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The reaction quotient is calculated during the reaction, rather than at the end. Depending on its value it can give you information about how the reaction will proceed (e.g. if Q>K then there are too many products and it will favour the left).
The reaction quotient can be calculated the same way as K. The concentration values used for the calculation of Q are the values before the reaction reaches equilibrium, and the values used to calculate K are the values when the reaction is at equilibrium.
Just to add on a little, the reaction quotient can be used to determine if the reaction will proceed forward or backward to reach equilibrium. For example, if the reaction quotient is smaller than the equilibrium constant, then the reaction will proceed forward to make more products to increase the value of Q until it equals the value of K.
K describes a reaction when it is at equilibrium, while the reactant quotient (value Q), can describe a reaction that is not at equilibrium, helping deduce whether the reaction is moving forward or in reverse depending on if it is sitting/shifting to the right or to the left, respectively.
Both K and Q are calculated the same way. K just describes the reaction at equilibrium and tells us whether there are more products or reactants at equilibrium. Q can be calculated at any part of the reaction and is used to determine the direction which a reaction will proceed.
Q expresses the relative ratio of products to reactants at a given instant not necessarily at equilibrium, which is why you compare Q and K to determine the direction of the reaction. The reaction shifts right if Q<K, shifts left if Q>K, and is at equilibrium when Q=K.
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