1.

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

Answer» 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`


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