Energy in reactions: enthalpy, exothermic and endothermic reactions, and Gibbs free energy
What enthalpy is, how exothermic and endothermic reactions differ, how Gibbs free energy decides if a reaction can happen, and Le Chatelier's principle.
By Zachery Casey · Published · Reviewed · Editorial policy
Enthalpy (H) is the heat content of a system. The enthalpy change, ΔH, is the heat a reaction gives out (an exothermic reaction, with a negative ΔH) or takes in (an endothermic reaction, with a positive ΔH). Some reactions happen on their own and some never do, however long you wait. Others can happen but take years. This guide explains the ideas chemists use to sort these out: enthalpy, entropy and Gibbs free energy. It also covers Le Chatelier's principle, which predicts what a reaction at balance does when conditions change. The examples come from everyday lab work and from the chemistry of the peptide bond.
Terms are defined in the glossary.
What is enthalpy?
Enthalpy (symbol H) is a measure of the heat energy stored in a substance. You can't measure it directly. What you can measure is the enthalpy change, ΔH (said "delta H"): the heat a reaction gives out or takes in when it runs at constant pressure, as most reactions in an open flask do.
ΔH is given in kilojoules per mole (kJ/mol): the heat for each mole of reaction as written. See moles, Avogadro's number and percentage yield for what a mole is.
The sign tells you the direction of heat flow:
| ΔH | Heat flows | Surroundings feel | |
|---|---|---|---|
| Exothermic | Negative | Out of the reaction | Warmer |
| Endothermic | Positive | Into the reaction | Colder |
Enthalpy changes come from bonds. Breaking a bond always takes energy. Forming a bond always releases it. If the bonds formed are stronger overall than the bonds broken, energy is left over and comes out as heat. See chemical bonds and polarity for bond strengths.
Exothermic and endothermic reactions
A reaction profile (an energy level diagram) shows the difference. The products sit lower than the reactants in an exothermic reaction and higher in an endothermic one. In both, the reactants first have to climb over an energy barrier, the activation energy.
Both kinds turn up in ordinary lab work.
Exothermic examples:
- Neutralising a strong acid with a strong base, such as hydrochloric acid with sodium hydroxide, releases about 57 kJ for each mole of water formed (LibreTexts, enthalpy change of neutralisation). Concentrated solutions get noticeably warm.
- Dissolving sodium hydroxide pellets in water releases a lot of heat, which is why the solution is made up slowly with stirring.
- Diluting concentrated acids, especially sulfuric acid, releases enough heat to boil water locally. That is the reason for the rule "add acid to water, never water to acid": the small amount of acid warms a large volume of water instead of the reverse.
- Mixing methanol with water warms slightly (Shimadzu). See HPLC and LC-MS solvents.
Endothermic examples:
- Dissolving ammonium nitrate in water takes in heat. Instant cold packs work this way.
- Mixing acetonitrile with water cools below room temperature, so freshly mixed mobile phase is left to reach room temperature before use.
- Melting ice and evaporating water both take in heat without any chemical change. That is why a wet cloth cools what it touches as it dries.
Heat from a reaction matters in practice. A warm solution may need to cool before its volume is made up in a volumetric flask, because glassware is calibrated at 20 °C and liquids expand as they warm.
Entropy
Heat isn't the whole story. Ice melts on its own at room temperature even though melting is endothermic. Something else is driving it.
That something is entropy (symbol S). Entropy measures how spread out energy and matter are: how many ways the molecules of a system can arrange themselves. Liquid water has more ways to arrange its molecules than ice, so melting increases entropy. Gases have more entropy than liquids, and a dissolved solid usually has more than the crystal it came from.
Left to themselves, systems tend towards higher overall entropy. Heat spreads from hot to cold. Dyes spread through water. Gases fill their containers.
Entropy also explains the hydrophobic effect. Water molecules form ordered cages around non-polar groups. When non-polar groups cluster together, fewer water molecules are held in order, so the overall entropy goes up. That is why hydrophobic side chains gather together, and why hydrophobic peptides stick to the C18 surface in reversed-phase HPLC.
