SATHEE: Thermodynamics and Thermochemistry 2 Question 26

Thermodynamics and Thermochemistry 2 Question 26

26. An intimate mixture of ferric oxide, $\mathrm{Fe}{2} \mathrm{O}{3} $, a n d a l u m i n i u m,$ \mathrm{Al} $, i s u s e d i n s o l i d f u e l r o c k e t s . C a l c u l a t e t h e f u e l v a l u e p e r g r a m a n d f u e l v a l u e p e r$ \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} $, D e n s i t y o f$ \mathrm{Al}=2.7 \mathrm{~g} / \mathrm{cc}$

$(1989, 2 M)$

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Solution:

$\mathrm{Fe}{2} \mathrm{O}{3}(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}{2} \mathrm{O}{3}(s)+2 \mathrm{Fe}(s)$

$Δ H_{r}^{\circ} = Δ H_{f}^{\circ}$ (products) $- Δ H_{f}^{\circ}$ (reactants)

$\begin{aligned} = - 399 - (- 199) & = - 200 kcal \end{aligned}$

Mass of reactants $= 56 \times 2 + 16 \times 3 + 27 \times 2 = 214 g$

$\Rightarrow$ Fuel value $/$ gram $= \frac{200}{214} = 0.93 kcal / g$

Volume of reactants $= \frac{160}{5.2} cc + \frac{54}{2.7} cc = 50.77 cc$

$\Rightarrow$ Fuel value $/ cc = \frac{200}{50.77} = 3.94 kcal / cc$

Thermodynamics and Thermochemistry 2 Question 26

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Thermodynamics and Thermochemistry 2 Question 26

26. An intimate mixture of ferric oxide, $\mathrm{Fe}{2} \mathrm{O}{3},andaluminium,\mathrm{Al},isusedinsolidfuelrockets.Calculatethefuelvaluepergramandfuelvalueper\mathrm{cc}$ of the mixture. Heats of formation and densities are as follows:

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