Question

The Born-Haber cycle for $KCl$ is evaluated with the following data :
$\Delta_{f} H ^{\ominus}$ for $KCl =-436.7 \,kJ \,mol ^{-1}$
$\Delta_{\text {sub }} H ^{\ominus}$ for $K =89.2 \,kJ\, mol ^{-1}$
$\Delta_{\text {ionization }} H ^{\ominus}$ for $K =419.0 \,kJ\, mol ^{-1} $;
$ \Delta_{\text {electron gain }} H ^{\ominus}$ for $Cl _{( g )}$
$=-348.6 \,kJ \,mol ^{-1} ; \Delta_{\text {bond}} H ^{\ominus}$ for $Cl _{2}=243.0\, kJ\, mol ^{-1}$
The magnitude of lattice enthalpy of $KCl$ in $kJ\, mol ^{-1}$ is _______(Nearest integer)

Answer 1

$\Delta_{ f } H _{ KCl }^{\ominus}=\Delta_{\text {sub }} H _{( K )}^{\ominus}+\Delta_{\text {ionization }} H _{( K )}^{\ominus}+\frac{1}{2} \Delta_{\text {bond }} H _{\left( Cl _{2}\right)}^{\ominus}+\Delta_{\text {electron gain }} H _{( Cl )}^{\ominus}+\Delta_{\text {lattice }} H _{( KCl )}^{\ominus} $
$\Rightarrow -436.7=89.2+419.0+\frac{1}{2}(243.0)+\{-348.6\} +\Delta_{\text {lattice }} H _{( KCl )}^{\ominus} $
$\Rightarrow \Delta_{\text {lattice }} H _{( KCl )}^{\ominus}=-717.8\, kJ\, mol ^{-1}$
The magnitude of lattice enthalpy of $KCl$ in $kJ\, mol ^{-1}$ is $718$ (Nearest integer).