An intimate mixture of `Fe_(2)O_(3) and Al_(2)O_(3)` is used in solid furl for rockets. Calculates the furl value per gram and fuel value per `cm^(3)` of the mixture.
`DeltaH(Fe_(2)O_(3))=1669.4kJ*mol^(-1)`
`DeltaH(Al_(2)O_(3))=832.6kJ*mol^(-1)`.

Explanation

The reaction is `2Al+Fe_(2)O_(3)to2Fe+Cl_(2)O_(3)`
The enthalpy change in this reaction is
`DeltaH^(0)=DeltaH_(f)^(0)(Al_(2)O_(3))-DeltaH_(f)^(0)(Fe_(2)O_(3))`
`=(1669-832.6)kJ=836.6kJ`
The total mass of the reactants `(2Al+Fe_(2)O_(3))`
`=[2xx27+(2xx55.85+3xx16)]g=213.7g`
Therefore, the fuel per gram of the mixture
`=(836.4)/(213.7)kg*g^(-1)=3.91kJ*g^(-1)`
The volume of mixture of the reactants
`=((2xx27)/(2.7)+(159.7)/(5.2))cm^(3)=50.7cm^(3)`
Therefore, the fuel value per `cm^(3)` of the mixture
`=(836.4)/(50.7)kJ*cm^(-3)=16.49kJ*cm^(-3)`.