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K is the equilibrium constant, while Q is the reaction quotient and can, therefore, be used at any time during the reaction. This means that Q can be calculated even when the reaction is not at equilibrium, leading to K and Q possibly being different numbers. by comparing the different values of K and Q, you can find the direction that the reaction is favoring at the time. If Q < K, then [R] > [P], so the forward reaction is favored. If Q > K, then [P] > [R], so the reverse reaction is favored.
K would be known as the equilibrium constant, Kc. K can also be used to calculate the partial pressure of a species at equilibrium, Kp. Q is the reaction quotient and it is used to determine which direction a reaction will proceed. Q or Qc or Qp are calculated the same way as K, but for Q, the reaction doesn't have to be in equilibrium.
K is a fixed ratio and will therefore always be the same number (for each reaction at a certain temperature), but Q is the P/R ratio calculated at any point in the reaction. Q can be used to figure out whether a reaction is at equilibrium, and if not, which direction the reaction is moving.
K and Q have the same values at equilibrium. That is why, if they are not equal you can see whether the reaction going forwards or backward by comparing the Q and the K. If Q is bigger than K, that means the reaction at this time has more products than it's equilibrium state, which is what the K value is. So we will see that this reaction will rely more on to the left side and produce more reactants to reach equilibrium.
K is the fixed equilibrium constant value for a certain reaction. Q is the reaction quotient and is used when it is certain that the reaction is not at equilibrium yet. For example, if you add more products, the reaction will not be at equilibrium the moment you add more products, so you would calculate the Q, compare it to K and see how the reaction would respond to make itself reach equilibrium.
The difference in K and Q is because K is taken when the reaction is at equilibrium and Q is taken at another point to determine if the reaction has reached equilibrium. The values of Q and K also help to determine which way the reaction will move from the point where Q was taken. This can also help with ICE tables to determine if the change will be positive or negative.
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