An equilibrium mixture of 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.
2SO3 (g) + CO2 (g) ⇄ CS2 (g) + 4O2 (g)
Me personally, I always find using tables makes things look pretty

I'll go step by step for you, so you can see what's happening.
NOTE THAT I ASSUME WE MUST FIND THE AMOUNT OF O2 FIRST otherwise the question makes no sense
| 2SO3 (g) + | CO2 (g) | ⇄ | CS2 (g) + | 4O2 (g) |
Initially: | ? | ? | | ? | ? |
Reacted: | ? | ? | | ? | ? |
Equilibrium: | 0.022 | 0.014 | | 0.028 | ? |
Now, since in the question it states that only sulfur trioxide and carbon dioxide are present initially, and CS
2 present in equilibrium, clearly the forward reaction dominated. Hence we know that 0.028mol of CS
2 formed and can calculate the amount of 2SO
3 and CO
2 reacted using stoichiometry:
| 2SO3 (g) + | CO2 (g) | ⇄ | CS2 (g) + | 4O2 (g) |
Initially: | ? | ? | | ? | ? |
Reacted: | 0.056 | 0.028 | | 0.028 | 0.112 |
Equilibrium: | 0.022 | 0.014 | | 0.028 | ? |
We can now complete the table, as follows:
| 2SO3 (g) + | CO2 (g) | ⇄ | CS2 (g) + | 4O2 (g) |
Initially: | 0.078 | 0.042 | | 0 | 0 |
Reacted: | 0.056 | 0.028 | | 0.028 | 0.112 |
Equilibrium: | 0.022 | 0.014 | | 0.028 | 0.112 |
Since we now have our amounts of products and reactants, we can go about calculating the equilibrium constant at that temperature

really hoping I didnt screw up somewhere, oh and ofc hoping it helps

EDIT: and... out ninja'd XD i knew i was taking too long on the tables