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K is a constant for a reaction that tells you the concentrations of products and reactants needed for the reaction to be at equilibrium. Q is not a constant, and can be calculated (and is different) at any point in a reaction. The value of Q compared to K tells you which way the reaction is going at that moment.
K is the constant that gives the ratio of equilibrium concentrations of a reaction whereas Q gives the ratio of the concentration of the products to the reactants at any given point in time as the reaction is occurring. They are both calculated the same way, however, Q can be calculated at any point in time whereas K is only calculated when the reaction has reached equilibrium. Calculating Q provides a way of knowing which way the reaction will proceed. For example, if Q < K, then the reaction has not reached equilibrium and the equilibrium ratios have not yet been attained and the reaction will proceed in the forward reaction. If Q > K, then the reaction will proceed in the reverse reaction since the equilibrium constant is smaller than the current ratios.
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