Why Do Some Reactions Get Hot?: Going Further 9–12

Turn the knob of a gas stove and strike a match, and a ring of blue flame roars up hot enough to boil a pot of dal in minutes. Yet the gas in the cylinder is cold. Touch the cylinder: it is no warmer than the kitchen. The oxygen in the air is cold too. Mix the two cold gases, give them a spark, and out comes heat. Where was it?

You learned in Grade 9 that reactions like this are exothermic: they give out heat Grade 9: Exothermic reaction. Others, like baking soda in vinegar, are endothermic: they take heat in, and the glass gets cooler Grade 9: Endothermic reaction. But why? Why does burning gas give out heat, while making nitric oxide in a lightning flash takes it in? The answer is in the bonds that hold the atoms together, and it is simpler than you might expect: breaking bonds takes energy, making bonds gives it out, and a reaction does both.

A bond is a pull

You met covalent bonds in Grade 9: two non-metal atoms share a pair of electrons Grade 9: Covalent bond. The shared electrons sit between the two nuclei, and both nuclei, being positive, pull on them. So the electrons hold the two atoms together, like a glue made of attraction.

Think of two strong magnets stuck together. To pull them apart, you have to pull hard, and keep pulling until they are well apart: you do work on them, and that energy comes from your arm. Now let them go near each other: they snap together, with a click, and the energy you put in comes out again, as the sound of the click, a little heat, and the motion of the magnets.

A bond is the same. Breaking a bond always takes energy in. Making a bond always gives energy out. There are no exceptions: atoms that attract each other never give out energy when you pull them apart.

Here are the two atoms of a hydrogen molecule, H₂, and a graph of their energy against the distance between their nuclei (in picometers: 1 pm = 10⁻¹² m). The graph is hydrogen’s, measured. Move the slider to pull the atoms apart, or push them together, and watch the energy. (A real molecule always jiggles a little, so it sits slightly above the very bottom of the valley; that is why the energy to break it is 436 kJ/mol, not the full depth.)

Distance: 74 pm

Distance between the nuclei: 74 pm
Energy (atoms apart = 0): −458 kJ/mol

At 74 pm the energy is lowest: the bottom of the valley. This is the bond. Each nucleus pulls on the pair of electrons the atoms share between them.

The energy needed to break a bond is its bond energy. The same amount comes out when that bond forms. Some bonds are much stronger than others: two atoms sharing two pairs of electrons (a double bond) or three pairs (a triple bond, Double and triple bonds) are held more tightly than by one.

Counting bonds by the mole

One bond is far too small to measure on its own. Chemists measure bonds in huge batches, the way eggs are sold by the dozen. Their batch is the mole: 6.02 × 10²³ of anything. It is a useful number because a mole of molecules has a mass, in grams, equal to the molecular mass you learned to work out in Grade 9 Grade 9: Molecular mass: a mole of hydrogen molecules, H₂, has a mass of 2 g; a mole of water, H₂O, 18 g; a mole of methane, CH₄, 16 g. So bond energies are written in kilojoules per mole (kJ/mol): the energy to break a mole of those bonds.

Bond	Found in	Bond energy (kJ/mol)
H–H	hydrogen, H₂	436
O=O	oxygen, O₂	498
N≡N	nitrogen, N₂	945
Cl–Cl	chlorine, Cl₂	242
O–H	water, H₂O	463
C–H	methane, CH₄	416
C=O	carbon dioxide, CO₂	804
N–H	ammonia, NH₃	391
H–Cl	hydrogen chloride, HCl	431
N=O	nitric oxide, NO	631

The same kind of bond is a little stronger in one molecule than in another, so tables give average values, and different books give slightly different numbers (C–H as 412, 413 or 416, for example). Answers worked out from them are close, but not exact.

Which of these is true for every chemical bond?

Pick an answer to see why.

Breaking and making: adding up a reaction

In a chemical reaction, the atoms don’t change: they swap partners. The bonds in the reactants break, and new bonds form to make the products. So we can model any reaction in two steps:

Break every bond in the reactants, leaving separate atoms. This takes energy in.
Make every bond in the products from those atoms. This gives energy out.

Then compare the two:

If making the new bonds gives out more energy than breaking the old ones took in, the extra comes out as heat: the reaction is exothermic.
If making the new bonds gives out less, the difference must be taken in from the surroundings: the reaction is endothermic.

Real molecules don’t fall completely to pieces and then rebuild: bonds break and form a few at a time, often at the same moment. But the total energy change is the same whichever way the reaction goes, so the two-step model gives the right answer. (This is Hess’s law, found in 1840: see the story below.)

