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At equilibrium, the rate of product formation and the rate of reactant formation cancel out but do not necessarily stop. This is what is meant by the saying "all chemical equilibria are dynamic" . K is a ratio of activity that is why pressure and concentration can both be used.
The equilibrium constant is when the concentrations of the reactants and products at equilibrium are calculated such that product concentration at equilibrium is divided by the reactant concentration at equilibrium. The k rate constant is referring to the rates in which the product is turning to reactant and vice versa. These rates cancel out at equilibrium as they are replacing each other at equal rates.
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