[BabyGoofball]

Question: There is a homogeneous solution with no solute at the bottom (no residue). This mixture can be in which state(s)?

a) Unsaturated
b) At equilibrium
c) Supersaturated

I know (a) and (c) are definitely right. My chemistry teacher from 23 years ago insisted that (b) is incorrect. Given the state of (a), (b), and (c) are technically a continuum, it doesn't make sense that it CANNOT be at equilibrium? Yes, I understand that you cannot be certain it is at equilibrium, but is it actually IMPOSSIBLE that the mixture in question is in fact, at equilibrium? Please help me find closure. Thanks.

[Corribus]

I do not think many people would agree with your teacher regarding (b), although I can anticipate the argument being made. From the standpoint of solubility equilibrium, the argument being made is something like this: without a precipitate, the solution cannot reach a point where Q = K. Therefore, the solution cannot be at equilibrium.

Solubility equilibria are a little unique because one of the participants in the “reaction” is a solid, which by definition has an activity of one. Therefore, Q only depends on the concentrations of the aqueous solutes. The solute(s) only begin to drop out of solution when their concentrations reach the point such that Q is equal to K. After that, any additional solute drops out of solution, and Q still is equal to K, because the precipitate does not contribute to the equilibrium expression. If you define the point of equilibrium strictly in terms of Q and K, then it is true that an unsaturated solution does not satisfy this criterion for equilibrium.

That’s all well and good, but if we take a broader view of equilibrium, this changes. Equilibrium is commonly defined as a state in which the forward and reverse rates of any process involved are equal. More importantly, there will be no tendency for the system to change without an external stimulus. The latter follows from the former. (Some non-equilibrium situations, like a supersaturated solution, might appear to be in equilibrium based on a “no tendency to change”. I would not consider this to be an equilibrium, more of a kinetic barrier to the equilibrium state.) An unsaturated solution satisfies the latter definition of equilibrium. There is no kinetic barrier in play here – the system will persist indefinitely unless the conditions are changed. It may be true in an unsaturated solution the backward reaction is faster than the forward reaction- any precipitate formed is instantly changed back to solute. An unsaturated solution does not satisfy a rate-based definition of equilibrium, either. But it does satisfy the "change" based definition of equilibrium, which I think is the most important because it defines how a system actually behaves.