5.2.1 Entropy & Entropy Change

• 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)

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

• 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

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

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)