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 :
`Delta H_(f)^(0)(Al_(2)O_(3))= 399 " kcal mol"^(-1), Delta H_(f)^(0)(Fe_(2)O_(3))= 199 " kcal mol"^(-1)`, Density of `Fe_(2)O_(3)= 5.2 g// c c`, Density of `Al= 2.7g// c c`.

Explanation

Reaction of Al & `Fe_(2)O_(3)`:
`2Al(s)+Fe_(2)O_(3)(s) to Al_(2)O_(3)(s)+2Fe(s)`
`therefore` Enthalpy change of the reaction, `Delta H^(0)`
`= Delta H_(f)^(0)(Al_(2)O_(3))+2Delta H_(f)^(0)(Fe)= 2Delta H_(f)^(0)(Al)- Delta H_(f)^(0)(Fe_(2)O_(3))`
= (399-199) kcal = 200 kcal
Mass of the mixture
`= 2xx27 g+(2xx56+3xx16)g= 214 g`
So, liberated heat for 1 g of the mixture
`= (200)/(214) ` kcal = 09345 kcal.
Hence, the fuel value per gram of the mixture = 0.9345 kcal.
Volume of mixture
`=((2xx27)/(2.7)+(2xx56+3xx16)/(5.2)) c c = 50.77 c c`
Hence, fuel value per c c of the mixture
`= (200)/(50.77)` kcal = 3.94 kcal