You have been asked to calculate the enthalpy change in the following
reaction: 2Al(s) + Fe2O3(s) → Al2O3(s) + 2Fe(s)
The reaction occurs in the following stages:
1. 2Al(s) + Fe2O3(s) → Al2O3(s) + 2Fe(l) ΔH = -732.5kJ mol–1
2. Al2O3(s) + 2Fe(l) → Al2O3(s) + 2Fe(s) ΔH = -27.6kJ mol–1
3. Al2O3(s) + 2Fe(l) → Al2O3(s) + 2Fe(s) ΔH = -91kJ mol–1
Note stages 2 and 3 look the same, but the reaction is cooling from 1700oC to 25oC
and hence the enthalpy change there. Calculate the overall enthalpy change for the
reaction.
The overall enthalpy change for the reaction is the sum of the enthalpy changes for each stage. Therefore:
ΔHoverall = ΔH1 + ΔH2 + ΔH3
ΔH1 = -732.5 kJ mol-1 (given in the problem statement)
ΔH2 = -27.6 kJ mol-1 (given in the problem statement)
ΔH3 = -91 kJ mol-1 (also given in the problem statement)
ΔHoverall = -732.5 kJ mol-1 + (-27.6 kJ mol-1) + (-91 kJ mol-1)
ΔHoverall = -851.1 kJ mol-1
Therefore, the overall enthalpy change for the reaction is -851.1 kJ mol-1.
To calculate the overall enthalpy change of the reaction, we need to sum up the enthalpy changes of all the stages involved.
Given:
1. ΔH₁ = -732.5 kJ mol⁻¹
2. ΔH₂ = -27.6 kJ mol⁻¹
3. ΔH₃ = -91 kJ mol⁻¹
Step 1:
The first stage of the reaction involves the conversion of solid aluminum (Al) and solid iron(III) oxide (Fe2O3) to solid aluminum oxide (Al₂O3) and liquid iron (Fe). The enthalpy change for this stage is -732.5 kJ mol⁻¹.
Step 2:
The second stage of the reaction involves the cooling of the system from 1700°C to 25°C while maintaining the same products (Al₂O3 and Fe). The enthalpy change for this stage is -27.6 kJ mol⁻¹.
Step 3:
The third stage is the same as the second stage and also involves cooling the system from 1700°C to 25°C. The enthalpy change for this stage is -91 kJ mol⁻¹.
To calculate the overall enthalpy change, we need to sum up the enthalpies of all the stages.
Overall enthalpy change = ΔH₁ + ΔH₂ + ΔH₃
Overall enthalpy change = -732.5 kJ mol⁻¹ + (-27.6 kJ mol⁻¹) + (-91 kJ mol⁻¹)
Calculating the sum:
Overall enthalpy change = -732.5 kJ mol⁻¹ - 27.6 kJ mol⁻¹ - 91 kJ mol⁻¹
Overall enthalpy change = -851.1 kJ mol⁻¹
Therefore, the overall enthalpy change for the reaction is -851.1 kJ mol⁻¹.