Solving Problems with a System at Equilibrium

Remembering our mathematical definition of equilibrium - that a system is at equilibrium when the equilibrium expression (Q) is equal to the value of the equilibrium constant (K) - we can imagine a set of relatively simple problems.

Here’s an example:

The system A + 2 B ⇄ C + D is at equilibrium when the [A] = 1.22 M, [B] = 0.56 M, [C] = 1.00 M and [D] = 0.805 M, what is the value of the equilibrium constant?

First, we need to write the equilibrium expression:

Since we know that the reaction is at equilibrium, we know that this mathematical statement is true and we can just solve for the missing piece - in this case K.

Sometimes we need to do a little algebra:

The system 2 W + A ⇄ 2 G has a K = 1.35x10^-7. If the system is at equilibrium when [W] = 2.50 M and when [A] = 1.00 M, what is the concentration of G?

Again, we know that the system IS at equilibrium, so the equilibrium expression is true:

In this case, what we need to solve for is part of the fraction, so we’ll need to rearrange

And then take the square root

Then, we can substitute in the values we know and solve: