Equilibrium Constant

In order to analyze the progress of a reversible chemical reaction, we can use a quantity known as the reaction quotient, denoted Q. For a chemical reaction with the form

mA(g) + nB(g) ⇌ xC(g) + yD(g)

the reaction quotient is

This is the reaction quotient. It's the concentrations of the products raised to the power of their stoichiometric coefficient divided by the concentrations of the reactants raised to the power of their stoichiometric coefficient. If Q = 1, then there's pretty as much products as reactants. If Q < 1, then there's more reactants than products and if Q>1, then there's more products than reactants.

The reaction quotient is dimensionless even though the quantities that comprise it do have units.

You can also express the reaction quotient in terms of partial pressures:

Note that for the reaction quotient, we made the reaction at the top of the page have all gaseous species. If a species is a solid or liquid, omit it from the reaction quotient because the concentrations of solids and liquids are pretty much 1.

NH₄Cl(s) ⇌ NH₃(g) + HCl(g)

So, for example, the reaction quotient of the reaction above would be:

This is the molar reaction quotient because we omit the solid ammonium chloride reactant.

When the reaction reaches equilibrium, we have a different name for the reaction quotient. When the system reaches equilibrium, Q become a quantity known as K, also known as the equilibrium constant. Note that K can also be expressed in terms of partial pressures like Q.

For the reaction system above, K would look this:

So, basically K = Q at chemical equilibrium.

If Q>K, then there is less products and more reactants at equilibrium than there currently is in the system. This means that as the system proceeds towards equilibrium, the reverse reaction will have a greater rate than the forward, so the amount of products will decrease and the number of reactants will increase as the system approaches equilibrium.

If Q=K, then the system has reached equilibrium. The relative amount of products and reactants is equal to that at equilibrium.

If Q<K, then there is less reactants and more products at equilibrium than there currently is in the system. This means that as the system proceeds towards equilibrium, the forward reaction will have a greater rate than the reverse, so the amount of products will increase and the number of reactants will decrease as the system approaches equilibrium.

So, the general structure of the equilibrium constant for reversible reactions is pretty simple. However, what if we add a bit of a layer to our analyses of equilibrium processes. For example, what if we flip the reaction so that the right side of the reaction becomes the left side and vice versa. Taking our example equation above, this means the flipped reaction is:

NH₃(g) + HCl(g) ⇌ NH₄Cl(s)

How do we find K(and Q) for this? Well, it's actually quite simple! Just pretend that this reaction was the original and find K by taking the amount of products over reactants, with each species raised to their stoichiometric coefficient.

Now, what happens when you multiply a reaction by an integer coefficient. In this case, let's multiply the ammonium chloride reaction by 7. Now, the reaction is:

7NH4Cl(s) ⇌ 7NH3(g) + 7HCl(g)

What is K(and Q) for this? You can also solve this straight up by just placing the products raised to the power of their stoichiometric coefficients divided by the reactants.

What happens when you take two reversible reactions and add them together? It's actually not too difficult. Let's take our ammonium chloride reversible reaction and couple it with the following reaction below:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

If we add the reaction above to our original ammonium chloride equation all the way above:

NH₄Cl(s) ⇌ NH₃(g) + HCl(g)

+

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

We get this:

NH₄Cl(s) + N₂(g) + 3H₂(g) ⇌ 3NH₃(g) + HCl(g)

If you find the equilibrium constant for this reaction, you get this:

If you notice, the equilibrium above is equal to the product of the two reactions that are added together to make it.

Thus, when you add two coupled reversible reactions together, you multiply their equilibrium constants together.

The same rule for equilibrium constants in this sub-topic are applied to reaction quotients.