An intimate mixture of ferric oxide , Fe_(2)O_(3), and aluminium, Al, is used in solid fuel rockets. Calculatethe 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.

An intimate mixture of ferric oxide , Fe_(2)O_(3), and aluminium, Al,

1.	An intimate mixture of ferric oxide , Fe_(2)O_(3), and aluminium, Al, is used in solid fuel rockets. Calculatethe 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» SOLUTION :We aim at `Fe_(2)O_(3) +2AL rarr 2 Fe+Al_(2)O_(3), DeltaH = ?` `Delta_(r)H= [2 xxDeltaH _(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 heatchanne thattakes PLACE when 1 moleof `Fe_(2)O_(3)`and 2 moles of Al combinei.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 `= 50.77c c ` `:. `Heat change per cc`= ( 200 kcal)/ ( 50.77 c c) ` `= 3.939 kcal`