Chapter Seventeen

1
Chapter Seventeen

• Thermodynamics
• Spontaneity, Entropy,
• and Free Energy

2
Introduction

• Thermodynamics examines the relationship between
  heat and work.
• Spontaneity is the notion of whether or not a
  process can take place unassisted.
• Entropy is a measure of how energy is spread out
  among the atoms and molecules of a system.
• Free energy is a thermodynamic function that
  relates enthalpy and entropy to spontaneity.
• Free energy can also be related to equilibrium
  constants.

3
Why Study Thermodynamics?

• With a knowledge of thermodynamics and by making
  a few calculations before embarking on a new
  venture, scientists and engineers can save
  themselves a great deal of time, money, and
  frustration.
• To the manufacturing chemist thermodynamics
  gives information concerning the stability of his
  substances, the yield which he may hope to
  attain, the methods of avoiding undesirable
  substances, the optimum range of temperature and
  pressure, the proper choice of solvent
• from the introduction to Thermodynamics and the
  Free Energy of Chemical Substances by G.N. Lewis
  M. Randall, 1923

4
Spontaneous Change

• A spontaneous process is one that can occur in a
  system left to itself no action from outside the
  system is necessary to bring it about.
• A non-spontaneous process is one that cannot take
  place in a system left to itself.
• If a process is spontaneous, the reverse process
  is non-spontaneous and vice versa.
• The spontaneous signifies nothing about how
  fast a process occurs.

5
Some Spontaneous Processes

• Water flows to the lower elevation.
• Ice cube melts at room temperature and 1 atm.
• Iron tool exposed to moist air rusts.
• A mixture of H2 and O2 burns when we set a match
  to it.

6
Spontaneous Change

• Thermodynamics determines the equilibrium state
  of a system. Thermodynamics is used to predict
  the proportions of products and reactants at
  equilibrium.
• Kinetics determines the pathway by which
  equilibrium is reached. A high activation energy
  can effectively block a reaction that is
  thermodynamically favored. Combustion reactions
  generally are thermodynamically favored, but
  fortunately for life on Earth, most also have a
  high activation energy.

7
Direction of Decrease in Energy
8
Spontaneous Change

• Early chemists proposed that spontaneous chemical
  reactions should occur in the direction of
  decreasing energy.
• The idea that exothermic reactions are
  spontaneous and that endothermic reactions are
  not, works in many cases.
• However, enthalpy change is not a sufficient
  criterion for predicting spontaneous change.
• Additional factors (entropy) must be considered.

9
Spontaneous Mixing of Gases
10
Formation of an Ideal Solution
11
The Concept Of Entropy

• The spontaneity of two gases mixing is without a
  significant enthalpy change and the
  intermolecular forces are negligible. Clearly,
  there is another factor involved in this process.
• The other factor is a thermodynamic quantity
  called entropy, a mathematical concept that is
  difficult to portray visually.
• Entropy (S) is a thermodynamic property that is a
  measure of the randomness or disorder in a
  system. Unit J/K

12
The Concept Of Entropy

• The more disordered the distribution of
  molecules, the greater the entropy.
• Liquids are more disordered and have higher
  entropies than solids. Sl gt Ss
• Gases are much more disordered and have much
  higher entropies than liquids. Sg gt Sl
• Mixtures are more disordered and have higher
  entropies than pure components.
• A substance has higher entropy at higher
  temperature.

13
Increase in Entropy in theVaporization of water
14
The Concept of Entropy

• The entropy is a state function.
• The difference in entropy (S) between two states
  is the entropy change (?S).
• ?S Sfinal Sinitial
• In general, entropy increases for the following
  processes
• Solids melt to liquids. ?S Sl Ss gt 0
  (since Sl gt Ss)
• Solids or liquids vaporize to form gases.
• ?S Sg Ss (or Sl) gt 0 (since Sg gt Ss or Sl)
• Solids or liquids dissolve in a solvent to form
  solution.
• A chemical reaction produces an increase in the
  number of gas molecules.
• A substance is heated.

