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

(a) From the first given equation.
2 moles of Al `( i.e., 2 xx 27 g = 54g)` on combustion give heat `= 1667.8 kJ`
`:. 1 g` of Al combustion givesheat ` = (1667.8 ) / ( 54) = 30.9 kJ`
From the second given equation, 1 mole of `H_(2) ( = 2g) ` on combustion gives heat `= 285.9 kJ`
`:. ` 1 g of `H_(2)` on combustion gives heat `= (285.9) /( 2) = 142.95kJ`
Thus, `H_(2)` is a better rocket fuel.
(b) Writing the reverse of the first reaction, we have
`Al_(2)O_(3)(s) rarr2Al(s) +1(1)/(2) O_(2)(g), Delta H = + 1667.8 kJ mol^(-1)`
Thus, for the reaction given in part (b) of the problem, `Delta H = + 1667.8 kJ mol^(-1)`