## Reaction quotients

If you let a chemical reaction run for long enough, it will reach equilibrium.  That’s just a fact of life.  Reaction + time = equilibrium.

However, how can you tell if a reaction has reached equilibrium yet?  The answer: Calculate the reaction quotient, Q.

Or you could ask this guy.

Let’s learn how.

What is Q?

Let’s consider the equation we’ve been looking at for the last few tutorials and take a look at the equilibrium expression:

Now, let’s take a look at the expression for the reaction quotient:

See anything familiar?  If not, go take a look again.  Yep, you got it:  K and Q are the same thing.  This leads to an obvious question:  Why do we have the same  expression for two different values?

Not exactly.  Check it out:

• K describes a system at equilibrium.  For the reaction above, K describes the concentrations of every chemical in your beaker when everything has reached equilibrium.
• Q describes a system which may or may not be at equilibrium.  The very instant you throw your reagents into a flask, you can start calculating Q.  Not surprisingly, Q will change over the course of the reaction as the concentrations of the reagents and products shift.  However, as the equation suggests, once the reaction finally reaches equilibrium, K and Q are the same.

Essentially, Q is just a way of monitoring the progress of a chemical reaction that hasn’t yet achieved equilibrium.

If I look at Q, what does it tell me?

It tells you whether a chemical reaction has reached equilibrium.

• If Q > K, this means that there are more products in your particular mixture than there will be at equilibrium.  As a result, as time progresses, you can expect to see some of the products revert back to reagents.
• If Q < K, this means that there are more reagents in your mixture than there will be at equilibrium.  As time passes, you’ll see more products being formed.
• If Q = K, you’ve reached equilibrium.  You’ve reached your final concentrations of products and reagents.

In a practical sense, Q allows you to figure out if your reaction is done yet.  When you throw a bunch of chemicals into a beaker, you can monitor the concentrations of each chemical to figure out what Q is.  When the Q you calculate is equal to the K value you know for the reaction, then you’re done!

Photo credits:

John de Lancie, the man who played “Q” on several Star Trek TV series:  By “Pinguino” (“Pinguino’s” flickr account) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)%5D, via Wikimedia Commons.

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