Solid propellant rocket motors frequently utilize an aluminothermic thermite mixture consisting of a

Question

Solid propellant rocket motors frequently utilize an aluminothermic thermite mixture consisting of an intimate blend of ferric oxide ($	ext{Fe}_2	ext{O}_3$) and aluminum ($	ext{Al}$) powder in stoichiometric proportions according to the reaction: $	ext{Fe}_2	ext{O}_3(s) + 2	ext{Al}(s) ightarrow 	ext{Al}_2	ext{O}_3(s) + 2	ext{Fe}(s)$. The thermochemical and physical properties of the propellant components are given below: Standard heat of formation of aluminum oxide, $\Delta H^\circ_f[	ext{Al}_2	ext{O}_3(s)] = -399.0	ext{ kcal mol}^{-1}$; Standard heat of formation of ferric oxide, $\Delta H^\circ_f[	ext{Fe}_2	ext{O}_3(s)] = -199.0	ext{ kcal mol}^{-1}$; Density of solid ferric oxide, $ho(	ext{Fe}_2	ext{O}_3) = 5.20	ext{ g cm}^{-3}$; Density of solid aluminum, $ho(	ext{Al}) = 2.70	ext{ g cm}^{-3}$. (Take atomic masses: $	ext{Fe} = 56	ext{ u}$, $	ext{Al} = 27	ext{ u}$, $	ext{O} = 16	ext{ u}$).

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See detailed solution for explanation.