15
The Concept of Entropy An Example

• Predict whether each of the following leads to
  an increase or decrease in the entropy of a
  system. If in doubt, explain why.
• NH3 (g) HCl (g) ? NH4Cl (s)
• 2 AgCl (s) ? 2 Ag (s) Cl2 (g)
• CO (g) H2O (g) ? CO2 (g) H2 (g)

16
The Concept of Entropy

• There are two natural tendencies behind
  spontaneous processes the tendency to achieve a
  lower energy state and the tendency toward a more
  disordered state.
• In many cases, however, the two factors work in
  opposition. One may increase and the other
  decrease or vice versa. In these cases, which
  factor predominates needs to be determined.

17
Entropy

• Sometimes it is necessary to obtain quantitative
  values of entropy changes.
• ?S qrev / T

18
The Third Law of Thermodynamics

• The entropy of a pure, perfect crystal can be
  taken to be zero at 0 K.

19
Entropy As A Function Of Temperature
boiling
melting
20
Entropy As A Function Of Temperature

• There are sharp increases in entropy at the
  melting point and boiling point.
• The entropy of CH3Cl (g) is significantly greater
  than that of H2 (g).
• In general, the more atoms in its molecules, the
  greater is the entropy of a substance.
• Entropy is an extensive property its value
  depends on the amount of substance.

21
Standard Molar Entropies

• The standard molar entropy, So, is the entropy of
  one mole of a substance in its standard state.
• Standard State
• for solids or liquids pure element or compound
  at
• 1 atm and temperature of interest.
• for gases pure gas behaving as an ideal gas at
• 1 atm and temperature of interest.
• Standard entropy changes for chemical reactions
• ?S? ?vp So(products) - ?vr So(reactants)

22

• ?S?(reaction) ?vp So(products) - ?vr
  So(reactants)
• So - standard molar value of entropy for a
  substance - usually at 298K
• vp, vr - the reaction stoichiometric coefficients
• This formula is similar to Hesss Law for
  enthalpy
• ?H?(reaction) ?vp Ho(products) - ?vr
  Ho(reactants)
• values tabulated in Appendix C

23
An Example

• Determine the value of ?S? for the reaction
• 2 NH3 (g) 5 O2 (g) ? 4 NO (g) 6 H2O (g).

24
The Second Law Of Thermodynamics

• In order to use the increase of entropy as a sole
  criterion for spontaneous change, the entropy
  change of a system and its surroundings must be
  considered. This total entropy change is called
  the entropy change of the universe.
• The Second Law of Thermodynamics establishes that
  all spontaneous or natural processes increase the
  entropy of the universe.
• ?Suniverse ?Ssystem ?Ssurroundings gt 0

25
?Stotal ?Suniverse ?Ssystem
?Ssurroundings Spontaneous ?Suniverse gt
0 Consider H2O(l) ? H2O(s) at
-15?C Spontaneous or not?
26
p. 743 Willard Gibbs recognized that qsurr -qp
-?Hsys
27
Free Energy And Free Energy Change

• The free energy change (?G) for a process at
  constant temperature and pressure is given by the
  Gibbs equation
• ?Gsys ?Hsys - T?Ssys
• If ?G lt 0 (negative), a process is spontaneous.
• If ?G gt 0 (positive), a process is
  non-spontaneous.
• If ?G 0, neither the forward nor the reverse
  process is favored there is no net change, and
  the process is at equilibrium.

