Thermodynamics and Thermochemistry 2 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 $\mathrm{cc}$ of the mixture. Heats of formation and densities are as follows:
$$ \begin{aligned} & H_{f}\left(\mathrm{Al}{2} \mathrm{O}{3}\right)=-399 \mathrm{kcal} / \mathrm{mol} \ & H_{f}\left(\mathrm{Fe}{2} \mathrm{O}{3}\right)=-199 \mathrm{kcal} / \mathrm{mol} \end{aligned} $$
Density of $\mathrm{Fe}{2} \mathrm{O}{3}=5.2 \mathrm{~g} / \mathrm{cc}$, Density of $\mathrm{Al}=2.7 \mathrm{~g} / \mathrm{cc}$
$(1989,2 M)$
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Solution:
- $\mathrm{Fe}{2} \mathrm{O}{3}(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}{2} \mathrm{O}{3}(s)+2 \mathrm{Fe}(s)$
$\Delta H_{r}^{\circ}=\Delta H_{f}^{\circ}$ (products) $-\Delta H_{f}^{\circ}$ (reactants)
$$ \begin{aligned} & =-399-(-199) \ & =-200 \mathrm{kcal} \end{aligned} $$
Mass of reactants $=56 \times 2+16 \times 3+27 \times 2=214 \mathrm{~g}$
$\Rightarrow$ Fuel value $/$ gram $=\frac{200}{214}=0.93 \mathrm{kcal} / \mathrm{g}$
Volume of reactants $=\frac{160}{5.2} \mathrm{cc}+\frac{54}{2.7} \mathrm{cc}=50.77 \mathrm{cc}$
$\Rightarrow \quad$ Fuel value $/ \mathrm{cc}=\frac{200}{50.77}=3.94 \mathrm{kcal} / \mathrm{cc}$
