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Q is when the reaction is not at equilibrium, K is when the reaction is at equilibrium. If Q<K, the reaction shifts right to favor the products. If Q>K the reaction shifts left to favor the reactants. Most of the time it is Q that changes, not K. K is changed by temperature only.
Q is called the "reaction quotient," and can be calculated anytime during the reaction. K is called the "equilibrium constant", and can be calculated only when the reaction has reached equilibrium. For a specific reaction (at a constant temperature and pressure), you can get different Q values depending on when during the reaction you calculate it and the initial concentrations of reactants/products, but you will only get one K value.
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