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Actually, I don't think that an inert gas affects the equilibrium constant at all because if the pressure of a reaction vessel is increased by adding an inert gas, the moles of reactant/product and the volume remain constant. Essentially, unless there is a change in reactant/product concentration, the introduction of inert gas will not have an effect on the reaction, so the equilibrium constant will not change.
Going off of what what previously said, the inert gas will change the pressure of the system. However, since this pressure isn't as a result of compression (which would decrease the volume and change the concentrations), it won't affect the calculations. Because of this, adding an inert gas will not affect the equilibrium constant.
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