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`.

Answer

`0.9346 (kcal)/(g), 3.94 (kcal)/("cc")`

Explanation

The reaction is `2AI+ Fe_(2)O_(3) to AI_(2)O_(3) + 2Fe`(Fuel mixture)
`Delta_(r)H^(@)` for the reaction is
`Delta_(r)H^(@) = [Delta_(f)H^(@)(AI_(2)O_(3) + 2Delta_(f)H^(@)(Fe)] -[2Delta_(f)H^(@)(AI) + Delta_(f)H^(@)(Fe_(2)O_(3))]`
` = [-399.0 + 2(0)] -[2(0)+(-199.0)]`
`= -200 kcal`.
Mol.wt.of fuel mixture = `2 xx 57 + 48) = 214g`
Fuel value = `(200)/(214) = 0.9346 kcal/g`
Calculation of fuel value per cc
Volume of AI` = (54)/(2.7) = 20` cc
Volume of `Fe_(2)O_(3) = (160)/(5.2) = 30.77` cc
Total Volume = `20 + 30.77 = 50.77` cc
Fule value per cc ` = (200)/(55.77) = 3.94 ("kcal")/("cc")`.