for this reaction:

2NO + heat <-> N2 +O2
which way would the equillibrium shift if catalyst is added?

A catalyst changes the RATE of a reaction, because it allows an alternative pathway for the reaaction to take place. Therefore, the reaction you have written may reach equilibrium faster, due to this increased rate; however, Keq (the equilibrium constant) remains the same and the point of equilibrium does not change(shift).

what if more NO is added?

More NO shifts the reaction in such a manner so as to relieve the stress which means the reaction will shift so as to use up the added NO. How can it do that? By shifting to the right the extra NO can be used. Adding N2 or O2 would shift it to the left. Adding heat would move it to the right.

The addition of a catalyst to a reaction does not affect the equilibrium position. Instead, it influences the rate at which the reactants are converted into products. A catalyst provides an alternate reaction pathway with a lower activation energy, allowing the reaction to occur more quickly. However, once the reaction reaches equilibrium, the catalyst does not have any impact on the distribution of products and reactants.

In the given reaction:

2NO + heat ā†” N2 + O2

The equilibrium position will not shift when a catalyst is added. The catalyst will only facilitate the forward and backward reactions, leading to a faster attainment of equilibrium.