• 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)