Question
The standard heat of formation, in $kcal/mol$ of ${Ba}^{2 +}$ is :
[Given: standard heat of formation of ${SO}_{4}^{2 -}$ ion (aq) $= - 216kcal/mol$, standard heat of crystallisation of ${BaSO}_{4}(\text{ }s) = - 4.5kcal/mol$, standard heat of formation of
${BaSO}_{4}(\text{ }s) = - 349kcal/mol$ ]
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Solution
Sol. [Key Concept: Standard heat of formation of Ba²⁺ (Hess's law / Born–Haber cycle)]
$\ S + 2O_{2} + 2e^{-} \longrightarrow {SO}_{4}^{2 -}$
$$\begin{array}{r} {Ba}^{2 +}(g) + {SO}_{4}^{2 -}(g) \longrightarrow {BaSO}_{4}(\text{ }s)\#(2) \end{array}$$
$$\begin{array}{r} Ba + S + 2O_{2} \longrightarrow {BaSO}_{4}(\text{ }s)\#(3) \end{array}$$
$$\begin{array}{r} \Delta H_{f} = - 216kcal/mol\#(1) \end{array}$$
From equation (1), (2) and (3) we get equation (4). Applying equation (3) - (1) - (2)
$$\begin{matrix} & \text{~}\text{So,}\text{~} - 349 - ( - 4.5) - ( - 216) \\ & \text{~}\text{So}\text{~} - 349 + 4.5 + 216 \\ & \ = - 349 + 220.5 \\ & \ = - 128.5kcal/mol \end{matrix}$$
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