Determining if a System is at Equilibrium

We know that a system is at equilibrium when the equilibrium expression IS equal to the value of the equilibrium constant. That is, when K = Q.

We can turn that statement on its head to say that if K=Q then the system must be at equilibrium. That allows us to solve some simple problems like this:

The system A + 2 B → C + D has a K = 4.12. If [A] = 1.00M and all of the other concentrations are 4.12 M, is the system at equilibrium?

If it is at equilibrium, then the math below will be true.

If we substitute in our values, we see that K is NOT equal to Q

so, our system is NOT at equilibrium.

A Note about Zeros

It is fairly common to be given a system where one or more of the compounds is missing - that is, where one or more of the concentrations = 0. This can present a mathematical problem.

As an example, you may find yourself trying to determine whether the following math is true?

Your math instructor will tell you that the question is unanswerable, since the fraction on the right is undefined. But this is not a math class. We don't care what the actual value on the right is. All we need to know is that it is NOT equal to the value of K on the left. Therefore the system is NOT at equilibrium.

If you prefer logic to "undefined" math, you can think about it this way. If one of the compounds in the system (reactant or product) is missing, then it CANNOT collide with anything else and that reaction CANNOT occur at any rate. Therefore, the other reaction, no matter how slow, MUST be faster. Therefore the system is NOT at equilibrium.