1. A guide for A level students KNOCKHARDY PUBLISHING
ENTROPY & FREE ENERGY
A guide for A level students
2008 SPECIFICATIONS
KNOCKHARDY PUBLISHING

2. ENTHALPY CHANGES www.knockhardy.org.uk/sci.htm INTRODUCTION
This Powerpoint show is one of several produced to help students understand selected topics at AS and A2 level Chemistry. It is based on the requirements of the AQA and OCR specifications but is suitable for other examination boards.
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3. ENTROPY CONTENTS Spontaneous changes Free enthalpy and entropy
Second Law of Thermodynamics
Change of state
Is a reaction spontaneous? - worked examples

4. FREE ENERGY & ENTROPY SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy

5. Energy is put in to overcome the electrostatic attraction between ions
FREE ENERGY & ENTROPY
SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy
However ...
Why should reactions with a positive DH value take place spontaneously ?
(some salts dissolve readily in water and the solution gets colder, not hotter)
ENDOTHERMIC
Energy is put in to overcome the electrostatic attraction between ions

6. FREE ENERGY & ENTROPY SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy
However ...
Why should reactions with a positive DH value take place spontaneously ?
(some salts dissolve readily in water and the solution gets colder, not hotter)
ENDOTHERMIC
Energy is put in to overcome the electrostatic attraction between ions
EXOTHERMIC
Energy is released as the ions are attracted to polar water molecules

7. FREE ENERGY & ENTROPY SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy
However ...
Why should reactions with a positive DH value take place spontaneously ?
(some salts dissolve readily in water and the solution gets colder, not hotter)
ENDOTHERMIC
EXOTHERMIC
If the energy released when the ions dissolve is less than that put in to break up the lattice, the overall process will be ENDOTHERMIC and the temperature of the solution will drop.

8. FREE ENERGY & ENTROPY SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy
However ...
Why should reactions with a positive DH value take place spontaneously ?
(some salts dissolve readily in water and the solution gets colder, not hotter)
This must mean that energy has to be put in for the reaction to take place

9. FREE ENERGY & ENTROPY SPONTANEOUS CHANGES
- occur in one particular direction and not the other
- take place without the need for work
Exothermic reactions are usually spontaneous
- this is because they go from higher to lower enthalpy
However ...
Why should reactions with a positive DH value take place spontaneously ?
(some salts dissolve readily in water and the solution gets colder, not hotter)
This must mean that energy has to be put in for the reaction to take place
The answer is that enthalpy change DH does not give the full story.
Free energy changes, DG, give a better picture.

10. FREE ENERGY & ENTROPY FREE ENERGY (G)
A reaction is only spontaneous if it can do work - it must generate free energy
A negative DG indicates a reaction capable of proceeding of its own accord

11. DG < 0 (- ive) Spontaneous reaction
FREE ENERGY & ENTROPY
FREE ENERGY (G)
A reaction is only spontaneous if it can do work - it must generate free energy
A negative DG indicates a reaction capable of proceeding of its own accord
DG < 0 (- ive) Spontaneous reaction
DG > 0 (+ ive) Non-spontaneous reaction
(will be spontaneous in reverse direction)
DG = 0 The system is in equilibrium

12. DG < 0 (- ive) Spontaneous reaction
FREE ENERGY & ENTROPY
FREE ENERGY (G)
A reaction is only spontaneous if it can do work - it must generate free energy
A negative DG indicates a reaction capable of proceeding of its own accord
DG < 0 (- ive) Spontaneous reaction
DG > 0 (+ ive) Non-spontaneous reaction
(will be spontaneous in reverse direction)
DG = 0 The system is in equilibrium
ENTROPY (S)
• Entropy (symbol S) is a measure of the disorder of a system
• The more the disorder, the greater the entropy
• If a system becomes more disordered, the value of DS is positive
• Values tend to be in JOULES - not kJ
DS = Sfinal - Sinitial

13. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’

14. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when • solids melt
• liquids boil
• ionic solids dissolve in water
• the number of gas molecules increases
• the temperature increases

15. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when SOLIDS MELT
Regular arrangement of particles in solids
Less regular arrangement; more disorder in liquids

16. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when LIQUIDS BOIL
Irregular arrangement; some disorder in liquids
Random nature and disorder of particles in a gas

17. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when IONIC SOLIDS DISSOLVE IN WATER
Regular arrangement in an ionic crystal lattice
Ions dissociate in water; there is less order

18. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when THE MOLES OF GAS INCREASE
Particles in gases move in a random way. The more gas molecules there are, the greater the degree of randomness.

