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

We aim at
`Fe_(2)O_(3) +2Al rarr 2 Fe+Al_(2)O_(3), DeltaH = ?`
`Delta_(r)H= [2 xx DeltaH _(f)(Fe) + DeltaH_(f)(Al_(2)O_(3))]-[DeltaH_(f)(Fe_(2)O_(3))+ 2 xx DeltaH_(f)(Al) ]`
`= ( 0 + 399) - ( 199 + 0 ) = 200 kcal`
This is the heat channe that takes place when 1 moleof `Fe_(2)O_(3)` and 2 moles of Al combine i.e., ` 2 xx 56 + 3 xx 16 ) + 2 xx 27 g = 214 g` of the mixture . Hence , heat change per gram
`= ( 200)/( 214) = 0.9346kcal`
Further, `160g Fe_(2)O_(3)= ( 160g)/( 5.2 g // c c ) = 30.77 c c`
and `54g Al= ( 54g)/( 2.7 g //c c)= 20 c c`
Total volume of the mixture `= 50.77 c c `
`:. ` Heat change per cc`= ( 200 kcal)/ ( 50.77 c c) `
`= 3.939 kcal`