Question

Solid fuel used in rocket is a mixture of Fe₂O₃ and Al (in ratio 1 : 2) the heat evolved (KJ) per gram of the mixture is ______ (Nearest integer)
Given \(\Delta H_f^{\circ}(Al_2O_3) = -1700 \, \text{KJ mol}^{-1}\)
\(\Delta H_f^{\circ}(Fe_2O_3) = -840 \, \text{KJ mol}^{-1}\) }

Hint:

To calculate the heat evolved per gram, divide the total heat by the total mass of the mixture.

Answer 1

Correct Answer: 4

The reaction is: \[ Fe_2O_3 + 2Al \rightarrow Al_2O_3 + 2Fe \] Now calculate the heat evolved: \[ \Delta H = (\Delta H_f^{\circ} (Al_2O_3)) - (\Delta H_f^{\circ} (Fe_2O_3)) \] Substitute the given values: \[ \Delta H = (-1700) - (-840) = -860 \, \text{KJ/mol} \] Moles of \(Fe_2O_3\) and Al are in the ratio 1 : 2. So, 1 mole of \(Fe_2O_3\) weighs \(112 \, \text{g}\), and 2 moles of Al weigh \(54 \, \text{g}\). Total mass of the mixture is: \[ 160 + 54 = 214 \, \text{g} \] Now, the heat evolved per gram of the mixture is: \[ \frac{-860 \, \text{KJ}}{214} \approx -4.01 \, \text{KJ/g} \] Thus, the heat evolved per gram is approximately 4 KJ. Hence, the correct answer is (4).