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Yes, increasing the pressure by decreasing the volume makes the side of the reaction (products or reactants) with less moles of gas favorable. The reason is that the concentrations of everything changes by the amount of volume lowered (aka if V halves, the concentration would double) which alters Q, and if Q < K, the equilibrium shifts right, and if Q > K, the equilibrium shifts left. However, if we are increasing the pressure by adding inert gas (and not decreasing the volume), then there is no shift to left or right.
A change in pressure or volume will result in an attempt to restore equilibrium by creating more or less moles of gas. For example, if the pressure in a system increases or the volume decreases, the equilibrium will shift to favor the side of the reaction that involves fewer moles of gas.
A change in volume will shift the equilibrium of a mixture. However, the change in pressure is not so cut and dry. If one changes the pressure by changing the volume, then there will be a shift in equilibrium. However, if one changes the pressure of the entire vessel by adding more of another gas. Then the concentration of the other gases will not change and thus there will be no shift.
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