The enthalpy of dissolution of ${\mathrm{BaCl}}_2\left(\mathrm{s}\right)\text{ and }{\mathrm{BaCl}}_2\cdot 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)$ are -20.6 and 8.8 kl mol^-1 respectively. The enthalpy of hydration for BaCl₂, that is,

${\mathrm{BaCl}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\to {\mathrm{BaCl}}_2\cdot 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)\text{ is }$

 

It is given that

${\mathrm{BaCl}}_2\left(\mathrm{s}\right)+\mathrm{aq}\to {\mathrm{BaCl}}_2\left(\mathrm{aq}\right);\mathrm{\Delta }H=-20.6\mathrm{kJ}{\mathrm{mol}}^{-1}$                    . . . . (1)

Also,

${\mathrm{BaCl}}_2\cdot 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)+\mathrm{aq}\to {\mathrm{BaCl}}_2\left(\mathrm{aq}\right);\mathrm{\Delta }H=+8.8\mathrm{KJ}{\mathrm{mol}}^{-1}$         . . . . (2)

Equation ( 1) can be split in two steps:

$\begin{array}{l}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{BaCl}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{BaCl}}_2\cdot 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right);\mathrm{\Delta }{H}_1=?\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{BaCl}}_2\cdot 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)+\mathrm{aq}\to {\mathrm{BaCl}}_2\left(\mathrm{aq}\right);\mathrm{\Delta }{H}_2=-8.8\mathrm{KJ}\\ \text{ Or, }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\Delta }{H}_1+\mathrm{\Delta }{H}_2=-20.6\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\Delta }{H}_1+8.8=-20.6\\ \text{ Or, }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\Delta }{H}_1=-29.4\end{array}$