Entropy

Entropy, in "simple" terms is a measure of randomness.

Okay, that's not really simple.

Let's think about a few specifics. A pane of glass in a window is much more organized than the pieces created when it is broken. So the pieces have more entropy than the window pane.

If you open a bottle of perfume, the liquid perfume will evaporate and spread around the room. The evaporated, spread-out molecules will be less organized than the liquid was (and therefore have more entropy than the liquid did).

Entropy also applies to heat. If you heat a penny to red-hot and then drop it into cool water, the penny will give away heat to the water until the penny has cooled down and the water has warmed up. So, the heat that started in the penny is now spread around all of the water (and the penny). There is more entropy in the spread out heat than there was when the heat was concentrated in the penny.

Entropy is measured in terms of energy. Specifically, entropy is the amount of energy you would need to remove from something to cool it down make it come together as a perfect crystal at absolute zero.

In human terms, the entropy of your room could be measured in terms of how much work you would have to do to clean it. A neat room has much less entropy than a messy one.

Why do we care?

We care about entropy, because it (along with heat) determines whether or not reactions occur.

Here's the basic idea: Nature is getting messier. 

That's not surprising, if you think about it. Your room gets messy without any effort, but it never accidental gets cleaner. Glass breaks, but glass shards never randomly form a juice glass. The smell of a skunk spreads out, it never re-concentrates. The sugar never settles out of soda.

The reason behind this is (arguably) about statistics. There are FAR MORE ways for the "stink" molecules from a skunk to spread around the neighborhood than there are ways for them to collect together in a small space. There are only so may ways that sugar molecules can come together to form solid crystals, but a HUGE number of ways that they can move around separately in the solution.

Here's another example think about it. One of the problems people had with corded ear-buds was that the cord always got tangled in your pocket. Even if you wrapped it carefully before you put it into your pocket, when you pulled them out, the cord was a mess. To understand this, simply imagine the carefully wound cord in your pocket. When you walk, the things in your pocket will move a little. If you think about ALL of the ways that the cord could shift, MOST of them will make the cord less neat. So, if all of the movements of the cord are random, MOST of the time those movement will make the cord messier.

But, what if I clean my room?

It is absolutely true that you can clean your room, or wind your ear-buds cord and your room or the cord will get neater. However, we need to look at the bigger picture. When you clean your room, you use energy. That energy started as food that you ate. The process of digesting that food and breaking it down into sugars made it messier. Then, inside your cells, you burned that sugar. So relatively organized molecules of sugar became carbon dioxide that you exhaled to mix with the atmosphere and water that you both exhaled and excreted.

In the end, the mess you make is always bigger than the mess you clean up.

Fortunately for you, in first year chemistry classes we generally focus on a small thing (like the state of your bedroom, or a single reaction) rather than looking at the big "universal" picture.

So, we can say that any reaction that increases entropy is likely to happen.

The math

The question that should have popped into your head is "How do I know if my reaction increases entropy?"

The answer is (actually) simple:

where ΔS_rxn is the change in entropy for the reaction, ΣS_products is the sum of the entropy values of the products, and ΣS_reactants is the sum of the entropy values of the reactants.

This formula is JUST like the formula for calculating heat of reaction from formation reactions. In fact the entropy values come from the same table (just a different column).

One last question: "What does the statement above mean by "likely" to happen? The answer to that question is about Gibb's Free Energy.