How much energy is evolved during the formation of 98.7 g of Fe, according to the reaction below?
Fe2O3(s) + 2 Al(s) → Al2O3(s) + 2 Fe(s)
ΔH°rxn = -852 kJ
A. 482 kJ
B. 753 kJ
C. 1.51 × 10ee3 kJ
D. 4.20 × 10ee3 kJ
B. 753
To calculate the energy evolved during the formation of 98.7 g of Fe, we need to use the balanced equation and the given enthalpy change.
The balanced equation is:
Fe2O3(s) + 2 Al(s) → Al2O3(s) + 2 Fe(s)
The molar mass of Fe2O3 is 159.7 g/mol.
To find the moles of Fe2O3, we divide the given mass by the molar mass:
moles of Fe2O3 = 98.7 g / 159.7 g/mol ≈ 0.618 mol
According to the balanced equation, the stoichiometric ratio between Fe2O3 and Fe is 1:2. Therefore, the moles of Fe formed will be twice the moles of Fe2O3:
moles of Fe = 2 * 0.618 mol = 1.236 mol
Now, we can use the given enthalpy change to calculate the energy evolved. The enthalpy change per mole of Fe is -852 kJ.
The energy evolved = enthalpy change * moles of Fe formed:
Energy evolved = -852 kJ/mol * 1.236 mol = -1052.472 kJ
Rounding to three decimal places, the energy evolved during the formation of 98.7 g of Fe is approximately -1052.472 kJ.
Since energy cannot be negative in this context, we can say the answer is approximately 1052.472 kJ.
Therefore, none of the given answer choices match the calculated value.
To find the amount of energy involved in the formation of 98.7 g of Fe, we need to use the concept of stoichiometry and the given enthalpy change of the reaction.
The given reaction is:
Fe2O3(s) + 2 Al(s) → Al2O3(s) + 2 Fe(s)
We are given the enthalpy change (ΔH°rxn) of the reaction as -852 kJ, which means that 852 kJ of energy is released when one mole of the reaction occurs.
To find the number of moles of Fe in 98.7 g, we need to use the molar mass of Fe. The molar mass of Fe is 55.845 g/mol.
Number of moles of Fe = Mass of Fe / Molar mass of Fe
= 98.7 g / 55.845 g/mol
Now, we can use the stoichiometry of the reaction to determine the energy evolved when 1 mole of Fe is formed:
From the balanced equation, we see that 2 moles of Fe are formed when 1 mole of the reaction occurs. Therefore, ΔH°rxn corresponds to 2 moles of Fe.
Energy evolved for 1 mole of Fe = ΔH°rxn / 2 = 852 kJ / 2
Finally, we can calculate the energy evolved for 98.7 g of Fe:
Energy evolved = Energy evolved for 1 mole of Fe * Number of moles of Fe
= (852 kJ / 2) * (98.7 g / 55.845 g/mol)
Simplifying the calculation, we find that the energy evolved is approximately 753 kJ.
Therefore, the correct answer is B. 753 kJ.
the molar mass of Fe is 55.8 g
[98.7 / (2 * 55.8)] * 852 kJ