# When do thermal and chemical equilibrium not coincide?

What is an example for a system, which is in chemical equilibrium, but not in thermodynamical equilibrium?

And what about the other way around?

It seems to me, that as long as Parameters like temperature $T$ and pressure $p$ are changing, there cannot not be chemical equilibrium, since chemical reactions depend on these quantities temperature and pressure. Hence, if there is chemical equilibrium the parameters are not changing, enforcing thermodynamical equilibrium.

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I think generically the answer is: they're in thermal equilibrium if they have equal temperatures, in chemical equilibrium if they have equal chemical potentials, and in both thermal and chemical equilibrium if both are equal. They do not need to be at equal pressures, which is what I assume you mean by $p$. Imagine a tall column of gas in a gravitational field. Divide it (mentally) into two systems, the one at the top and the one at the bottom. The pressure at the top and bottom will differ, but they will be in chemical equilibrium.

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