To determine the fuel value per milliliter of the intimate mixture of Fe2O3 and Al used in solid fuel rockets, we need to calculate the heat released during the reaction between aluminum and iron(III) oxide. This reaction is a thermite reaction, which can be represented by the following equation:
The Reaction
The balanced chemical equation for the reaction is:
- 2 Al + Fe2O3 → Al2O3 + 2 Fe
Enthalpy Change Calculation
To find the enthalpy change (ΔH) for this reaction, we can use the standard enthalpy of formation values provided:
- ΔHf° (Al2O3) = -399 kcal/mol
- ΔHf° (Fe2O3) = -199 kcal/mol
The enthalpy change for the reaction can be calculated using the formula:
ΔH = ΣΔHf° (products) - ΣΔHf° (reactants)
Substituting the values into the equation:
- ΔH = [ΔHf° (Al2O3) + 2 × ΔHf° (Fe)] - [2 × ΔHf° (Al) + ΔHf° (Fe2O3)]
- ΔH = [-399 + 0] - [2 × 0 - 199]
- ΔH = -399 + 199 = -200 kcal
Calculating the Density of the Mixture
Next, we need to find the density of the mixture. The densities of Fe2O3 and Al are given as:
- Density of Fe2O3 = 5.2 g/ml
- Density of Al = 2.7 g/ml
Assuming we have a 1:1 molar ratio for simplicity, we can calculate the mass of each component in 1 ml of the mixture:
- Mass of Fe2O3 in 1 ml = 5.2 g
- Mass of Al in 1 ml = 2.7 g
The total mass of the mixture is:
Total mass = 5.2 g + 2.7 g = 7.9 g
Calculating the Fuel Value per Milliliter
Now, we can calculate the fuel value per milliliter of the mixture. The fuel value is essentially the amount of energy released per gram of the mixture:
Fuel value = ΔH / Total mass
Fuel value = -200 kcal / 7.9 g
Fuel value ≈ -25.32 kcal/g
To find the fuel value per milliliter, we can multiply this by the density of the mixture:
Fuel value per ml = Fuel value per gram × Density of the mixture
Fuel value per ml = -25.32 kcal/g × 7.9 g/ml
Fuel value per ml ≈ -200 kcal/ml
Final Result
The fuel value per milliliter of the intimate mixture of Fe2O3 and Al is approximately 25.32 kcal/ml. This value indicates the energy released during the combustion process, which is crucial for understanding the efficiency of the rocket fuel.
