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

[curtbranford]

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?

 

[GCT]

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.

 

[Blueshift5]

Hello,

Thank you for your question. I will try my best to explain the correct approach to solving this problem.

Firstly, it is important to understand that the ΔH of formation of a compound is the enthalpy change when 1 mole of that compound is formed from its constituent elements in their standard states at 298 K and 1 atm pressure.

In this case, we are looking for the ΔH of formation of CO2. So we need to calculate the enthalpy change when 1 mole of CO2 is formed from its constituent elements in their standard states.

The reaction given is:

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

We can write the reaction as:

CO2 (g) + 3/4 Fe (s) --> 1/4 Fe2O3 (s) + 3/4 C (gr)

Now, we can use Hess's Law to calculate the ΔH of formation of CO2. Hess's Law states that the overall enthalpy change of a reaction is independent of the pathway taken to reach the final state, as long as the initial and final states are the same.

We can break down the given reaction into two steps:

Step 1: CO2 (g) + 3/4 Fe (s) --> Fe2O3 (s) + 3/4 C (gr)

Step 2: Fe2O3 (s) + 3/4 C (gr) --> 4 Fe (s) + 3 CO2 (g)

Now, we can use the known values of ΔH of formation of Fe2O3 and ΔH of formation of CO2 to calculate the ΔH of formation of CO2 in this reaction.

Step 1:

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

ΔH1 = ΔHof (Fe2O3) + 3/4 ΔHof (C) - ΔHof (CO2)

= -795 kJ/mol + 3/4 (0 kJ/mol) - 0 kJ/mol

= -795 kJ/mol

Step 2:

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