Introduction to Entropy (College Board AP® Chemistry): Revision Note
Entropy & Phase Changes
Entropy (S) in a system reflects the variety of ways particles and their energy can be arranged
Entropy increases when matter becomes more dispersed and when energy is dispersed
The more possible arrangements (microstates) of the particles and their energy, the higher the entropy
Entropy is not a measure of energy or stability
Whether a process is thermodynamically favored depends on ΔG°, which combines ΔH° and ΔS°
Take the thermal decomposition of calcium carbonate (CaCO3) as an example:
CaCO3 (s) → CaO (s) + CO2 (g)
The reaction forms 1 mol of gas from 0 mol of gas: CO2 is a new substance, and its particles move freely and occupy a much larger volume than the solid reactant, so matter becomes more dispersed
This results in a higher overall entropy
Entropy and phase changes
Consider another example: when a solid transitions to a liquid, like the melting of ice:
H2O (s) → H2O (l)
In the solid state, water molecules in ice are fixed in position with limited movement
In the liquid state, the molecules are free to move past one another, so there are many more possible arrangements of the particles and their energy
As a result, matter is more dispersed in the liquid, leading to an increase in entropy compared to the solid state (ΔS° > 0)
The same is true when a liquid boils as the gas particles are freer to move and occupy a much larger volume
In both cases, the particles and their energy become more dispersed, so entropy increases
A higher entropy alone does not make a process thermodynamically favored
Water still freezes below 0 °C, although its entropy decreases
Increasing entropy in a system
For reactions involving gas-phase reactants or products, the entropy generally increases when the total number of moles of gas-phase products is greater than the total number of moles of gas-phase reactants
For a gas at constant temperature, entropy also increases when its volume increases, because the particles can move within a larger space
Entropy and temperature
Entropy increases when energy is dispersed
As the temperature of a gas increases, the distribution of kinetic energy among its particles broadens, as described by kinetic molecular theory
So, the entropy of the system increases with an increase in temperature
Worked Example
In which reaction would you expect the largest decrease in entropy?
A CH4 (l) + 2O2 (g) → CO2 (g) + 2H2O (g)
B CH4 (g) + 2O2 (g) → CO2 (s) + 2H2O (g)
C CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (g)
D CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l)
Answer:
The correct answer is D
Each equation has 3 mol of reactants and 3 mol of products
So, compare the phases by counting the moles of gas on each side
Reaction A will show an increase in entropy as one of the reactants is a liquid but all products are gases
Therefore, reaction A cannot be the correct answer
Reaction B will show a decrease in entropy as the three gaseous reactants form one solid and two gaseous products
Reaction C will show only a small change in entropy as there are 3 mol of gas on each side
Therefore, reaction C cannot be the correct answer
Reaction D will show a decrease in entropy as the three gaseous reactants form one gaseous and two liquid products
Between reactions B and D:
Reaction D will have the biggest decrease in entropy as the moles of gas fall from 3 to 1, while in reaction B they fall from 3 to 2
Examiner Tips and Tricks
Justify the sign of an entropy change at the particle level: name the phases and count the moles of gas on each side.
Words such as “disorder”, “chaos” or “more random” earn no credit on their own; say how matter or energy becomes more dispersed.
A reaction that forms a gas makes a new substance, so it is not a phase change
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