An intimate mixture of ferric oxide and aluminium is used as solid fuel in rockets. Calculate the fuel value per `cm^(3)` of the mixture. Heats of formation and densities are as follows:
`H_(f(Al_(2)O_(3)))=-399kcal" "mol^(-1),H_(f(Fe_(2)O_(3)))=-199kcal" "mol^(-1)` ltbr. Density of `Fe_(2)O_(3)=5.2g//cm^(3)," Density of "Al=2.7g//cm^(3)`

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`.