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An intimate mixture of ferric oxide (Fe_(2)O_(3)) and aluminium (Al) is used as solid rocket fuel. Calculate fuel value per gram and fuel value per c c of the mixture. Heats of formation and densities are as follows : DeltaH_(f)(Al_(2)O_(3))=399"kcal//mole" DeltaH_(f)(Fe_(2)O_(3))=199"kcal//mole" Density of Fe_(2)O_(3)=5.2 g// c c Density of Al =2.7 g// c c |
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Answer» Solution :Given that, (i) `2Al+3//2O_(2) to Al_(2)O_(3),DeltaH=-399 "kcal"` (ii) `2Fe+3//2O_(2) to Fe_(2)O_(3),DeltaH=-199 "kcal"` Applying the inspection METHOD, [Eqn. (i)-Eqn.(ii], we get, `2Al+Fe_(2)O_(3) to Al_(2)O_(3)+2Fe, DeltaH=-399-(-199)=-200"kcal"` Now, 2 moles of AL weigh `(2xx27), i.e., 54 g and 1 MOLE of `Fe_(2)O_(3)` weighs 160g. Total weight of the MIXTURE `=54+160=214 g. `:.` fuel value per gram of the mixture `=(200)/(214)=0.9345 "kcal/g"` Further, volume of 2 moles of `Al=(54)/(2.7)=20 c c` and volume of 1 mole of `Fe_(2)O_(3)=(160)/(5.2)=30.76 c c`. `:.` total volume of the mixture`=50.76 c c` `:.` fuel value per c c of the mixture `=(200)/(50.76)` `=3.94 "kcal/ c c"` |
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