Question About working out K

[t35t]

Hi,

I came across a most unorthodox question (in my opinion)

Carbon disulfide gas (CS2), which is used in the manufacture of rayon, can be made
using an endothermic gas phase reaction between sulfur trioxide gas (SO3) and carbon
dioxide. Oxygen gas is also produced in the reaction.
a)Write a balanced chemical equation for the reaction.
b)Write an expression for the equilibrium constant of the reaction.
c)An equilibrium mixture of these gases was made by mixing sulfur trioxide and
carbon dioxide. It consisted of 0.028 mol of CS2, 0.022 mol of SO3 and 0.014 mol
of CO2 in a 20 L vessel. Calculate the value of the equilibrium constant at that
temperature

I struggle with c) as thus, my concentration fraction is: [CS2][O2]^4/[SO3]^2[CO2]

How exactly do I work out the equilibrium constant if I am not given oxygen?
I had a look at the worked solutions, and, drawing on from unit 3, they have derived the concentration of oxygen from using the concentration of CS2 at 0.0014M multiplied by the mole ratio of 4. I'm not exactly sure what they did here, and moreover I did not know that we could do that- I had thought that the whole purpose of equilibrium was that the mol and the concentrations of mixtures were not as static as the given mol ratio (in this case, 4/1).

Could someone explain how they got 0.0014M for oxygen? I'm very confused!

[t35t]

Sorry moderators! I might have jumped the gun there a bit, I figured it out.... sorry for the inconvenience.

-btw, for anyone else who might be curious as to how it was done, I solved it by drawing on from the fact that, to begin with, the mol of CS2 would be 0 mol at the start of a reaction. Therefore, as the concentration fraction is now at equilibrium, where CS2 is at 0.028mol, the change in mol from 0 mol to 0.028mol would be 0.028. Therefore, we can use this mol change to figure out the mol change of oxygen, which, at the beginning of the reaction would also be at 0mol. So,
n(O2)=n(O2)/n(CS2)
n(O2)=4/1
n(O2)= 4/1 x n(CS2)
n(O2)=0.028mol x 4
C(O2)=0.112mol/20L
C(O2)=0.0056M

The book at skipped those steps and went straight to 0.0014 x 4- hence I was a bit confused (unless this is some form of a shortcut???)

[thushan]

no worries, it's alright

[Graphite]

c)An equilibrium mixture of these gases was made by mixing sulfur trioxide and
carbon dioxide. It consisted of 0.028 mol of CS2, 0.022 mol of SO3 and 0.014 mol
of CO2 in a 20 L vessel. Calculate the value of the equilibrium constant at that
temperature.

Yeah, you've got the point but basically you need to read very carefully here.
The first sentence implies there was no added CS2 or O2 to the mixture.
The second sentence indicates the amount of 3 of the 4 species in the mixture. From that you are expected to realise that the amount of CS2 formed is proportional to the O2 formed as they are both initially not present, and are products of CO2+SO3

Btw, I understand what you're trying to show but some of your equations might be incorrect to assessors. Perhaps your first line should be:
n(O2)=coefficient(O2)/coefficient(CS2) x n(CS2)

Note that the molar concentrations of CS2 is proportional to O2 because the volume is the same.