Calc ΔH of Formation CO2 in Fe2O3 + 3C --> 4Fe + 3CO2 Reaction

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SUMMARY

The discussion centers on calculating the ΔH of formation for CO2 in the reaction Fe2O3 (s) + 3 C (gr) → 4 Fe (s) + 3 CO2 (g) at 298 K. The user initially calculates ΔHo using the equation ΔGo = ΔHo - TΔSo, arriving at an incorrect value of 217.5 kJ for ΔH (CO2). The correct ΔH of formation for CO2 is -114 kJ/mol, as confirmed by the equilibrium constant (Keq = 5.80 x 10-53) and the standard entropy change (ΔSorxn = 0.522 kJ/K). The user is advised that the reaction is not balanced, which is a critical error in their calculations.

PREREQUISITES
  • Understanding of thermodynamic concepts such as ΔH, ΔG, and ΔS
  • Familiarity with the Gibbs free energy equation: ΔGo = ΔHo - TΔSo
  • Knowledge of chemical equilibrium and the significance of Keq
  • Basic skills in balancing chemical reactions
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  • Learn how to balance chemical equations accurately
  • Study the relationship between equilibrium constants and thermodynamic quantities
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Chemistry students, chemical engineers, and professionals involved in thermodynamics and reaction kinetics will benefit from this discussion.

curtbranford
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Hi. It's my first time posting here. I did a quick search, but I couldn't find any existing threads addressing my question, so here it is:

Fe2O3 (s) + 3 C (gr) --> 4 Fe (s) + 3 CO2 (g)

What is the ΔH of formation of CO2 (g) at 298 K if the following is true of the above reaction at 298 K:
  • Keq = 5.80 x 10-53
  • ΔSorxn = 0.522 kJ/K
  • ΔHoformation of Fe2O3 (s) = -795 kJ/mol

I know that the correct answer is -114 kJ/mol, but I can't figure out how to get there. Here's what I've done so far:

ΔGo = -RT lnK
=-298kJ

ΔGo = ΔHo -TΔSo
ΔHo = -298kJ + (298K)(.522kJ/K)
= -142.44 kJ

-142.44kJ = 3ΔH (CO2) - 795 kJ
3ΔH (CO2) = 652.5 kJ
ΔH (CO2) = 217.5 kJ

Which obviously isn't the right answer, but I don't see where I went wrong. Anybody see what I don't?
 
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curtbranford said:
Hi. It's my first time posting here. I did a quick search, but I couldn't find any existing threads addressing my question, so here it is:

Fe2O3 (s) + 3 C (gr) --> 4 Fe (s) + 3 CO2 (g)

What is the ΔH of formation of CO2 (g) at 298 K if the following is true of the above reaction at 298 K:
  • Keq = 5.80 x 10-53
  • ΔSorxn = 0.522 kJ/K
  • ΔHoformation of Fe2O3 (s) = -795 kJ/mol

I know that the correct answer is -114 kJ/mol, but I can't figure out how to get there. Here's what I've done so far:

ΔGo = -RT lnK
=-298kJ

ΔGo = ΔHo -TΔSo
ΔHo = -298kJ + (298K)(.522kJ/K)
= -142.44 kJ

-142.44kJ = 3ΔH (CO2) - 795 kJ
3ΔH (CO2) = 652.5 kJ
ΔH (CO2) = 217.5 kJ

Which obviously isn't the right answer, but I don't see where I went wrong. Anybody see what I don't?


The reaction is not balanced , and next your last portion of work is wrong.
 

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