[MrTeo]

Here is the exercise; I'd like to check my answer with you (and to receive some help, if possible, on the part of the problem I didn't manage to solve ):

– • –

FeO_(g) is reduces to Fe_(s) treating it with CO_(g), according to the following equation:



Knowing that at T temperature the equilibrium constant of the reaction is 5, calculate the volume of CO needed to produce 100kg of Fe_(s) , working at T=400 K

[M(Fe)=55.8]

– • –

As the equilibrium is heterogeneous I write K_eq without including solid species involved (I suppose that the reaction occurs in a closed environment with a fixed volume):



Now, x must be equal to number of moles of iron produced so i can calculate the number of moles of CO_g needed:



Now I don't know how to get the volume needed starting from this, I tried using the K_p but the only thing I found out is this:



Have you got any ideas?

[Borek]

How many moles of CO₂ were produced?

[renge ishyo]

If you assume the reaction is at atmospheric pressure then maybe you can use PV=nRT? Using this approach, you could solve for V = nRT/P. For beginning chem at least this seems like a decent way to go about things.

[MrTeo]

How many moles of CO₂ were produced?

I think that they're equal to the numebr of moles of Fe_(s), so 1790.6. But this in fact doesn't make sense with the last equation... If I work with molar fractions I get:

$$ K_{eq}= \frac{{\left[{CO_{2(g)}} \right]}}{{\left[{CO_{(g)}} \right]}}= \frac{x}{{1-x}}=5 /$$
$$ x_{CO_2 }= \frac{5}{6}\;x_{CO_{(g)} }= \frac{1}{6} /$$

And this should be right (using molar fractions I don't care about volume).

If you assume the reaction is at atmospheric pressure then maybe you can use PV=nRT? Using this approach, you could solve for V = nRT/P. For beginning chem at least this seems like a decent way to go about things.

I thought about that too, but I'm not sure. Is there a way to find out the volume needed without asuming any of the values required?

[Borek]

I was editing my previous post, got distracted and I see now that I have not posted what I originally intended to do. Sorry about that.

No idea why you think number of moles of CO₂ is incorrect - it is perfectly right 

Your calculation of initial number of moles of CO is correct - all you need now is an assumption about the pressure. You can't avoid it.

[MrTeo]

Yeah, I got confused looking at the last equation written:

I was in a hurry before going to school and I didn't think that n_CO(g) was the number of moles at the equilibrium and not the starting number of moles, so I found a contradiction between the first and last equation written...

Anyway I'm happy to hear that more data is needed to calculate volume, that's just what puzzled me 

Thank you all for you help