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Q is representative of a chemical system's direction towards products/reactants at any given moment; so it can represent a system out of equilibrium or possibly a system in equilibrium at a very specific moment. Q can equal K in a given moment in time during a chemical reaction; it simply means that in that specific moment during the reaction, Q=K and the reaction favors neither reactants or products and is in an equilibria state.
Q can be calculated at any point during the reaction, whether the reaction is at equilibrium or not. As such, the value of Q could indicate that a reaction is not yet at equilibrium (such as Q<K or Q>K) or that it is at equilibrium (Q=K).
Q can only be equal to K when the reaction is at equilibrium. Q is just used to check to see if a reaction is at equilibrium if you are unsure. If Q is less than K, that means there is more reactants than products, so the reaction is still going to the right, while if Q is more than K, that means there is more products than reactants, and so the reaction should be proceeding to the left.
Q can be calculated at any time (including when it has already reached equilibrium) during the reaction and is compared to K to see the direction of the reaction, if Q equals K then that just means the reaction is at equilibrium.
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