The equilibrium constant \( K \) for a given reaction is affected by changes in temperature but is not affected by changes in concentration of reactants or products, volume, or the addition of a catalyst. Here's how each option impacts the equilibrium constant:
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Decreasing the concentration of a product: This changes the position of equilibrium but does not change the value of \( K \).
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Increasing volume: This can shift the position of equilibrium (depending on the number of moles of gas on either side of the reaction), but does not change \( K \).
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Increasing the concentration of a reactant: Like decreasing a product, this affects the position of equilibrium but does not change \( K \).
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Adding a catalyst: A catalyst speeds up the rate at which equilibrium is reached but does not affect the value of \( K \).
Therefore, none of these factors (decreasing the concentration of a product, increasing volume, increasing the concentration of a reactant, adding a catalyst) will change the value of the equilibrium constant \( K \). The only factor that does change \( K \) is a change in temperature.