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(AI_(2)O_(3)))^(Theta)=-399kcal mol^(-1),H_(f(Fe_(2)O_(3)))^(Theta)=-199kcal mol^(-1)`
Density of `Fe_(2)O_(3)=4.0 g cm^(-3)`, Density of `AI = 2.0 g cm^(-3)`

Explanation

The required equation is:
`2AI +Fe_(2)O_(3)rarr AI_(2)O_(3) +2Fe, DeltaH = ?`
`DeltaH^(Theta)("product") -Delta_(f)H^(Theta)("reactants")`
`=[Delta_(f)H_((AI_(2)O_(3)))^(Theta)+2Delta_(f)H_((Fe))^(Theta)]`
`[2Delta_(f)H_((AI))^(Theta)+Delta_(f)H_((Fe_(2)O_(3)))^(Theta)]`
`=(-399 +2 xx 0) -[2xx0+(-99)]`
`=- 399 +199 =- 200 kcal`
Atomic mass of aluminium `= 27`
Molecular mass of `Fe_(2)O_(3) = 160`
Volume of reactents `= (160)/(4.0) +(2xx27)/(2.0) = 67.0 cm^(3)`
Fuel value per `cm^(3) = (200)/(67) = 2.98 kcal`