Concentrations of gases at equilibrium

Question

The equilibrium constant for the reaction: $$\ce{2NO(g) <=> N2(g) + O2(g)}$$ is $2.60 \cdot 10^{-3}$ at $\pu{1000^\circ C}$. If $\pu{0.820 mol}$ of $\ce{NO}$ and $\pu{0.223 mol}$ each of $\ce{N2}$ and $\ce{O2}$ are mixed at $\pu{1100^\circ C}$, what are the concentrations of $\ce{NO}$, $\ce{N2}$ and $\ce{O2}$ at equilibrium?

I'm really stuck, because with these types of questions usually the concentration of at least one reactant or product at equilibrium is provided, so I know the direction of the equilibrium shift.

Usually I allow the variable $x$ to equal the change in concentration of each product/reactant, where I subtract or add different ratios of it from the initial concentrations of the reactants and products (depending on the direction of equilibrium shift).

However, since I do not know the direction of equilibrium shift, how am I supposed to know whether to subtract or add $x$ to the reactants/products?

Answer 1

In cases like this calculate the reaction quotient, Q (https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Equilibria/Chemical_Equilibria/The_Reaction_Quotient) using the initial concentrations, and compare the value with the equilibrium constant, K:

• Q=K implies that the system is at equilibrium
• Q > K means that there is an excess of products so the system will evolve towards the equilibrium consuming products (which means that you should subtract x from the products)
• Q < K just the other way around, the system will shift to the right to reach equilibrium (subtract x from the reactants)