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Knowing whether Q in relation to K would tell you at what point the reaction is at. For example, if Q is less than K you would know that it is at a pre-equilibrium state for the forward reaction because the concentration of reactants is higher than the concentration of products. And in terms of when would we have to compare the two, my guess would be that a problem would tell you K of a certain reaction and provide concentrations of the products and reactant and ask you what stage the reaction is in, or something along those lines. Hope this helps.
We can compare K and Q values to see if a reaction has reached equilibrium or not. If Q < K, the forward reaction is still favored, and we have to wait longer for the reaction to reach equilibrium; [R] > [P] . If Q > K, the reverse reaction is favored; [P] > [R].
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