Question

An intimate mixture of ferric oxide, $F{e}_2{O}_3$, and aluminium, Al, is used in solid fuel in rockets. Calculate the fuel value (in kcal) per cc of the mixture. Heats of formation and densities are as follows :

Data given : $\Delta H_f\left(A{l}_2{O}_3\right)=399$ kcal/mol, $\Delta H_f\left(F{e}_2{O}_3\right)=199$ kcal/mol, density of $F{e}_2{O}_3=\frac{16}{3}$ gm/cc, density of Al = $2.7$ gm/cc.

Answer 1

$2Al+F{e}_2{O}_3\to 2Fe+A{l}_2{O}_3$

$\Delta H=-399-(-199)=-200kcal$

Volume of fusion mixture $=\frac{54}{2.7}+\frac{160}{\frac{16}{3}}=50ml$

$\because$ $50$ ml mixture produces $200$ kcal

$\therefore$ $1$ ml mixture produces $=\frac{200}{50}=4$ kcal.