Entropy & Entropy Change (Cambridge (CIE) A Level Chemistry): Revision Note

Defining Entropy

• The entropy (S) of a given system is the number of possible arrangements of the particles and their energy in a given system

  • In other words, it is a measure of how disordered a system is

• When a system becomes more disordered, its entropy will increase

• An increase in entropy means that the system becomes energetically more stable

• For example, during the thermal decomposition of calcium carbonate (CaCO₃) the entropy of the system increases:

CaCO₃ (s) → CaO (s) + CO₂ (g)

• In this decomposition reaction, a gas molecule (CO₂) is formed

• The CO₂ gas molecule is more disordered than the solid reactant (CaCO₃), as it is constantly moving around

• As a result, the system has become more disordered and there is an increase in entropy

• Another typical example of a system that becomes more disordered is when a solid is melted

• For example, melting ice to form liquid water:

H₂O (s) → H₂O (l)

• The water molecules in ice are in fixed positions and can only vibrate about those positions

• In the liquid state, the particles are still quite close together but are arranged more randomly, in that they can move around each other

• Water molecules in the liquid state are therefore more disordered

• Thus, for a given substance, the entropy increases when its solid form melts into a liquid

• In both examples, the system with the higher entropy will be energetically the most stable (as the energy of the system is more spread out when it is in a disordered state)

Entropy between physical states

Melting a solid will cause the particles to become more disordered resulting in a more energetically stable system

Entropy Changes

• All elements have positive standard molar entropy values

• The order of entropy for the different states of matter are as follows:

gas > liquid > solid

• There are some exceptions such as calcium carbonate (solid) which has a higher entropy than mercury (liquid)

• Simpler substances with fewer atoms have lower entropy values than complex substances with more atoms

  • For example, calcium oxide (CaO) has a smaller entropy than calcium carbonate (CaCO₃)

• Harder substances have lower entropy than softer substances of the same type

  • For example, diamond has a smaller entropy than graphite

Change in state

• The entropy of a substance changes during a change in state

• The entropy increases when a substance melts (change from solid to liquid)

  • Increasing the temperature of a solid causes the particles to vibrate more

  • The regularly arranged lattice of particles changes into an irregular arrangement of particles

  • These particles are still close to each other but can now rotate and slide over each other in the liquid

  • As a result, there is an increase in disorder

• The entropy increases when a substance boils (change from liquid to gas)

  • The particles in a gas can now freely move around and are far apart from each other

  • The entropy increases significantly as the particles become very disordered

• Similarly, the entropy decreases when a substance condenses (change from gas to liquid) or freezes (change from liquid to solid)

  • The particles are brought together and get arranged in a more regular arrangement

  • The ability of the particles to move decreases as the particles become more ordered

  • There are fewer ways of arranging the energy so the entropy decreases

Graph of entropy against temperature

The entropy of a substance increases when the temperature is raised as particles become more disordered

• The entropy also increases when a solid is dissolved in a solvent

• The solid particles are more ordered in the solid lattice as they can only slightly vibrate

• When dissolved to form a dilute solution, the entropy increases as:

  • The particles are more spread out

  • There is an increase in the number of ways of arranging the energy

• The crystallisation of a salt from a solution is associated with a decrease in entropy

  • The particles are spread out in solution but become more ordered in the solid

Entropy changes during the dissolving of a solid

When a solid is dissolved in a solvent to form a dilute solution, the entropy increases as the particles become more disordered

Entropy changes in reactions

• Gases have higher entropy values than solids

• So, if the number of gaseous molecules in a reaction changes, there will also be a change in entropy

• The greater the number of gas molecules, the greater the number of ways of arranging them, and thus the greater the entropy

• For example the decomposition of calcium carbonate (CaCO₃)

 CaCO₃ (s) → CaO (s) + CO₂ (g)

• The CO₂ gas molecule is more disordered than the solid reactant (CaCO₃) as it can freely move around whereas the particles in CaCO₃ are in fixed positions in which they can only slightly vibrate

  • The system has therefore become more disordered and there is an increase in entropy

• Similarly, a decrease in the number of gas molecules results in a decrease in entropy causing the system to become less energetically stable

• For example, the formation of ammonia in the Haber process

N₂ (g) + 3H₂ (g) ⇋ 2NH₃ (g)

• In this case, all of the reactants and products are gases

  • Before the reaction occurs, there are four gas molecules (1 nitrogen and 3 hydrogen molecules) in the reactants

  • After the reaction has taken place, there are now only two gas molecules (2 ammonia molecules) in the products

  • Since there are fewer molecules of gas in the products, there are fewer ways of arranging the energy of the system over the products

  • The system has become more ordered causing a decrease in entropy

  • The reactants (N₂ and H₂) are energetically more stable than the product (NH₃)