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

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The discussion revolves around calculating the ΔH of formation for CO2 in the reaction Fe2O3 + 3C → 4Fe + 3CO2 at 298 K. The user initially calculates ΔGo and ΔHo but arrives at an incorrect ΔH value for CO2. Key points raised include the need for proper balancing of the reaction and identifying errors in the calculations. The correct ΔH of formation for CO2 is noted as -114 kJ/mol, prompting further examination of the user's methodology. The conversation emphasizes the importance of accurate calculations and balancing in thermodynamic equations.
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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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