Question

Thermochemical equation for two rocket fuels are given below:

$2 space Al left parenthesis straight s right parenthesis space plus space 1 1 half straight O subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space space Al subscript 2 straight O subscript 3 left parenthesis straight s right parenthesis semicolon space space increment subscript straight r straight H to the power of 0 space equals space minus 1667.8 space kJ straight H subscript 2 left parenthesis straight g right parenthesis space plus space 1 half straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space space straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon space increment subscript straight r straight H to the power of 0 space equals space minus 285.9 space kJ$

If equal masses of aluminium and hydrogen are used, which is better rocket fuel?

Solution

Given that,
$2 Al left parenthesis straight s right parenthesis space plus space 1 1 half straight O subscript 2 left parenthesis straight g right parenthesis space rightwards arrow space space space space stack Al subscript 2 straight O subscript 3 left parenthesis straight s right parenthesis semicolon with 2 space cross times 27 space equals space 54 space straight g below space increment subscript straight r straight H to the power of 0 space equals space minus 1667.8 space kJ therefore space space 54 space straight g space produce space heat space equals space 1667.8 space kJ space space$
$1 space straight g space would space produce space heat space equals space fraction numerator 1667.8 over denominator 54 end fraction space equals space 30.88 space kJ Also space given space that space space space space space space straight H subscript 2 left parenthesis 2 straight g right parenthesis space plus space 1 half straight O subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space space space straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon space space increment straight H space equals space minus 285.9 space kJ Now space 2 straight g space straight H subscript 2 space produced space heat space equals space 285.9 space kJ therefore space space space 1 straight g space straight H subscript 2 space would space produce space heat space equals space fraction numerator 285.9 over denominator 2 end fraction space equals space 142.95 space kJ Hence space straight H subscript 2 space is space straight a space better space rocket space fuel.$

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Thermodynamics

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