Can $K_\mathrm{eq}$ (not $Q$) be equal to $0$?

My book says:

$K_\mathrm{eq}$ is always positive because the concentration at equilibrium, small or large, are always positive.

But it says $Q$ can be $0$, when the concentration of the products is $0$. Why can't $K_\mathrm{eq}$ be $0$? In other words, why can't a reaction exist such that the equilibrium condition doesn't produce any products?

  • $\begingroup$ because it wouldn't be a reaction. I guess your question is OK if we are asking if there are sets of reactants and products that contain the same set of atoms but in which the reactants are so much more stable that we don't get any products. I think that the answer would be that if a set of reactants could become a set of products, given a large enough sample at least some will be in the form of products. $\endgroup$ – Joseph Hirsch Dec 28 '16 at 4:12
  • $\begingroup$ Ah, good point. $\endgroup$ – K-Feldspar Dec 28 '16 at 4:18
  • 1
    $\begingroup$ It may be "possible" that since energy is quantized, you might have a situation where there is no product. Energy in a system is not uniform so even unlikely rearrangements can occur with some frequency, but maybe since energy is also not continuously distributed, but is quantized at all levels so you could have a situation with low enough energy that you don't get any product, but heck if the universe can result from "nothing" then I don't think so. $\endgroup$ – Joseph Hirsch Dec 28 '16 at 4:24

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