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I'm not entirely sure if there is a high pressure that there will be an higher equilibrium constant. All that is important is that the equilibrium constant stays the same if we change the pressure or the volume. Only a change in temperature will change the k value.
According to the lecture from last Friday, only temperature can change the equilibrium constant. So if the temperature remains constant, I don't think starting with a higher pressure will result in a larger K value.
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