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We only use Kp when the reaction system is at equilibrium, other than that, we will always calculate Q and compare it with Kp (or sometimes Kc if the question is about concentrations) to see which direction (products or reactants) the reaction will move towards. Hope this helps :)
Q looks at the system when it is not at equilibrium(when it ratio of products to reactants is equal to Kc). Q is compared to Kc to see whether the reaction proceeds to the right or the left. If Q<Kc then the reaction will "shift" to the right. If Q>K then the reaction will "shift" to the left. If Q=Kc, then the system is at equilibrium.
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