# Determining the equilibrium constant

This is freely translated, I hope it's not too bad.

The reaction to dehydrate methylcyclohexane to toluene in the gaseous phase: Formulate the reaction equilibrium's constant.

Now, that's not a problem - the problem is that I don't know the aggregate state. I know that $$\ce{H2}$$ is a gas and that other thing left of it seems to be toluene, which is also a gas according to the text above. So how should I now know what aggregate state the methylcyclohexane is in? I also assume everythings at standard conditions.

The solution is apparently (but it might be wrong, since it's not an official solution)

$$K_1 = a_\ce{C7H14}^{-1}\cdot a_\ce{C7H8}^1\cdot a_\ce{H2}^3 = \left(\frac{c_\ce{C7H14}}{c^\circ}\right)^{-1}\left(\frac{c_\ce{C7H8}}{c^\circ}\right)^{1}\left(\frac{p_\ce{H2}}{p^\circ}\right)^{3}$$

$$K_2=a_\ce{C7H14}^{1}\cdot a_\ce{C7H8}^{-1}\cdot a_\ce{H2}^{-3} = \left(\frac{c_\ce{C7H14}}{c_\ce{C7H8}}\right)^1\left(\frac{p_\ce{H2}}{p^\circ}\right)^3$$

whereas $$K_1$$ is right and $$K_2$$ is left.

I mean that's clear and everything but how do I know the aggregate state of $$\ce{C7H14}$$?

• I think you read is as "(dehydrate Methylcyclohexane to Toluene) in the gaseous phase", so everything is in the gas phase. – Karsten Theis Jan 21 at 18:22
• ok - that's what I first did but then the the solution given here would be wrong. No? – xotix Jan 21 at 18:29
• For species in the gas phase you have a choice of describing their approximate activity either in terms of concentration or partial pressure. Your standard conditions are well-defined as $c^\circ$ for the organic molecules and $p^\circ$ for dihydrogen. Different choices are possible. – Karsten Theis Jan 21 at 18:35

The standard for equilibrium constants of gas phase substances is to use $$K_p$$, so in this case $$p^\circ$$ would be more appropriate than $$c^\circ$$ for the organics as well as the hydrogen. If you use $$c^\circ$$, you should use it for all gas phase components and indicate your $$K$$ as $$K_c$$. Using different standards for gas phase components in the same reaction is unorthodox. And if you use your equilibrium constant for calculation of $$\Delta G$$ for example, the simple form of the equation $$\Delta G^\circ = -RT\ln K$$ requires that the $$K$$ be $$K_p$$ for gas phase reactions. Using $$K_c$$ will give an incorrect result.
• The thing is I am very unsure about the aggregate state of all components, so it's hard to formulate $K_{1,2}$. The text might indicate that all components are a gas but then it might just say the product is a gas. Was wondering if I somehow should be able to know. – xotix Jan 22 at 8:14