Question

The standard enthalpies of formation of ${\mathrm{Al}}_2{\mathrm{O}}_3$ and $\mathrm{CaO}$ are $–1675\mathrm{kJ}{\mathrm{mol}}^{-1}\mathrm{and}–635\mathrm{kJ}{\mathrm{mol}}^{-1}$ respectively. For the reaction $3\mathrm{CaO}+2\mathrm{Al}\to 3\mathrm{Ca}+{\mathrm{Al}}_2{\mathrm{O}}_3$ the standard reaction enthalpy ${\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}^0=\mathrm{\_\_\_\_\_\_}\mathrm{kJ}$

Answer 1

Given:

The standard enthalpy of ${\mathrm{Al}}_2{\mathrm{O}}_3$: $–1675\mathrm{kJ}{\mathrm{mol}}^{-1}$

and The standard enthalpy of $\mathrm{CaO}$: $–635\mathrm{kJ}{\mathrm{mol}}^{-1}$

Given reaction: $3\mathrm{CaO}+2\mathrm{Al}\to 3\mathrm{Ca}+{\mathrm{Al}}_2{\mathrm{O}}_3$

The expression used for the calculation of the standard reaction enthalpy:

${\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}={\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left(\mathrm{Products}\right)–{\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left(\mathrm{Reactants}\right)$

Putting values in the above expression:

$\begin{array}{rcl}{\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}& =& {\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left(\mathrm{Products}\right)–{\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left(\mathrm{Reactants}\right)\end{array}$

$\begin{array}{rcl}{\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}& =& {\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)–3\times {\mathrm{\Delta }}_{\mathrm{r}}{{\mathrm{H}}^0}_{\mathrm{f}}\left(\mathrm{CaO}\right)\\ & =& -1675-3\times (-635)\\ & =& -1635+1905\\ & =& 230\mathrm{kJ}\end{array}$

Therefore, the standard enthalpies of formation of ${\mathrm{Al}}_2{\mathrm{O}}_3$ and $\mathrm{CaO}$ are $–1675\mathrm{kJ}{\mathrm{mol}}^{-1}\mathrm{and}–635\mathrm{kJ}{\mathrm{mol}}^{-1}$ respectively. For the reaction $3\mathrm{CaO}+2\mathrm{Al}\to 3\mathrm{Ca}+{\mathrm{Al}}_2{\mathrm{O}}_3$ the standard reaction enthalpy ${\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}^0=230\mathrm{kJ}$