How can a balanced chemical equation be used to write an equilibrium-constant expression?

An equilibrium constant expression relates the concentrations of the species when the system reaches equilibrium. It allows us to calculate how the equilibrium concentrations change when we change the concentrations of any of the reactants or products.
We often consider a generic reaction of the form
2A + B ⇌ 3C +2D
The equilibrium constant expression for this reaction is
Keq = [C]³[D]²/[A]²[B]
where Keq is the equilibrium constant for the reaction. Keq does not depend on the original concentrations.Rather, the concentrations adjust during the reaction so that at equilibrium the concentrations satisfy the Keq expression.
The concentration of a solid of a liquid does not change during a reaction (although the amount does), so we omit it from the equilibrium constant expression.
For example, if we had the reaction 2A(aq) + B(s) ⇌ 3C(aq) + 2D(l), we would omit the concentrations of A and D from the equilibrium constant expression and write Kc = [C]³/[A]², where the subscript c indicates that we are using concentrations.
For gaseous reactions, we can use the partial pressures of the gases in the reaction instead of the molar concentrations. This equilibrium constant is denoted Kp.
Kp =Pc³Pd²/Pa²Pb. Again, if any of the components is a solid or a pure liquid, we omit its pressure from the equilibrium constant expression.
Let’s use the balanced for some reactions to write the corresponding equilibrium constant expressions.
N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
Kc = [NH₃]²/[N₂][[H₂]³
Kp = P(NH3)²/{P(N2)P(H2)³}
BaO(s) + CO₂(g) ⇌ BaCO₃(s)
Kc = 1/[CO₂]
Kp = 1/P(CO₂)
CH₃COOH(aq) + C₂H₅OH(aq) ⇌ CH₃COOC₂H₅(aq) + H₂O(l)
Kc = [CH₃COOC₂H₅]/{[CH₃COOH][C₂H₅OH]}
Note again that, whenever a component is a solid or a liquid, that component does not appear in the equilibrium constant expression.
Here’s a lecture video on this topic:

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