## Equilibria – our little busy friend in the beaker

I fell down one time when I was walking on the street.  When this happened, I said that I had lost my sense of equilibrium and fallen down.  People were very sympathetic, though I could tell they were laughing on the inside because they all knew that I just wasn’t paying attention and tripped on a crack in the sidewalk.  Not that any of this is relevant to equilibria.  I’m just sayin.

Artist’s conception of me falling over.

Anyway, when your chemistry teacher talks about equilibria, he or she means something different than not tripping on the sidewalk.  Instead, what they mean is that some process is in balance, and is stable – in perfect harmony, if you will.

Or something like that.  Let’s just keep reading.

What’s an equilibrium?

Let’s say that there’s a lovely young lady on one side of your school gymnasium.  Given her looks, all of the gentlemen in your school are attracted to her and walk on over to say hello.  There are 100 male students in your school, and 90% will walk over to say hello every minute.

I’m pretty sure she didn’t go to my school.

The problem is that once they get to the other side of the room, they find that she smells as if she never heard of deodorant and wrestles with unwashed dogs in her spare time.  This drives 10% of the boys away every minute.  As a result, the number of boys around her constantly changes. Here’s how:

Before the boys start walking at all, there are 100 boys on the left side of the gym and 0 boys on the right side.

• After one minute, there are 10 boys on the left side of the gym, and 90 boys on the right side.
• After two minutes, there are 10 boys on the left side of the gym, and 90 boys on the right side.
• After three minutes, there are 10 boys on the left side of the gym, and 90 boys on the right side.

Wait a sec… what’s happening here?  How can you possibly balance out the number of boys on each side if the proportions that move are so different?

Let’s go back to the two minute mark:

• Of the 10 boys on the left side of the gym, 90%, or 9 boys, walk over to the right.
• Of the 90 boys on the right side of the gym, 10%, or 9 boys, walk over to the left.

Since 9 boys are walking in both directions, the population of both sides remains the same.  This works because 90% of a small number is equal to 10% of a very large number.

Important things about equilibria:

Though this example is weird, it does a pretty good job of clarifying the nature of chemical equilibra.  For instance:

Equilibria have to be reversible.¹  In our example, boys were free to move back and forth across the gym.  However, if the girl cut off their legs, the number of boys on the right would just keep growing and the number on the left would keep shrinking.

An equilibrium process is dynamic.  No matter how long we let everybody hang around in the gym, some of the boys will move toward the girl and some will move away.  In this equilibrium process, something is always happening.  However, this doesn’t always mean that an equilibrium always looks dynamic.  For example, if the school principal were to ask what the heck was going on in the gymnasium, a teacher visiting two minutes after everybody showed up would tell the principal that 90 boys were talking to the girl and 10 weren’t.  If another teacher showed up one minute later, they’d say the same thing.  The principal might conclude that everybody was staying in one place because he can’t see everything that happens – in reality, people are moving back and forth all the time.²

At equilibrium, the concentrations of products and reagents don’t change.  However, please remember that just because the concentrations of these compounds don’t change doesn’t mean that nothing is happening.  Instead, products and reagents are just going back and forth at the same rates.

Le Châtelier’s principle:  When changes are introduced to chemical equilibria, the equilibrium will shift to minimize the effect of this change.  This idea can be used to our advantage when doing reactions, as we’ll see later.  For now, let’s imagine that the girl pulled out a dead squirrel at the four minute mark and started playing with it.³

Or, even worse, used it for an afternoon snack.

As a result, perhaps only 80% of the boys on the left side of the gym will go say hi, while 40% of the boys who are already there will be creeped out and leave.  As a result, the equilibrium will look like this from four minutes onward:

• Four minutes:  7 boys move from left to right (80% of 9) and 36 (40% of 90) will go from right to left.  This gives us a population of 38 on the left and 62 on the right.
• Five minutes:  30 boys move from left to right (80% of 38) and 25 (40% of 62) will move from right to left.  This leaves us with 33 boys on the left and 67 on the right.
• Six minutes:  27 boys go left to right (80% of 33) and 27 boys go from right to left.  This leaves the population of boys unchanged.  And it will continue like this for good.

Of course, there are chemistry equations and stuff that go along with all of this, but if you really understand this example, then you really understand how equilibria work.  And you also understand how teenage boys work.

On the one hand, she eats squirrels. On the other hand, boobs. OK, let’s do this!

Chemical equilibria you might have seen:

So, let’s look at some equilibria you might have bumped into over the years:

• The reason your ice cream turns rubbery if left uneaten is due to equilibria processes. Basically, what happens is that in your freezer, some of the water is able to turn directly from the solid to gas phase (ice to vapor) and back again.  As a result, the total amount of ice and water in the freezer is the same, but the ice doesn’t necessarily end up where it started.  As a result, the water that makes your ice cream smooth recrystallizes on the top of the container, which isn’t very awesome.
• Similarly, the reason your ice cubes get all weird and bent over time is due to the same equilibrium process.
• If you make a saturated solution of sugar, the crystals will change appearance over time.  This takes place because some of the sugar molecules dissolve, while others are redeposited at the same time in different places.

Behold! The magic of chemistry!

• Ice water in the fridge.  If you put a glass of ice water in the fridge, you’ll notice that given optimal conditions, the ice neither melts nor increases.  Under these ideal conditions, ice molecules melt at the same rate that water molecules freeze.

Enough of that.  We’ll talk more about equilibria in the next tutorial.

Footnotes:

1. The way this is phrased suggests that some reactions are reversible and some are irreversible. In one sense this is right and in another it’s not. According to the principle of microscopic reversibility, any reaction that takes place can – and does operate in reverse as well, regenerating reagents from products.  In practice, however, this reverse rate is frequently so small that it’s easily ignored. For this reason, I probably wouldn’t wait around for a log to unburn itself if I were you.
2. Please don’t say that at equilibrium things stop happening.  They don’t.  Not at all.  So don’t say it!  Just because they happen at the same rate in both directions doesn’t mean that nothing happens.
3. I actually knew a girl who did this when I was in high school, but she was one of those weird kids who never showers and picks her nose.  I think she won an art award at some point, though, which I guess confirms the idea that artists are eccentric.

Photo credits:

• Falling over:  Image courtesy of Stuart Miles at FreeDigitalPhotos.net
• Stinky girl: Image courtesy of radnatt at FreeDigitalPhotos.net
• Squirrel eating girl:  Image courtesy of radnatt at FreeDigitalPhotos.net
• Vampire girl: Image courtesy of Stuart Miles at FreeDigitalPhotos.net
• Go for it guy: Image courtesy of imagerymajestic at FreeDigitalPhotos.net
• Ice water:  Image courtesy of taesmileland at FreeDigitalPhotos.net
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