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

Given that,
(i) `2Al+3//2O_(2) to Al_(2)O_(3),DeltaH=-399 "kcal"`
(ii) `2Fe+3//2O_(2) to Fe_(2)O_(3),DeltaH=-199 "kcal"`
Applying the inspection method, [Eqn. (i)-Eqn.(ii], we get,
`2Al+Fe_(2)O_(3) to Al_(2)O_(3)+2Fe, DeltaH=-399-(-199)=-200"kcal"`
Now, 2 moles of Al weigh `(2xx27), i.e., 54 g and 1 mole of `Fe_(2)O_(3)` weighs 160g.
Total weight of the mixture `=54+160=214 g.
`:.` fuel value per gram of the mixture `=(200)/(214)=0.9345 "kcal/g"`
Further, volume of 2 moles of `Al=(54)/(2.7)=20 c c`
and volume of 1 mole of `Fe_(2)O_(3)=(160)/(5.2)=30.76 c c`.
`:.` total volume of the mixture`=50.76 c c`
`:.` fuel value per c c of the mixture `=(200)/(50.76)`
`=3.94 "kcal/ c c"`