An intimate mixture of ferric oxide, `Fe_(2)O_(3)`, and aluminium is used in solid-fuel rocket. Calculate the fuel value per gram and the fuel value per c c of the mixture. Heats of formation densities are as follows:
`._(f)H(AI_(2)O_(3)) =- 399 kcal mol^(-1)`
`_.(f)H(Fe_(2)O_(3)) = - 199 kcal mol^(-1)` ltbegt Density of `Fe_(2)O_(3) = 4.0 g c c^(-1)`
Density of `AI = 2.0 g c c^(-1)`

Explanation

`Fe_(2)O_(3)(s) + 2Al(s) to Al_(2)O_(3)(s) + 2Fe (s)`
`Delta H_(r)^(@) = Delta H_(f)^(@) ("product") - Delta H_(f)^(@) ("reactants") = -399 - (-199) = - 200 k cal`
Mass of reactants = `56 xx 2 + 16 xx 3 + 27 xx 2 = 214g`
`implies "Fuel value/gram" = (200)/(214) = 0.93 k cal//g`
Volume of reactants = `(160)/(5.2) cc + 54/2.7 cc = 50.77 cc implies "Fuel value/c c" = (200)/(50.77) = 3.94 cal//cc`.