Question on the reduction of FeO by CO

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Discussion Overview

The discussion revolves around the thermodynamics of the reduction of FeO by CO, specifically analyzing the spontaneity of the reaction FeO + CO = Fe + CO2 at elevated temperatures. Participants explore the implications of calculated Gibbs free energy changes and the equilibrium constant in the context of a blast furnace operation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents calculated values for standard molar enthalpies and entropies, leading to a Gibbs free energy change that suggests spontaneity at 1200 K.
  • Another participant questions the assumptions made regarding the temperature effects on enthalpy, noting that both reactants and products are at the same temperature.
  • A later reply indicates a correction in the calculation method for enthalpy, suggesting that the temperature adjustment is significant and affects the spontaneity conclusion.
  • One participant asks for clarification on the definitions of G and G0, and whether the blast furnace operates at equilibrium, proposing that additional CO may be used to drive the reaction forward.
  • Another participant discusses the complexity of calculating Gibbs free energy changes due to varying heat capacities with temperature and describes the operational dynamics of the blast furnace, including the thermodynamic balance of CO and CO2 ratios.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions made in the calculations and the operational conditions of the blast furnace. There is no consensus on the correct interpretation of the Gibbs free energy changes or the equilibrium conditions.

Contextual Notes

Participants note that the heat capacity (Cp) changes with temperature, which complicates the calculations. There are also unresolved questions regarding the equilibrium state of the blast furnace and the actual ratios of gases present.

hurreechunder
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Some numbers below: these are the standard molar enthalpies and entropies at 298K that I got from a website.
In the reaction FeO + CO = Fe + CO2, the deltas are:
delta H = (0+ -393) - (-266.5+ -110.5) = -16.3 KJ/mol.
delta S = (27.2+213.8) - (197.9+54) = -10.9 J/mol/K
Now at 1200 K,
Go = -16.3 + (1200)(-10.9) = -3.23
I have ignored the effect of temperature on enthalpy as both the reactants and the products are at the same temperature.
The issue with this is that it suggests that the reaction is spontaneous at 1200K. Therefore, in G = Go + RT ln Q, ln Q is >0 and therefore pCO2/pCO>1. However, we know the opposite to be the case in real life where pCO2/pCO = 1/2.3 in the blast furnace
Where am I going wrong??

Hf (KJ/mol K)Sf (J/mol K)
FeOs
-266.5​
54​
COg
-110.5​
197.9​
CO2g
-393.3​
213.8​
Fes
0​
27.2​
 
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hurreechunder said:
I have ignored the effect of temperature on enthalpy as both the reactants and the products are at the same temperature.
hurreechunder said:
Where am I going wrong??
 
Thanks - I took a second look at the calcs, and it appears that I was dividing the Cp in KJ/Kg by the molar mass instead of multiplying it. With that adjustment, the temperature adjustment of the enthalpy is no longer negligible. I am still getting a number different than 2.3, but at least Ln(Q) is negative.
 
hurreechunder said:
Therefore, in G = Go + RT ln Q, ln Q is >0
What are you taking as G and G0 here?
Are you assuming that the blast furnace is at equilibrium? Is that true? Do they add extra CO to force the reaction to the right?
 
dG (note: should have used the deltas in the original post) = 0 in the limiting case. I'm trying to find the corresponding value of ln Q = pCO2/pCO

dGo = dH-TdS; where for every reactant and product, H = Ho + Cp(T-298K). It's a bit complicated because the Cp itself changes with temperature.

The blast furnace has many zones in it, corresponding to different temperatures, as the iron ore travels down from the top and the CO comes up from the bottom. The CO is not injected externally. The ratio of CO2 to CO comes about from thermodynamic balance as the CO travels up from the bottom and reduces the iron ore in the layers above.