Thermodynamics And Thermochemistry Result Question 26
26. An intimate mixture of ferric oxide, $\mathrm{Fe} _2 \mathrm{O} _3$, and aluminium, $\mathrm{Al}$, is used in solid fuel rockets. Calculate the fuel value per gram and fuel value per cc of the mixture. Heats of formation and densities are as follows:
$H _f\left(\mathrm{Al} _2 \mathrm{O} _3\right) =- 1582$ $ \mathrm{kcal} / \mathrm{mol}$
$H _f\left(\mathrm{Fe} _2 \mathrm{O} _3\right) =- 199$ $ \mathrm{kcal} / \mathrm{mol}$
Density of $\mathrm{Fe} _2 \mathrm{O} _3 = 5.7 \mathrm{~g} / \mathrm{cc}$
Density of Al $= 2.7 \mathrm{~g} / \mathrm{cc}$
(1989, 2M)
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Solution:
- $ \mathrm{Fe}_2 \mathrm{O}_3(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}_2 \mathrm{O}_3(s)+2 \mathrm{Fe}(s) $
$ \Delta H_r^{\circ}=\Delta H_f^{\circ} \text { (products) }-\Delta H_f^{\circ} \text { (reactants) } $
$ =-399-(-199) $
$ =-200\ \mathrm{kcal}$
$ \text { Mass of reactants }=56 \times 2+16 \times 3+27 \times 2=214 \mathrm{~g} $
$ \Rightarrow \text { Fuel value } / \mathrm{gram}=\frac{200}{214}=0.934$ $ \mathrm{kcal} / \mathrm{g} $
$ \text { Volume of reactants }=\frac{160}{5.2} \mathrm{cc}+\frac{54}{2.7} \mathrm{cc}=50.77 $ $\mathrm{cc} $
$ \Rightarrow \text { Fuel value } / \mathrm{cc}=\frac{200}{50.77}=3.94 $ $\mathrm{kcal} / \mathrm{cc} $
BETA
