# 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 '19 at 18:22
• ok - that's what I first did but then the the solution given here would be wrong. No? – xotix Jan 21 '19 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 '19 at 18:35

## 1 Answer

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 '19 at 8:14
• I see how you could read it to mean that only toluene is in the gas phase, but in that case, the phase of the starting material would be separately indicated. The problem really only makes sense if it means that all components are in the gas phase. – Andrew Jan 22 '19 at 16:07