3.5.1 Thermodynamics - Entropy and entropy change (ΔS)


Students should:
  • understand that ΔH, whilst important, is not sufficient to explain spontaneous change (e.g. spontaneous endothermic reactions)
  • understand that the concept of increasing disorder (entropy change ΔS) accounts for the above deficiency, illustrated by physical change (e.g. melting, evaporation) and chemical change (e.g. dissolution, evolution of CO2 from hydrogencarbonates with acid)
  • be able to calculate entropy changes from absolute entropy values


Entropy is the term given to the natural disorder of the universe. If left to itself the universe tends towards disorder. It can be thought of as an inevitable driving force. Entropy has been called 'nature's arrow'. It is the natural tendency of systems to become disordered.

If we look at a solid, we can see that all of the particles are carefully arranged in specific locations. This is a highly organised and ordered system. Its entropy is said to be very low. However, in a gas the particles are free to move randomly and with a range of speeds. The entropy of gases is high.

A liquid has more entropy than a crystalline solid, but much less than a gas. A solution contains a mixture of solute and solvent particles and has more entropy than a simple liquid but once again, far less than a gas.

State Entropy
solid very low
liquid low
gas high


Factors affecting entropy

Disorder can be increased by increasing the number of particles that have freedom of movement.

Gas particles have three degrees of freedom:

  • 1 Translation
  • 2 Rotation
  • 3 Vibration

Translation means moving in a specific direction. Rotation is motion about an axis, and vibration means movement of the atoms with respect to one another within molecules, with respect to one another (stretching and bending of bonds).

Gases then, have a large amount of entropy.

The amount of entropy depends on the number of possible energy levels that the individual particles can have. This is a function of the temperature. As the temperature increases the number of energy states available to the particles also increases. The number of possible arrangements of energy over all of the particles increases. This gives the system a greater choice of arrangements, i.e. more entropy.

Hence, entropy is a function of the number of particles and the total energy available to those particles.

The symbol for entropy in chemistry is capital S.


Absolute Entropy

Entropy is defined as the degree of disorder inherent in a system. Unlike the chemical potential energy of a substance, entropy can be measured from an absolute baseline.

When a system has no disorder, i.e. it is perfectly arranged, and it has no energy, i.e. it is at absolute zero kelvin, it can have no entropy.

These conditions are met in a perfect crystallline substance at absolute zero.

This allows us to measure, or calculate, absolute entropy values, i.e. the entropy when compared to this absolute zero entropy baseline. There are various calculations that make this possible, based on thermodynamic data as well as statistics. Explainations of these go beyond the scope of this book.

Tables of absolute entropy values are available and may be used to calculate entropy changes from one situation to another. Absolute entropy is measured in J K-1.

Element S / J K-1 compound S / J K-1 compound S / J K-1
hydrogen 130 methane 186 carbon dioxide 213
nitrogen 191 ethane 229 water(g) 186
oxygen 205 propane 270 water(l) 119
fluorine 203 ethene 220 sulfur dioxide 248
chlorine 223 propene 267 sulfur trioxide 256
carbon 2.4 ethyne 200 hydrogen fluoride 173
sulfur 33 propyne 248 hydrogen chloride 187
phosphorus 44 1,3-butadiene 278 hydrogen bromide 198
magnesium 33 benzene 269 hydrogen sulfide 206
Ref: CRC Handbook of Chemistry and Physics - Ed. 44

Notice There are two important trends.

1 Gases have much more entropy than the solids.
2 Entropy increases as the mass and complexity of a molecule increases.


Entropy change

The difference in entropy in any process, chemical or physical, is the entropy of the final situation minus the entropy of the initial situation. For a chemical reaction this is the difference between the products entropy and the reactants entropy, called the entropy change. IThe entropy change is symbolised by ΔS, delta S. When the entropy increases, ΔS is positive.

ΔS = S(final) - S(initial)

When the entropy is determined under standard conditions it is called the standard entropy, ΔS.

Example: Does the entropy of the system increase or decrease when a kettle boils?

Before boiling the water is a liquid and has low entropy. After boiling the water becomes a gas and has much higher entropy. Therefore the entropy has increased and ΔS is positive.

Example: Does the entropy of the following reaction increase or decrease ?

N2(g) + 3H2(g) 2NH3(g)

On the left hand side of the equation there are four moles of gas and on the right hand side of the equation there are two moles of gas. The total amount of gas particles is decreasing and therefore the entropy is decreasing, ΔS is negative.

One point to note is that the effect of energy input (temperature increase) on entropy is not the same at all temperatures, but rather depends on the absolute temperature. There is a greater increase in entropy at lower temperatures for a given energy input.

Hence, the entropy change is dependent on the temperature at which the change takes place. This can be expressed by the equation:

ΔS = q/T

where q is the energy input.


Influence of entropy on reaction

The very fact that endothermic reactions proceed spontaneously tells us that enthalpy is not a definitive explanation for why reactions happen. However, it can be shown that all endothermic reactions have an increase in disorder, i.e. an increase in entropy.

It is clear then that entropy is also involved in some way in the driving force behind reactions. The actual relationship is explained in the next section.