Topic 5.4: Elementary Reactions

Elementary reactions: the freezer at the top of the world

This is Svalbard, a group of Norwegian islands about thirteen hundred kilometers from the North Pole, so far north that you’re not allowed to leave town without a way to scare off polar bears. And sticking out of the side of this mountain, there’s a door that leads to what might be the most important freezer on Earth.

Behind it, a tunnel runs more than a hundred meters into the rock, to a room that stays at minus eighteen degrees Celsius all year round. This is the Svalbard Global Seed Vault, and on these shelves sit more than a million samples of seeds, wheat and rice and beans and barley, sent from genebanks all over the world as a backup.

Each sample is a sealed foil packet holding about five hundred seeds, on average, and those seeds are alive, just very, very quiet. In 2020, scientists started an experiment in here that covers thirteen crops and runs until the year twenty-one twenty. Every ten years someone opens a packet and checks whether the seeds still sprout, so the people who started it won’t be around to see how it ends.

The seeds go in dry, and then the plan rests on one piece of chemistry, the fact that cold slows down the chemistry of aging. And that should puzzle you a little, because of something about the air in this room. Compared with the air in a warm room, how much slower do you think the air molecules in here are moving?

So these molecules are barely slower than the ones in your bedroom, and yet cold, dry storage like this keeps seeds alive for decades, and some for much longer. How can a little slower make that much difference? By the end of this lesson, you’ll be able to answer that, all the way down at the level of one collision between two molecules.

You’ll write the math for how often collisions happen, tell which collisions actually make something, and draw the energy map of the climb, which, it turns out, the cold never changes. A seed ages through a lot of slow chemical changes, and each one breaks down into single events between molecules, most of them collisions, so let’s shrink way down and watch just one.

One collision, one rate law

Here’s a simple model of one reaction, where an atom we’ll call A meets a molecule we’ll call BC. They collide, and B leaves with A, so we started with A and BC, and we ended with AB and C. A reaction that happens in a single molecular event, exactly as it’s written, is called an elementary reaction, and this one happens in one collision.

Now, back when we first met rate laws, the equation for peroxide and iodide said two iodide ions, but the experiment said first order in iodide, so we decided you can’t read a rate law off a balanced equation. That’s still true for an overall equation like this one, because it only tells you where the reaction starts and ends.

But an elementary reaction is different, because the equation describes the event itself, and here that’s one collision. If one A and one BC have to meet, the equation tells you exactly who’s in that collision, and that gives you the rate law, rate equals k times the concentration of A times the concentration of BC. This exact setup is a classic AP question. When a question tells you a step is elementary, that one word is your permission to read the rate law straight off the equation, and when it doesn’t, you’re not allowed to.

To see why, here’s a crowd of a dozen A atoms and a dozen BC molecules, and each faint thread joins an A to a BC it could run into. This meter counts the reactions every second, so let’s double the A and leave the BC alone. Twice as many A’s means twice as many threads, twice the chances to collide, and twice the rate.

Now we’ll go back to the start and double the A and the BC at the same time. What do you think happens to the rate?

So for an elementary step, you count the particles that take part in the step. One particle falling apart or rearranging on its own is unimolecular, with a rate law of k times its concentration. When two particles collide, like A and B, it’s bimolecular, and the rate law is k times A times B.

Here’s the one that trips people up, where two A’s collide. It’s one kind of molecule but two particles, so it’s still bimolecular, and the rate law is k times A times A, k times A squared. So two A’s never make it unimolecular, and the two doesn’t go in front of the k, it goes up in the exponent.

What about three at once? A faint ring flickers every time two particles meet, which happens all the time, but a bright ring means three hit at the same instant, and you can see how rare those are.

Three particles colliding at once is called termolecular, and you’d write its rate law the same way, like k times A squared times B, but those steps are rare, because three particles almost never reach the same spot at the same moment.

Let’s put numbers into the reaction we started with, and say k is four point oh oh times ten to the second per molar per second. A is one point oh oh times ten to the minus three molar, and BC is two point oh oh times ten to the minus three molar.

The rate is k times A times BC, so we multiply all three, units and all. One molar cancels the per molar in k, and we’re left with molar per second, which is exactly what a rate should be.

The numbers give eight point oh oh times ten to the minus four molar per second, with three significant figures because every value we started with had three. And doubling just the A would double it.

Now you try one. This step is elementary, and two A particles collide. With k equal to zero point two oh oh per molar per second and A at zero point three oh oh molar, what’s the rate?

And one more on your own. For which of these can you write the rate law just by reading the equation? So the rate law of an elementary reaction counts the chances to collide. But if you watch the crowd closely, something doesn’t add up.