# Relationship in equilibrium constants

$\ce{2CH4(g) + O2(g) \rightleftharpoons 2CO(g) + 4H2(g)}$

Equal numbers of moles of $\ce{CH4}$ and $\ce{O2}$ are drawn into a sealed container and the system is left until it reaches equilibrium. Which of the following relationships pertaining to this particular system are true at equilibrium?

1. $\ce{[CH4]<[H2]}$
2. $\ce{[CH4]>[O2]}$
3. $\ce{[H2]>[CO]}$

I know that the equation for $\ce{K_{eq}}$ is

$$\ce{\dfrac{[H2]^4[CO]^2}{[CH4]^2[O2]}}$$

I think that 3. is wrong because if $\ce{CH4}$ and $\ce{O2}$ are equal, then $\ce{H2}$ and $\ce{CO}$ have to be the same. Now I'm confused about 1 and 2. I'm not sure how to distinguish between the two.

Let's say that the amount of $\ce{CH4}$ and $\ce{O2}$ at the start is $x$.

After the reaction is complete, let's say that $y$ moles of $\ce{O2}$ reacted.

The amount of moles of $\ce{CH4}$ left is $x-2y$;

The amount of moles of $\ce{O2}$ left is $x-y$;

The amount of moles of $\ce{CO}$ formed is $2y$;

The amount of moles of $\ce{H2}$ formed is $4y$;

That should make one of the choices clearly false, one clearly true and one might not be so obvious, unless you assume that the forward reaction path is less favourable ($\ce{CO}$ is not very stable)

• ok after looking at and using the equations I think I have the answers. Please correct me if i'm wrong. 1 is correct because 4y is bigger than x-2y, also looking at the equation at equilibrium, 4 moles is bigger compared to 2. I believe that 2 is clearly false because since x-y is bigger than x-2y, O2 has to be bigger CH4. I'm confused about 3 but i'm guessing that it's false because 1 and 3 is not an answer choice and 1 is true – sloth1111 Jan 4 '14 at 18:20
• @sloth1111 Well, 1. is the choice that is not obvious. Try putting x = 5 and y = 2. Then try using x = 100 and y = 1. But 3. is always true because 4y > 2y. – Jerry Jan 4 '14 at 18:24
• oh boy sorry! Since you get different answers for 1 under certain conditions would that mean its incorrect? – sloth1111 Jan 4 '14 at 18:37
• @sloth1111 It's just that there might not be enough information to clearly say whether it's true or not, but since it's a multiple choice, you usually have to pick the best possible answer. – Jerry Jan 4 '14 at 18:51
• I think i'm going to go with 3 because it is the most clear since 1 and 3 isn't an option. Thank you for your help! All my teacher does is give us worksheets and i'm trying to understand the concepts – sloth1111 Jan 4 '14 at 18:57