19. ‘Entropy tends to a maximum’
THE SECOND LAW
The Second Law of Thermodynamics is based on entropy and states that…
‘Entropy tends to a maximum’
This infers that ‘all chemical and physical changes
involve an overall increase in entropy’
Entropy increases when THE TEMPERATURE INCREASES
Lower temperature; less energy
Higher temperature; more energy and more disorder

20. This occurs during changes of state (melting, boiling etc)
FREE ENERGY & ENTROPY
Free energy, enthalpy and entropy are related ... DG = DH - TDS
Special
case For a reversible reaction at equilibrium the value of DG is zero
If DG = ZERO then DH = T DS
and DS = DH T
This occurs during changes of state (melting, boiling etc)

21. and DS = DH T FREE ENERGY & ENTROPY
Free energy, enthalpy and entropy are related ... DG = DH - TDS
Special
case For a reversible reaction at equilibrium the value of DG is zero
If DG = ZERO then DH = T DS
and DS = DH T
Worked Example
Calculate the entropy change when water turns to steam at 100°C (373K).
The enthalpy of vaporisation of water is +44 kJ mol-1
DS = DH = kJ mol = J K -1 mol -1
T K (+ive as gases have more disorder)
Entropy change values are much smaller than enthalpy
change values; they tend to be in Joules rather than kJ

22. IS A REACTION SPONTANEOUS?
A reaction should be spontaneous if DG is negative, so ...
• Work out if it is exothermic (DH -ive) or endothermic (DH +ive)
• Is there an increase in disorder ? If YES then DS will be positive.
• Is the temperature high or low ? This can affect the value of TDS°

23. IS A REACTION SPONTANEOUS?
A reaction should be spontaneous if DG is negative, so ...
• Work out if it is exothermic (DH -ive) or endothermic (DH +ive)
• Is there an increase in disorder ? If YES then DS will be positive.
• Is the temperature high or low ? This can affect the value of TDS°
General examples
• If DH is –ive and DS is +ive then DG must be negative
• If DH is +ive and DS is -ive then DG must be positive

24. IS A REACTION SPONTANEOUS?
Specific examples
DG = DH - TDS
(1) H2(g) F2(g) —> 2HF(g)
DH - ive highly exothermic process
DS same number of gas molecules
DG - ive must be negative
(taking 0 away from a negative number)

25. IS A REACTION SPONTANEOUS?
Specific examples
DG = DH - TDS
(2) Na+(g) Cl¯(g) —> NaCl(s)
DH - ive highly exothermic (Lattice Enthalpy)
DS - ive more order in a solid
DG - ive mostly due to the high value of lattice enthalpy

26. IS A REACTION SPONTANEOUS?
Specific examples
DG = DH - TDS
(3) NH4NO3(s) —> NH4+(aq) NO3¯(aq)
DH +ive endothermic (the solution goes colder)
DS +ive more disorder as lattice breaks up
DG - ive if T is high or the value of DS is big enough

27. IS A REACTION SPONTANEOUS? Specific examples - summary
(1) H2(g) F2(g) —> 2HF(g)
DH - ive highly exothermic process
DS same number of gas molecules
DG - ive must be negative (taking 0 away from a negative number)
(2) Na+(g) Cl¯(g) —> NaCl(s)
DH - ive highly exothermic (Lattice Enthalpy)
DS - ive more order in a solid
DG - ive mostly due to the high value of lattice enthalpy
(3) NH4NO3(s) —> NH4+(aq) NO3¯(aq)
DH +ive endothermic (the solution goes colder)
DS +ive more disorder as lattice breaks up
DG - ive if T is high or the value of DS is big enough

28. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reaction ?
Give reasons for your decision.
What is the sign of DG?
CaCO3(s) —> CaO(s) CO2(g)
DG = DH T DS

29. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reaction ?
Give reasons for your decision.
What is the sign of DG?
CaCO3(s) —> CaO(s) CO2(g)
Temperature is ALWAYS positive
DG = DH T DS + + +
Endothermic
increase in the number of gas molecules
Because DS is positive; TDS must be positive
DH is positive (very endothermic reaction)
For DG to be NEGATIVE, TDS must be bigger than DH
This is more likely with a higher temperature
The reaction is more likely to be spontaneous if heated

30. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reaction ?
Give reasons for your decision.
What is the sign of DG?
b) NH3(g) HCl(g) —> NH4Cl(s)
DG = DH T DS

31. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reaction ?
Give reasons for your decision.
What is the sign of DG?
b) NH3(g) HCl(g) —> NH4Cl(s)
Temperature is ALWAYS positive
DG = DH T DS +
Exothermic
decrease in the number of gas molecules
Because DS is negative; TDS must be negative
DH is negative
For DG to be negative TDS must be less negative than DH
This is more likely if the value of T is lower
The higher the temperature the less likely that the reaction will proceed

32. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
Na(s) —> Na(g) (Equivalent to Enthalpy of Atomisation)
DG = DH T DS

33. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
Na(s) —> Na(g) (Equivalent to Enthalpy of Atomisation)
Temperature is ALWAYS positive
DG = DH T DS + + +
Endothermic
increase in the number of gas molecules
Because DS is positive; TDS must be positive
DH is positive
For DG to be NEGATIVE, TDS must be bigger than DH
This is more likely with a higher temperature so the reaction
Solids are more likely to become gases if heated

34. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
d) C6H12(l) O2(g) —> 6CO2(g) H2O(g)
DG = DH T DS

35. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
d) C6H12(l) O2(g) —> 6CO2(g) H2O(g)
Temperature is ALWAYS positive
DG = DH T DS + +
COMBUSTION
is exothermic
increase in the number of gas molecules
Because DS is positive; TDS must be positive
DH is negative
Taking a +ive value away from a –ive value must give a –ive value
DG must be NEGATIVE so the reaction is SPONTANEOUS

36. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
e) C(s) O2(g) —> CO2(g)
DG = DH T DS

37. IS A REACTION SPONTANEOUS?
What is the sign of the entropy change in the following reactions ?
Give reasons for your decision.
What is the sign of DG?
e) C(s) O2(g) —> CO2(g)
Temperature is ALWAYS positive
DG = DH T DS +
very small
COMBUSTION
is exothermic
no change in the number of gas molecules
DS is very small (could be –ive or +ive)
TDS will therefore not be a large number
DH will be have a relatively large negative value
Taking a small +ive value away from a –ive value must give a –ive value
DG must be NEGATIVE so the reaction is SPONTANEOUS

38. Give reasons for your decision.
ANSWERS
What is the sign of the entropy change (DS) in the following reactions ?
Give reasons for your decision.
a) CaCO3(s) —> CaO(s) CO2(g)
b) NH3(g) HCl(g) —> NH4Cl(s)
c) Na(s) —> Na(g)
d) C6H12(l) + 9O2(g) —> 6CO2(g) + 6H2O(g)
e) C(s) + O2(g) —> CO2(g)

39. Give reasons for your decision.
ANSWERS
What is the sign of the entropy change (DS) in the following reactions ?
Give reasons for your decision.
a) CaCO3(s) —> CaO(s) CO2(g)
b) NH3(g) HCl(g) —> NH4Cl(s)
c) Na(s) —> Na(g)
d) C6H12(l) + 9O2(g) —> 6CO2(g) + 6H2O(g)
e) C(s) + O2(g) —> CO2(g) + -
‘0’
more gas molecules
fewer gas molecules
goes from solid to gas
‘similar’ moles of gas

40. © 2009 JONATHAN HOPTON & KNOCKHARDY PUBLISHING
ENTROPY & FREE ENERGY
The End
© 2009 JONATHAN HOPTON & KNOCKHARDY PUBLISHING