Question

Ok, so the equilibrium constant in terms of pressure is the ratio of partial pressures at equilibrium of gaseous products to reactants (all raised to the powers equal to the stoichiometric coefficients). But if I have multiple equilibriums taking place simultaneously, where, let's say, there is one (gaseous) product common to both reactions, then that means the partial pressure of that substance will actually be equal to the sum of partial pressures of the moles of that substance created from both reactions.

For example:

X(s) ⇌ Y(g)+Z(g)

R(s) ⇌ Y(g)+S(g)

Here, let's say at equilibrium the partial pressure of Y and Z (the amount of them created from reaction 1) are P₁, and that of Y and S created in reaction 2 is P₂.

My teacher said that the partial pressure of Y in the entire reaction mixture would be P₁+P₂, which makes sense. But if we write the expression for K₁ and K₂, my teacher says we will take the partial pressure of Y to be P₁+P₂. I'm having a hard time understanding why we won't just take the partial pressures of Y created in those specific reactions?

Also, is it not true that the equilibrium constant of each of these reactions would change if we put them in a mixture together, since the concentration of Y
would change because that is present as a product in both reactions? Or would it just be that the equilibrium will move in the backward direction since more product is added?

If the answer to (2) is that K will not change, then that means if I only had reaction 1 taking place, equilibrium constant for that would also take pressure of Y to be P₁+P₂, which seems obviously wrong to me- it should only be P₁.
Overall, stuff is not adding up in my mind for simultaneous equilibriums, if anyone could clear my concepts I would appreciate it!

Answer 1

The equilibrium constant, K, for each gas-phase reaction remains the same. However, simultaneous reactions affect the equilibrium position, not the constant value. When common products are present, the combined partial pressures are used in the K expressions for each reaction.

Step-by-step explanation:

When calculating the equilibrium constant (K) for a gas-phase reaction, the partial pressures of all gaseous species involved in the reactions are considered. In your example of simultaneous equilibriums, if a gas product Y is common to both reactions, the partial pressure of Y used in each equilibrium expression will indeed be P1 + P2, as the equilibrium constant expressions are based on the actual partial pressures of each species in the whole system at equilibrium.

The value of the equilibrium constant K, for a given reaction at a certain temperature, remains unchanged whether the reaction is occurring alone or simultaneously with other reactions. However, the presence of another reaction that produces or consumes a common species can alter the equilibrium position, shifting it left or right according to Le Chatelier's principle. Nevertheless, the individual value of K for each reaction stays the same because it is a ratio that only changes with temperature.