The thermochemical equation for solid and liquid rocket fuel are given below:
`2AI(s) +1(1)/(2)O_(2)(g) rarr AI_(2)O_(3)(s), DeltaH =- 1667.8 kJ`
`H_(2)(g) +(1)/(2)O_(2)(g) rarr H_(2)O(l), DeltaH =- 285.9 kJ`
a. If equal masses of aluminium and hydrogen are used, which is a better rocket fuel?
b. Determine `DeltaH` for the reaction
`AI_(2)O_(3)(s) rarr 2AI(s)+1(1)/(2)O_(2)(g)`

Explanation

From the first equation
a. `2` moles of `AI (i.e. 2 xx 27g = 54 g)`
On combustion given hate `= 1667.8 kJ`
`:. 1g of AI` givens `rArr (1667.8)/(54) rArr 39.9 kJ`
From the second equation:
`1"mole of" H_(2)(=2g)` on combustion gives heat
`= 285.9 kJ`
`:.1 g of H_(2)` gives `rArr (285.9)/(2) rArr 142.95 kJ`
Thus, `H_(2)` is a better rocket fuel.
b. Writing the reverse of the first reaction, we have
`DeltaH = 1667.8 kJ mol^(-1)`