Chapter 2 Entropy

Question 1

The entropy (S) of a given system

Answer 1

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

Question 2

When a system becomes more disordered, its entropy will

Answer 2

• 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)

Question 3

CaCO₃(s) → CaO(s) + CO₂(g)

• In this decomposition reaction, a gas molecule

Answer 3

• (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

Question 4

• 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)

Answer 4

• 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

Question 5

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

Answer 5

Question 6

• All elements have positive standard molar entropy values
• The order of entropy for the different states of matter are as follows:

Answer 6

gas > liquid > solid

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

Question 7

Simpler substances with fewer atoms have

Answer 7

lower entropy values than complex substances with more atoms

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

Question 8

Harder substances have

Answer 8

lower entropy than softer substances of the same type

• For example, diamond has a smaller entropy than graphite

Question 9

• The entropy of a substance changes during a change in state
• The entropy …. when a substance melts (change from solid to liquid)

Answer 9

Increases

• 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

Question 10

The entropy ….. when a substance boils (change from liquid to gas)

Answer 10

increases

• 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

Question 11

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

Answer 11

decreases

• 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

Question 12

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

Question 13

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

Answer 13

Question 14

The entropy also increases when a solid is

Answer 14

• 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

Question 15

The crystallisation of a salt from a solution is associated with a

Answer 15

decrease in entropy

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

Question 16

Gases have higher entropy values than

Answer 16

• 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

Question 17

• 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

Answer 17

• 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

Question 18

Similarly, a decrease in the number of gas molecules results in a

Answer 18

decrease in entropy causing the system to become less energetically stable

Question 19

The standard entropy change (ΔS_system^ꝋ ) for a given reaction can be calculated using the

Answer 19

• standard entropies (S^ꝋ ) of the reactants and products
• The equation to calculate the standard entropy change of a system is:

ΔS_system^ꝋ = ΣΔS_products^ꝋ - ΣΔS_reactants^ꝋ

(where Σ = sum of)

Question 20

• For example, the standard entropy change for the formation of ammonia (NH₃) from nitrogen (N₂) and hydrogen (H₂) can be calculated using this equation

Answer 20

N₂(g) + 3H₂(g) ⇋ 2NH₃(g)

ΔS_system^ꝋ = (2 x ΔS^ꝋ(NH₃)) - (ΔS^ꝋ(N₂) + 3 x ΔS^ꝋ(H₂))

Question 21

The feasibility of a reaction does not only depend on the entropy change of the reaction, but can also be affected by the

Answer 21

• enthalpy change
• Therefore, using the entropy change of a reaction only to determine the feasibility of a reaction is inaccurate

Question 22

The Gibbs free energy (G) is the energy change that takes into account

Answer 22

both the entropy change of a reaction and the enthalpy change

Question 23

• The Gibbs equation is:

Answer 23

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• The units of ΔG^ꝋ are in kJ mol^-1
• The units of ΔH_reaction^ꝋ are in kJ mol^-1
• The units of T are in K
• The units of ΔS_system^ꝋ are in J K^-1 mol^-1 (and must therefore be converted to kJ K^-1 mol^-1 by dividing by 1000)

Question 24

• The Gibbs equation can be used to calculate the Gibbs free energy change of a reaction

Answer 24

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• The equation can also be rearranged to find values of ΔH_reaction^ꝋ, ΔS_system^ꝋ or the temperature, T

Question 25

• The Gibbs equation can be used to calculate whether a reaction is feasible or not

Answer 25

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• When ΔG^ꝋ is negative, the reaction is feasible and likely to occur
• When ΔG^ꝋis positive, the reaction is not feasible and unlikely to occur

Question 26

The feasibility of a reaction can be affected by the

Answer 26

• temperature
• The Gibbs equation will be used to explain what will affect the feasibility of a reaction for exothermic and endothermic reactions

Question 27

Exothermic reactions

• In exothermic reactions, ΔH_reaction^ꝋ is negative

Answer 27

• If the ΔS_system^ꝋ is positive:
  
  • Both the first and second term will be negative
  • Resulting in a negative ΔG^ꝋ so the reaction is feasible
  • Therefore, regardless of the temperature, an exothermic reaction with a positive ΔS_system^ꝋ will always be feasible

Question 28

Exothermic reactions

• In exothermic reactions, ΔH_reaction^ꝋ is negative
• If the ΔS_system^ꝋ is positive:

Answer 28

• Both the first and second term will be negative
• Resulting in a negative ΔG^ꝋ so the reaction is feasible
• Therefore, regardless of the temperature, an exothermic reaction with a positive ΔS_system^ꝋ will always be feasible

Question 29

Exothermic reactions

• In exothermic reactions, ΔH_reaction^ꝋ is negative
• If the ΔS_system^ꝋ is negative:

Answer 29

• The first term is negative and the second term is positive
• At high temperatures, the -TΔS_system^ꝋ will be very large and positive and will overcome ΔH_reaction^ꝋ
• Therefore, at high temperatures ΔG^ꝋ is positive and the reaction is not feasible
• The reaction is more feasible at low temperatures, as the second term will not be large enough to overcome ΔH_reaction^ꝋ resulting in a negative ΔG^ꝋ

Question 30

This corresponds to Le Chatelier’s principle which states that for exothermic reactions an increase in temperature will cause the

Answer 30

equilibrium to shift position in favour of the reactants, i.e. in the endothermic direction

• In other words, for exothermic reactions, the products will not be formed at high temperatures
• The reaction is not feasible at high temperatures

Question 31

The diagram shows under which conditions exothermic reactions are feasible

Answer 31

Question 32

Endothermic reactions

• In endothermic reactions, ΔH_reaction^ꝋ is positive
• If the ΔS_system^ꝋ is negative:

Answer 32

• • Both the first and second term will be positive
    
    • Resulting in a positive ΔG^ꝋ so the reaction is not feasible
    • Therefore, regardless of the temperature, endothermic with a negative ΔS_system^ꝋ will never be feasible

Question 33

Endothermic reactions

• In endothermic reactions, ΔH_reaction^ꝋ is positive
• If the ΔS_system^ꝋ is positive:

Answer 33

• The first term is positive and the second term is negative
• At low temperatures, the -TΔS_system^ꝋ will be small and negative and will not overcome the larger ΔH_reaction^ꝋ
• Therefore, at low temperatures ΔG^ꝋ is positive and the reaction is less feasible
• The reaction is more feasible at high temperatures as the second term will become negative enough to overcome the ΔH_reaction^ꝋ resulting in a negative ΔG^ꝋ

Question 34

This again corresponds to Le Chatelier’s principle which states that for endothermic reactions an increase in temperature will cause the

Answer 34

equilibrium to shift position in favour of the products

• In other words, for endothermic reactions, the products will be formed at high temperatures
• The reaction is therefore feasible

Question 35

The diagram shows under which conditions endothermic reactions are feasible

Answer 35