Consider the endothermic reaction

2 NO(g) <-> N2(g) + O2(g)

-If I decrease the volume of the vessel and increasing the total pressure in the vessel, what direction will the equilibrium will shift? (left/right)
(I know that decreasing the volume would shift to produce less moles of gas, but the reaction has both 2 moles of gas left and right? What do I say in this case?)

-Added a catalyst, what direction will the equilibrium will shift? (left/right) and the concentrations of the products and reactants?
(I know catalysts don't affect equilibrium at all, but should I just write "N/A" for the direction and "no change" for NO, N2, and O2???)

Thanks in advance!

You're right. There are 2 mols gas on the left and 2 mols gas on the right; therefore, pressure has no effect.

You're right again on the catalyst. A catalyst will change the speed of a rxn but not the equilibrium point (that is, the rxn will get to equilibrium faster) but the end result is no changer in the equilibrium. Therefore, the rxn doesn't shift when a catalyst is added.

To determine the direction of the equilibrium shift when you decrease the volume and increase the total pressure, you need to analyze the reaction stoichiometry. Although there are 2 moles of gas on both sides of the reaction, the number of moles of gas does not directly determine the direction of the shift in this case.

Instead, you can consider Le Chatelier's principle. When you decrease the volume and increase the total pressure, the equilibrium will shift in the direction that reduces the total number of moles of gas. In this reaction, the forward reaction produces 3 moles of gas (2 moles of NO and 1 mole of O2), while the reverse reaction produces 1 mole of gas (1 mole of N2).

Therefore, to decrease the total number of moles of gas, the equilibrium will shift in the direction of the reverse reaction. In this case, the equilibrium will shift to the left.

Regarding the addition of a catalyst, you are correct that catalysts do not affect the position of the equilibrium. They facilitate the conversion of reactants to products and vice versa, but they do not change the concentrations of the reactants or products at equilibrium.

Hence, you can state that the addition of a catalyst would have no effect on the equilibrium position. And for the concentrations of the reactants and products, you can mention that they remain the same.