# Can the equilibrium constant be equal to 0? [duplicate]

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?