Chemists write the energy change of a reaction as ΔH (“delta H”), the change in the energy of the chemicals. It is negative for an exothermic reaction (the chemicals lose energy, to the surroundings) and positive for an endothermic one.

Pick a reaction, then press the steps in order. Watch the atoms come apart and join up again, and the energy climb and fall on the ladder below. The energies are for the amounts in the equation, in moles (2H₂ + O₂ means 2 moles of hydrogen and 1 of oxygen). Which reaction is endothermic?

Reaction:

Step:

Taken in, breaking bonds: —
Given out, making bonds: —
Overall: —
Measured: —

Start: the molecules of 2H₂ + O₂. Every bond in them holds its atoms together. Break them all to see what it costs.

Worked example

Lightning makes nitric oxide

In a lightning flash, nitrogen and oxygen from the air combine: N₂ + O₂ → 2NO. Work out the energy change. Why does this reaction need lightning?

Answer

Break: 1 N≡N + 1 O=O = 945 + 498 = 1,443 kJ in.

Make: 2 N=O = 2 × 631 = 1,262 kJ out.

Energy change: ΔH = 1,443 − 1,262 = +181 kJ.

Making the new bonds gives out less than breaking the old ones took in, so the reaction is endothermic: it takes in 181 kJ (the measured value is 181 kJ too). The main reason is nitrogen’s triple bond, one of the strongest bonds there is, at 945 kJ/mol. Breaking it takes a huge amount of energy, which is why the nitrogen that makes up most of the air hardly reacts with anything. The intense heat of a lightning flash, around 30,000 °C, breaks enough of those bonds for the reaction to happen.

Bright, branching bolts of lightning from a purple night sky down to a dark, flat landscape with an electricity pole — **Figure 2.1** Lightning near Bengaluru, India. A flash heats the air in its channel to around 30,000 °C, hot enough to break the triple bonds of nitrogen. The nitric oxide it makes ends up, after more reactions, in the soil as nitrates, a natural fertilizer. Photo: Ezhuttukari, CC BY-SA 3.0

In a reaction, breaking the bonds of the reactants takes in 2,000 kJ, and making the bonds of the products gives out 1,700 kJ. What happens?

Pick an answer to see why.

A story from science

A doctor in Siberia and the sum that never changes

Germain Hess was born in Geneva, in Switzerland, in 1802, and taken to Russia by his family when he was a small boy. He trained as a doctor, and worked for a time in Irkutsk, in Siberia. But chemistry was his love, and he became a professor of chemistry in St Petersburg.

There Hess spent years measuring the heat given out by reactions, especially the mixing of acids with water and with bases. He noticed something remarkable. Whether he made a product in one step or in several, the total heat came out the same. In 1840 he published the rule: the heat of a reaction depends only on where it starts and where it ends, not on the path in between. This is Hess’s law.

Hess found it before anyone had stated the law of conservation of energy (Julius Robert Mayer in 1842, James Joule in 1843, Hermann von Helmholtz in 1847). Today we see that Hess’s law follows from it: if two paths from the same start to the same end gave different amounts of heat, you could go one way and come back the other, and make energy from nothing. It is also why the break-everything-then-make-everything model works: it is just one more path.

Energy diagrams

Chemists draw a reaction’s energy as a diagram: the energy of the reactants on one level, the products on another, and the reaction as a path from one to the other. Here the reacting chemicals are the system; everything else, the test tube, the water, the air, your hand, is the surroundings. Energy is never made or destroyed. When the system’s energy falls, exactly that much goes into the surroundings, mostly as heat; when the system’s energy rises, exactly that much comes out of the surroundings.

In an exothermic reaction the products are lower than the reactants. The difference goes out to the surroundings, and they get hotter.
In an endothermic reaction the products are higher. The difference comes in from the surroundings, and they get colder, unless heat is supplied.

But there is a hill on the way. You met it in Grade 10: particles react only if they collide with at least the activation energy Grade 10: Why reactions happen at all. Now you can see what that energy is for: before new bonds can form, some old ones must start to break, and that takes energy first.

Figure 2.2 The energy of a reaction and its reverse, to scale. Left: nitrogen dioxide and carbon monoxide climb a hill of 132 kJ, then fall to products 226 kJ lower: exothermic. Right: the same reaction backwards climbs a hill of 132 + 226 = 358 kJ and ends 226 kJ higher than it started: endothermic. Both go over the same top. (132 kJ is the usual textbook value, for the reaction as it goes in one step at high temperatures; below about 225 °C it takes a different path, in two steps.)

This is why the gas from a stove doesn’t catch fire by itself: its molecules and the oxygen molecules in the air hardly ever collide hard enough to get over the hill. A match or a spark gives a few of them the energy to do it. Once they react, they give out far more energy than the hill took, and that heat lifts their neighbors over the hill too. So a fire keeps itself going, as long as there is fuel and oxygen. An endothermic reaction can’t keep itself going like this: limestone turns into lime only while the kiln is kept hot.

In the energy diagram of a reaction, the products are 50 kJ higher than the reactants, and the top of the hill is 120 kJ above the reactants. Which statement is right?

Pick an answer to see why.

Did you know?

A reaction that freezes water

Mix two white powders, barium hydroxide and ammonium chloride, in a flask, and stir. The solids turn into a wet slush that smells of ammonia, and the flask gets so cold, to around −20 °C or below, that a puddle of water under it freezes it to the bench. (The barium hydroxide must be the crystals with water in them, Ba(OH)₂·8H₂O.) It is one of the most endothermic reactions you can do by just mixing. (It is a teacher’s demonstration only: barium compounds are poisonous.)

Why does it happen at all, if the products have more energy? Because the products, a watery solution and ammonia gas, are far more spread out and mixed up than two neat solids, and in chemistry, spreading out counts too. That is a story for another topic: Why do some reactions stop halfway?

How much heat? From the reaction to the pot

To compare fuels, we want the heat from each gram. Burning a mole of methane gives out about 800 kJ, and a mole of methane has a mass of 16 g (12 for the carbon, 4 × 1 for the hydrogens). So each gram gives about 800 ÷ 16 = 50 kJ.

That heat goes into the surroundings. In a kitchen, we want it to go into the pot. You learned in Grade 10 how to work out the heat needed to warm water: Q = ms(T₂ − T₁), with s = 4,200 J/(kg °C) for water Grade 10: Calculating heat.

Worked example

Boiling water on biogas

How much methane must burn to heat 1 kg of water from 20 °C to 100 °C, if all the heat went into the water?

Answer

Heat needed:
$Q = ms(T_2 - T_1) = 1\ \text{kg} \times 4200\ \text{J/(kg °C)} \times (100 - 20)\ \text{°C} = 336\,000\ \text{J} = 336\ \text{kJ}$
Methane needed: each gram gives 50 kJ, so
$\frac{336\ \text{kJ}}{50\ \text{kJ/g}} = 6.7\ \text{g of methane}$
A real stove needs more: much of the heat goes into the air around the pot, often half or more. Energy is still conserved, but it doesn’t all go where we want it.

A round gas burner with rings of small blue flames, with a few orange streaks — **Figure 2.3** A biogas burner. The gas is mostly methane; a clean blue flame means it is getting enough oxygen to burn completely to carbon dioxide and water. Photo: SuSanA Secretariat, CC BY 2.0

A large bell-shaped rocket engine hanging in a test stand, firing downwards; white vapor around the nozzle, and below it an almost invisible exhaust with a glowing patch — **Figure 2.4** A Space Shuttle main engine being tested. It burns liquid hydrogen with liquid oxygen. Its flame is almost invisible: burning hydrogen makes only water, as very hot steam, and no glowing soot. (The bright patch below the engine is a shock wave in the exhaust, not soot.) Photo: NASA, Public domain

Your body uses the same reactions, slowly and at 37 °C. In respiration, glucose and oxygen make carbon dioxide and water, giving out about 2,800 kJ for each mole of glucose (180 g), about 16 kJ per gram. Food labels count carbohydrates as 17 kJ per gram.

Activity

How much heat is in a candle?

You need: an empty drink can, a stand and clamp (or a rod or pencil through the can’s ring-pull hole, laid across two stacks of bricks), a thermometer, a short candle on a jar lid, a measuring jug, a balance that reads to 0.1 g (at school; a kitchen scale reading to 1 g will do if you burn the candle for longer), and matches. Do this with an adult, away from anything that can catch fire.

Put 100 mL (100 g) of cold water in the can, and fix the can so that the tip of the candle’s flame will be just below its base.
Weigh the candle on its lid. Measure the water’s temperature.
Light the candle and put it under the can. Stir the water gently with the thermometer.
When the water has warmed by about 20 °C, blow the candle out. Measure the highest temperature the water reaches.
Weigh the candle on its lid again.
Work out the heat the water took in, Q = ms(T₂ − T₁), then divide by the mass of wax burned to find the heat per gram.

Figure 2.5 The setup, with the can drawn cut open to show the water inside. The can is clamped so that the flame’s tip is just below its base; the thermometer’s bulb is in the water, not touching the can.

What you should see

A typical result: the water warms from 22 °C to 42 °C, taking in 0.1 × 4,200 × 20 = 8,400 J = 8.4 kJ, while the candle loses about 0.4 g. That gives about 8.4 ÷ 0.4 = 21 kJ per gram. Wax actually gives out about 42 kJ per gram when it burns, so about half the heat went somewhere else: into the air around the can, into the can itself, and into the soot (black on the can’s base, unburned carbon) and gases that didn’t burn completely. School results are often about half the true value, sometimes less. To do better: shield the flame from draughts, put the flame closer, and stir. The result is never better than the true value: energy can be lost from the water, but not made.

In short

A bond holds two atoms together by attraction. Breaking a bond always takes energy in; making one gives the same energy out. That energy, for a mole of bonds, is the bond energy.
A reaction can be modeled as breaking all the reactants’ bonds, then making all the products’ bonds. Energy change ΔH = energy to break bonds − energy from making bonds.
If making the new bonds gives out more than breaking took in, the reaction is exothermic (ΔH negative); if less, it is endothermic (ΔH positive).
Energy is conserved: what the chemicals (the system) lose, the surroundings gain, and the other way round.
On an energy diagram, the products are lower than the reactants for an exothermic reaction, and higher for an endothermic one; the hill between them is the activation energy, needed to start breaking bonds.

Questions

Which statement explains why burning methane gives out heat?

Pick an answer to see why.

In an endothermic reaction, the energy of the products is

Pick an answer to see why.

Hydrogen peroxide, H–O–O–H, breaks down into water and oxygen: 2H₂O₂ → 2H₂O + O₂. The O–O single bond has a bond energy of 146 kJ/mol. Use this and the table to work out the energy change. Is the reaction exothermic or endothermic?

Hint

Each H₂O₂ has two O–H bonds and one O–O bond. Each water keeps two O–H bonds; the O₂ has one O=O bond.

Answer

Break: in 2H₂O₂, 4 O–H + 2 O–O = 4 × 463 + 2 × 146 = 1,852 + 292 = 2,144 kJ in.
Make: in 2H₂O, 4 O–H = 1,852 kJ; in O₂, 1 O=O = 498 kJ; total 2,350 kJ out.
ΔH = 2,144 − 2,350 = −206 kJ: exothermic. (Notice that the O–H bonds break and form again, so they cancel: only the two weak O–O bonds and the strong O=O bond matter. The measured value, with the water as steam, is −211 kJ.) This is why a strong solution of hydrogen peroxide gets hot when it breaks down quickly.

Draw an energy diagram for burning hydrogen (2H₂ + O₂ → 2H₂O, ΔH = −484 kJ). Mark the reactants, the products, the activation energy and the energy change. Then explain, using your diagram, why a jet of hydrogen doesn’t burn until a spark reaches it, but then keeps burning by itself.

Answer

The diagram: energy upwards, the progress of the reaction across. A level on the left labeled 2H₂ + O₂; a lower level on the right labeled 2H₂O, 484 kJ below it (an arrow down, “484 kJ given out”). Between them a hill rising above the reactants’ level; the height from the reactants’ level to its top is labeled “activation energy”.

Without a spark, very few colliding hydrogen and oxygen molecules have enough energy to get over the hill, so almost none react. The spark gives some of them that energy. They react, and as they fall to the much lower level of the products they give out far more energy than the hill took. That heat gives the neighboring molecules the activation energy, so they react too, and so on: the reaction supplies its own activation energy, and keeps going while there is hydrogen and oxygen.

A student says: “When ice melts, it takes in heat, so melting must be breaking bonds; and when the water freezes again, the bonds form and heat comes out.” Is the student right? What bonds are they?

Answer

Partly right, and the reasoning is good. Melting does take in heat because attractions are being pulled apart, and freezing gives the same heat out as they form again. But the bonds that break are not the covalent O–H bonds inside each water molecule: the molecules stay H₂O. They are the much weaker attractions between water molecules, which hold them in the ice’s crystal. This is not a chemical reaction, because no new substance forms; but the energy rule is the same: pulling apart things that attract takes energy, letting them come together gives it out. (Why some substances hold on to each other much more strongly than others is another topic: Why does salt melt at 801 °C but ice at 0 °C?)

Making quicklime from limestone, CaCO₃ → CaO + CO₂, takes in 178 kJ for each mole (100 g) of limestone. Putting quicklime in water, CaO + H₂O → Ca(OH)₂, gives out 65 kJ for each mole. (i) Draw both on one energy diagram. (ii) A lime kiln burns wood or coal to make quicklime. Explain why it must keep burning fuel the whole time the limestone is turning into lime.

Answer

i.Three levels, each with all the chemicals there at that stage, water included. CaCO₃ + H₂O at the bottom left; CaO + CO₂ + H₂O 178 kJ higher, in the middle (an arrow up, “178 kJ taken in”); Ca(OH)₂ + CO₂ on the right, 65 kJ lower than the middle level (an arrow down, “65 kJ given out”), so still 113 kJ above where it started.
ii.Breaking down limestone is endothermic: the products have 178 kJ more energy per mole than the limestone. That energy must come in from somewhere, every moment the reaction is going on. Unlike burning, an endothermic reaction can’t supply its own heat, so the moment the fire stops, the limestone stops turning into lime. (The kiln must also keep the limestone very hot, above about 800 °C, for it to break down at a useful speed.)

Use bond energies to show that 2H₂O → 2H₂ + O₂, splitting water, is endothermic. How much energy must be supplied to split 36 g of water? Suggest how it could be supplied.

Answer

This is burning hydrogen backwards, so every bond that formed then breaks now, and every bond that broke then forms now.
Break: 4 O–H = 1,852 kJ in. Make: 2 H–H + 1 O=O = 1,370 kJ out. ΔH = 1,852 − 1,370 = +482 kJ: endothermic.
36 g of water is 2 moles, so about 482 kJ must be supplied (measured: 484 kJ, for water as steam; a little more for liquid water). It can be supplied as electricity, by passing a current through water (electrolysis), or as sunlight, which plants use to split water in photosynthesis. Energy is conserved: you can’t get more energy back by burning the hydrogen than it took to make it.

Bond-energy calculations give −800 kJ for burning a mole of methane, while the measured value is −802 kJ (water as steam). Give two reasons why such calculations are close but not exact.

Answer

Bond energies in tables are averages over many molecules. A C–H bond in methane is not exactly as strong as one in another molecule, and the two O–H bonds in water have slightly different energies to break (the first one is harder).
Bond energies are for molecules as gases. If any reactant or product is a liquid or solid (liquid water, for example), extra energy is given out or taken in as it condenses or melts, which bond energies don’t include. (Rounding the values in the table adds a little more.)

Design an investigation to compare how much heat two fuels give out per gram, for example kerosene and ethanol in two small spirit lamps. Say what you would measure, what you would keep the same, and how you would make it a fair test.

Answer

Measure: the mass of each lamp before and after burning (so the mass of fuel burned), and the temperature of the water before and after.
Keep the same: the same can, the same mass of water (say 100 g), the same starting temperature, the same distance from the wick to the can, the same rise in temperature (say 20 °C), the same draught shield, and stirring in the same way.
Work out for each fuel: heat taken in by the water, Q = ms(T₂ − T₁), divided by the mass of fuel burned, in kJ per gram.
Fair test: change only the fuel; repeat each three times and take the average; a soot-blackened can absorbs heat differently, so clean it between runs. The heat lost to the air means both answers will be too low, but if the setup is the same, the comparison is still fair. (Measured in a proper calorimeter, kerosene gives about 46 kJ/g and ethanol about 30 kJ/g.)

Think about it

Why is nitrogen in the air, and not in the rocks?

Most of the oxygen on Earth is locked up in rocks and water, combined with other elements. Yet most of the nitrogen floats in the air as N₂ gas, uncombined. Using bond energies, can you suggest why?

Answer

The N≡N triple bond, at 945 kJ/mol, is one of the strongest bonds in chemistry. For nitrogen to combine with anything, that bond must break first, and the new bonds nitrogen can make often don’t give back enough energy to pay for it: making nitric oxide, for example, is endothermic. Even where a reaction would give out energy overall, like making ammonia, the hill to climb is so high that it hardly happens without a catalyst (iron in a factory, or the enzymes of some bacteria in the soil). So nitrogen stays as N₂. Oxygen’s O=O bond is much weaker (498 kJ/mol), and the bonds oxygen makes are strong, so oxygen combines with almost everything.

Where to go next

What makes a reaction go faster? The hill in the energy diagram, collisions, and why heat, crowding and catalysts speed reactions up.
Why do some reactions stop halfway? Why an endothermic reaction can happen at all, and why some reactions run both ways at once.
Why does salt melt at 801 °C but ice at 0 °C? The forces between particles, and the energy to pull them apart.