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)`

Answer

`0.9345" k Cal g"^(-1), 3.94" kCal cm"^(-3)`

Explanation

`Fe_(2)O_(3)+2Al rarr Al_(2)O_(3) +2Fe`
`DeltaH=-399+199=-200`
Total m wt of mixture `=214`
`214 g rArr -200 rArr 1 g=-200/214=0.9345" kCal g"^(-1)`
Vol. of `Fe_(2)O_(3)=160/5.2 =30.7rArr` Vol. of `Al_(2)O_(3)=54//2.7=20`
Total `=30.7+20=50.7 c crArr 50.7 c c=200 rArr 1 c c=200/50.7=3.94" kCal cm"^(-3)`