Gibbs free energy
Gibbs free energy (symbol G) combines enthalpy and entropy into one number that decides whether a change can happen on its own at a given temperature:
ΔG = ΔH − TΔS
where T is the temperature in kelvin.
| ΔG | Meaning |
|---|---|
| Negative | The change can happen on its own (it is "spontaneous") |
| Zero | The system is at equilibrium |
| Positive | The change won't happen on its own; the reverse will |
The two parts can pull in opposite directions:
| ΔH | ΔS | Result |
|---|---|---|
| Negative (exothermic) | Positive | Favoured at every temperature |
| Positive (endothermic) | Negative | Never favoured on its own |
| Negative | Negative | Favoured at low temperature |
| Positive | Positive | Favoured at high temperature, as with ice melting above 0 °C |
Spontaneous doesn't mean fast
"Spontaneous" has a narrow meaning here: the reaction is allowed by energy. It says nothing about speed. Diamond turning into graphite has a negative ΔG at room temperature, but it is so slow that it never happens in practice.
The peptide bond is a good lab example. Breaking it with water (hydrolysis) has a negative ΔG in water, so it is favoured. Yet without a catalyst, at neutral pH and room temperature, it is extremely slow (Radzicka & Wolfenden, 1996). The reaction has to get over a high activation energy first. Whether a reaction can happen is a matter of free energy; how fast it happens is a matter of kinetics. See rates of reaction and the Arrhenius equation.
The same fact explains how peptides are made. Because forming a peptide bond in water is uphill, synthesis doesn't simply mix amino acids together. Each amino acid is first activated with a coupling reagent, turning it into a high-energy form that reacts readily. See solid-phase peptide synthesis.
Free energy and equilibrium
ΔG also tells you where a reaction settles. The standard free energy change, ΔG°, is linked to the equilibrium constant K by:
ΔG° = −RT ln K
where R is the gas constant (8.314 J/(mol·K)). At 25 °C, each change of about 5.7 kJ/mol in ΔG° shifts K by a factor of ten. A reaction with ΔG° of −5.7 kJ/mol ends with about ten times as much product as starting material at equilibrium. One with −11.4 kJ/mol ends with about a hundred times as much.
Le Chatelier's principle explained, with examples
Le Chatelier's principle says that when a system at equilibrium is disturbed, the equilibrium shifts in the direction that partly undoes the disturbance (LibreTexts, Le Chatelier's principle).
Many reactions don't go all the way. They reach an equilibrium, where the forward and reverse reactions run at the same rate and the amounts stop changing. The table shows what the principle predicts for each kind of disturbance.
| Change | Equilibrium shifts | Example |
|---|---|---|
| Add a reactant | Towards products, using some of it up | Adding acid to an acetate buffer converts acetate to acetic acid |
| Remove a product | Towards products, replacing some of it | Removing water drives the formation of esters and amides |
| Raise the temperature | In the endothermic direction, taking in heat | The pH of Tris buffer falls as it warms |
| Lower the temperature | In the exothermic direction | |
| Raise the pressure (gases) | Towards fewer gas molecules | Industrial ammonia synthesis |
The first row is how a buffer works. Added acid is soaked up by the base form of the buffer, so the pH barely moves. See buffers and pH.
Two things Le Chatelier's principle doesn't do:
- It doesn't change K, except with temperature. Adding or removing material moves the amounts, but the ratio at equilibrium stays the same. Only temperature changes the equilibrium constant itself.
- A catalyst doesn't move the equilibrium. It speeds up the forward and reverse reactions equally, so equilibrium is reached sooner but in the same place.
Related guides
For how temperature changes the speed of a reaction, see the Arrhenius equation and accelerated stability testing. For the reaction that most often breaks peptides down, see hydrolysis. For electron transfer reactions, see oxidation and reduction. For how fast reactions go and how that is measured, see rates of reaction.
More on peptide chemistry
- Rates of reaction: what speeds a reaction up or slows it downWhat a rate of reaction is, how to calculate it, what changes it, how zero-, first- and second-order reactions differ, and how to work out a half-life.
- Moles, Avogadro's number and percentage yieldPercentage yield and theoretical yield with worked examples, plus what a mole is, what Avogadro's number means and how to calculate moles from mass.
- GHK-Cu: the chemistry of a peptide–copper complexGHK-Cu structure and chemistry: how the GHK peptide binds copper(II), why the complex is blue, how pH affects it, and how its identity is confirmed.