Solid fuel used in rocket is a mixture of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and Al (in ratio \(1: 2\) ). The heat evolved ( kJ ) per gram of the mixture is ____ (Neatest integer) Given : \(\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)=-1700 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \[ \Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-840 \mathrm{~kJ} \mathrm{~mol}^{-1} \] Molar mass of \(\mathrm{Fe}, \mathrm{Al}\) and O are 56, 27 and 16 g \(\mathrm{mol}^{-1}\) respectively.

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Chemical Thermodynamics

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 ____ (Neatest 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.

Answer: 4

The thermite reaction:

Fe_{2} O_{3} + 2 Al \to Al_{2} O_{3} + 2 Fe

Δ H_{reaction} = [Δ H_{f}^{θ} (Al_{2} O_{3}) + 2Δ H_{f}^{θ} (Fe)] - [Δ H_{f}^{θ} (Fe_{2} O_{3}) + 2Δ H_{f}^{θ} (Al)]

= [- 1700 + 0] - [- 840 + 0] = - 860

kJ/mol

Molar mass of

Fe_{2} O_{3}

= 2(56) + 3(16) = 160 g/mol
Molar mass of Al = 27 g/mol

Total mass of mixture (1:2 molar ratio) = 160 + 2(27) = 214 g

Heat evolved per gram =

\frac{860}{214} = 4.02 \approx 4

kJ/g

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer