Solid fuel used in rocket is a mixture of and Al (in ratio 1 : 2). The heat evolved (kJ) per gram of the mixture is ________ (Nearest Integer) Given: Molar mass of Fe, Al and O are 56, 27 and 16 g respectively. [2

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Solution

Q.
Solid fuel used in rocket is a mixture of ${Fe}_{2} O_{3}$ and Al (in ratio 1 : 2). The heat evolved (kJ) per gram of the mixture is ________ (Nearest Integer)

Given: $Δ H_{f}^{θ} ({Al}_{2} O_{3}) = - {1700 kJ mol}^{- 1}$

$Δ H_{f}^{θ} ({Fe}_{2} O_{3}) = - {840 kJ mol}^{- 1}$

Molar mass of Fe, Al and O are 56, 27 and 16 g ${mol}^{- 1}$ respectively. [2023]

Ans.
(4)

${Fe}_{2} O_{3} + 2 Al \to {Al}_{2} O_{3} + 2 Fe$

$Molar mass 160 g 27 g$

${({Δ H}_{f}^{0})}_{reaction} = [{(Δ H_{f} °)}_{{Al}_{2} O_{3}} + 2 {(Δ H_{f} °)}_{Fe}] - [{(Δ H_{f} °)}_{{Fe}_{2} O_{3}} + 2 {(Δ H_{f} °)}_{Al}]$

$= [- 1700 + 0] - [- 840 + 0]$

$= - 860 kJ/mol$

$Total mass of mixture = {Fe}_{2} O_{3} + Al (1 : 2 molar ratio)$

$= 160 + 2 \times 27 = 214 g/mol$

$Heat evolved per gram = \frac{860}{214} = 4 kJ/g$

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