}} \mathrm{H}$
i.e., electron gain enthalpy
$\mathrm{Na}^{+}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$
$\Delta_{\text {lattice }} \mathrm{H}^{\circ}$
- Born - Haber Cycle
- Steps to measure lattice enthalpy from Born - Haber cycle
- Sublimation of sodium metal
(1) $\mathrm{Na}(\mathrm{s}) \rightarrow \mathrm{Na}(\mathrm{g}) ; \Delta_{\mathrm{sub}} \mathrm{H}$
(2)Ionisation of sodium atoms
$\mathrm{Na}(\mathrm{g}) \rightarrow \mathrm{Na}^{+}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) ; \Delta_{\mathrm{r}} \mathrm{H}$
i.e., Ionisation enthalpy
(3) Dissociation of chlorine molecule
$\frac{1}{2} \mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{Cl}(\mathrm{g}) ; \frac{1}{2} \Delta_{\text {bond }} \mathrm{H}$
i.e., One-half of bond dissociation enthalpy
(4) $\mathrm{Cl}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{Cl}^{-}(\mathrm{g}) ; \Delta_{\mathrm{eg}} \mathrm{H}$
i.e., electron gain enthalpy
$\mathrm{Na}^{+}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$
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