Topic 5.1: Reaction Rates

Reaction rates: the beetle’s boiling spray

This is a creek in Madera Canyon, in the mountains of southern Arizona, and this beetle, a little over a centimeter long, is a bombardier beetle. It looks like an easy meal. That’s exactly what this ant thinks, right up until it grabs one of the beetle’s legs.

Did you catch that? The beetle swung its tail end around and blasted the ant with a hot, stinging spray, and the ant wants nothing more to do with it. Let’s slow it down. That spray comes out at about a hundred degrees Celsius, as hot as boiling water, and it’s really a string of tiny bursts, hundreds of them every second.

So how does a beetle make boiling chemicals on demand? Inside, it keeps two chemicals mixed together in a little storage sac, hydrogen peroxide and molecules called hydroquinones, and as long as they stay in that sac, they barely react at all. When it’s attacked, muscles squeeze some of that mixture through a one-way valve into a tiny, hard-walled chamber lined with enzymes.

In there, the same chemicals react so fast that the mixture boils, the pressure slams the valve shut and blasts the spray out, and then the valve reopens and it all happens again. Scientists have even filmed these tiny explosions inside living beetles with X-rays. Let’s go inside the chamber ourselves. Peroxide molecules bump into an enzyme and come apart into water and oxygen gas, one after another, so fast that the whole batch is gone in a split second.

The storage sac on the left and the chamber on the right hold the very same molecules, yet in the sac almost nothing happens, and in the chamber it’s all over almost instantly. By the end of this lesson, you’ll be able to put a number on how fast a reaction goes, and explain how this beetle turns a slow reaction into a split-second one.

You’ll also be able to look at a few experiments and predict whether doubling a chemical makes a reaction twice as fast, four times as fast, or no faster at all, and the balanced equation can’t tell you that. But first, a question that sounds almost too simple. When we say a reaction is fast, how fast is fast?

To put a number on fast, let’s take the beetle’s fuel back to the lab. Hydrogen peroxide slowly breaks down into water and oxygen, the same reaction that makes the beetle’s gas. Here’s a flask of it at forty degrees Celsius, from a textbook example, and we’ll check how much peroxide is left every six hours for a day. It starts at one mole per liter, drops to point five after six hours, and keeps falling, to point two five, point one two five, and point oh six two five.

Here are those readings in a table. And here they are on a graph, with time across the bottom and the peroxide concentration up the side. A reaction rate is how much of something gets used up or made, divided by how long it took, so for the peroxide, it’s the change in its concentration over the change in time.

A table of times and concentrations with ‘find the average rate between these two times’ is a classic AP question, and the point often gets lost on the sign or the units, so let’s watch both. Over the first six hours, it goes from one point oh oh oh to point five oh oh molar, a change of negative point five oh oh molar. It’s negative because the peroxide is disappearing, so the minus sign in front makes the rate of disappearance positive.

Divide by the six hours, and the peroxide disappears at point oh eight three three molar per hour. On the graph, that’s the slope of this line, without its minus sign, and a steeper line means a faster reaction.

Let’s do the next six hours together. From six to twelve hours it drops from point five oh oh to point two five oh molar, so the rate is point two five oh over six, point oh four one seven molar per hour. It slowed to half its earlier rate, because there’s less peroxide left. We’ll come back to that idea in a big way.

Those are average rates over a stretch of time. The rate at one instant comes from the slope of the line that just touches the curve at that moment. This one touches it at the very start, where the curve is steepest, so it gives the initial rate. Twelve hours in, the tangent is much flatter, so by then the reaction is going more slowly.

Now see if you can find the average rate at which the peroxide disappears over the first twelve hours, from the two readings shown here. Give it in molar per hour. In that textbook flask, it took six hours to use up half the peroxide, and in the beetle’s chamber, a split second.

Two rates in one reaction

Back inside the beetle’s chamber, let’s freeze the action. Two reactions are going on in here, so let’s follow just the one that makes the gas. Two peroxide molecules come apart into two waters and one oxygen molecule, like this, in slow motion. For every two peroxides used up, just one oxygen appears.

This next burst will split twenty peroxide molecules. How many oxygen molecules do you think come out? Here it comes. Watch the counters. Twenty peroxides used up, twenty waters made, and ten oxygens, so oxygen appears half as fast as peroxide disappears. It’s one reaction at one moment, yet each substance has its own rate, and the coefficients in the balanced equation link them.

Let’s put numbers on it. Say a flask of peroxide with catalase uses up point oh two oh oh moles in ten seconds. That’s point oh two oh oh moles over ten seconds, two point oh oh times ten to the minus three moles per second. For oxygen, multiply by one mole of oxygen per two moles of peroxide, the peroxide cancels, and oxygen appears at one point oh oh times ten to the minus three moles per second.

Water has the same coefficient as peroxide, so it appears at two point oh oh times ten to the minus three. So the substances in a reaction don’t all change at the same rate, and you don’t need molar masses for this, only the coefficients in the balanced equation. This next one is from the 2024 AP exam. Nitrogen dioxide breaks down at the rate shown here. At what rate does oxygen appear?

What changes the speed

The same peroxide reaction takes hours in that textbook flask and a split second in the beetle, so something is changing the speed. Four big things do it, and the beetle’s favorite is the first one, a catalyst.

Here are two identical flasks of peroxide, each with a syringe to catch the oxygen. Into one goes a drop of yeast, which is full of catalase, the same kind of enzyme the beetle uses. That one fizzes and the plunger climbs, and the other barely moves. A catalyst gives the reaction a faster way to happen, and it isn’t used up, so the same enzyme keeps working.

For the other three, let’s use a reaction we can weigh, marble in hydrochloric acid. As carbon dioxide escapes, the flask gets lighter, and the laptop plots the mass it’s lost. First, concentration, with matching pieces of marble in one molar and in two molar acid. The more concentrated acid’s curve climbs faster, because more acid particles in every bit of liquid hit the marble more often each second.

Next, temperature, with one flask in ice and one in a warm bath. The warm one wins easily, because faster particles collide more often and hit harder. Last, surface area, with two marble samples of exactly the same mass, two point oh oh grams each, and you get to crush one of them.

Now it’s your turn. Crush the marble, with three strokes of the pestle. Both go into plenty of acid at the same moment. Which curve do you think the crushed marble will make?

The crushed marble fizzes from all its new faces and races ahead, but both curves level off at the same height, because it’s the same two grams of marble, so it makes the same amount of carbon dioxide, just sooner. Inside the chunk, most of the marble is hidden from the acid, and crushing it exposes new faces, so more particles can meet the acid at once. Now let’s bring all four of them together on the board, side by side.

Each factor works for a reason you can see at the particle level, and that’s what the AP exam wants you to write. With the same amount of marble or peroxide each time, none of them changed how much product we got, only how fast. Here are four trials a student ran with marble and hydrochloric acid. Every trial uses the same two grams of marble, and each one has its own temperature, acid concentration and form of marble.

So which two of these trials test only the effect of temperature? Change one thing at a time and hold the rest steady, because rate laws, coming up next, run on exactly that habit. So more concentrated acid is faster, but how much faster? Double the concentration, and does the rate double? In the peroxide flask, the rate halved when the peroxide halved, but is that a rule?