28
Criterion For Spontaneous Change ?G ?H - T?S
29
An Example

• Predict which of the four cases in Table 17.1
  you expect to apply to the following reactions.
• (a) 2 NH4NO3 (s) ? 2 N2 (g) 4 H2O (g) O2 (g)
• ? Ho -236 kJ
• (b) Cl2 (g) ? 2 Cl (g)

30
Standard Free Energy Change

• The standard free energy change, ?Go, of a
  reaction is the free energy change when reactants
  and products are in their standard states.
• The standard free energy of formation, ?Gof, is
  the free energy change that occurs in the
  formation of 1 mol of a substance in its standard
  state from the reference forms of its elements in
  their standard states.
• The standard free energy change in chemical
  reactions
• ?Go(rxn) ?vp ?Gof (products) - ?vr ?Gof
  (reactants)

31
Some important reference points for enthalpy,
entropy and free energy By definition, the
enthalpy of formation and free energy of
formation of the elements in their normal phases
at standard conditions (1 atm 298K) is ZERO In
contrast, the entropy of a substance is zero only
at 0K in a perfect crystalline solid. Entropies
for substances at standard conditions are always
positive. Entropies enthalpies and free energies
for substances are found in Appendix C of your
text.
32
Standard Free Energy Change
Two ways to calculate ?Go (1) ?Go ?Ho -
T?So (2) ?Go(rxn) ?vp ?Gof (products) - ?vr
?Gof (reactants)
33
An Example

• Calculate ?Go in two different ways for reaction
• 4 NH3 (g) 5 O2 (g) ? 4 NO (g) 6 H2O (g).
• ?Ho -905.4 kJ, ?So 177.9 JK-1
• ?Gof (NH3(g)) -16.48 kJ/mol
• ?Gof (O2(g)) 0
• ?Gof (NO(g)) 86.57 kJ/mol
• ?Gof (H2O(g)) -228.6 kJ/mol

34
Free Energy Change And Equilibrium

• At equilibrium, ?G 0. Therefore, at the
  equilibrium temperature, the free energy change
  expression becomes
• ?H T?S or ?S ?H / T
• At standard condition, ?Ho T?So
• This is a particularly valuable equation for
  phase transitions boiling, freezing, melting,
  etc.

35
Relationship Between ?Go And Keq

• ?G 0 is a criterion for equilibrium at a
  single temperature, the one temperature at which
  the equilibrium state has all reactants and
  products in their standard states.
• Although it is beyond the scope of the current
  discussion to demonstrate this fact, ?G and ?Go
  are related through the reaction quotient, Q, by
  the following equation
• ?G ?Go RTlnQ
• Under the conditions of ?G 0 and Q Keq, the
  equation above becomes
• ?Go - RTlnKeq

36
The Equilibrium Constant, Keq

• Activities are the dimensionless quantities
  needed in the equilibrium constant Keq.
• For pure solid and liquid phases The activity, a
  1.
• For gases Assume ideal gas behavior, and replace
  the activity by the numerical value of the gas
  partial pressure in atm.
• For solutes in aqueous solution Assume that the
  inter-molecular or inter-ionic attractions are
  negligible - that is, that the solution is
  dilute - and replace solute activity by the
  numerical value of the solute molarity.

37
The Equilibrium Constant,Keq,Expression An
Example

• Write the expression for Keq for each of the
  reactions.
• NH4Cl (s) º NH3 (g) HCl (g)
• MgCO3 (s) 2 H3O (g) º 2 H2O (l) Mg2 (aq)
  CO2 (g)

38
Calculating The Equilibrium Constant, Keq An
Example

• Use data from Appendix C to determine Keq at 25oC
  
• for the reaction CaCO3 (s) º CaO (s) CO2 (g) .
• What is the partial pressure of CO2 at 25oC?

39
The Significance Of The Sign And Magnitude Of ?Go

• In the case where the free energy of the products
  is much lower than that of the reactants, ?Go is
  a large, negative quantity and equilibrium is
  very far to the right.
• In the case where the situation is reversed, ?Go
  is a large, positive quantity and equilibrium is
  very far to the left.
• In the case where the difference in free energies
  of the reactants and products is small, the
  equilibrium lies more toward the interior of the
  reaction profile.

40
The Sign And Magnitude Of ?Go

• Large and negative equilibrium lies far to the
  right
• Large and positive equilibrium lies far to the
  left
• Equilibrium lies within the profile.

41
Summary

• A spontaneous change is one that occurs by itself
  without outside intervention.
• The third law of thermodynamics states that the
  entropy of a pure, perfect crystal at 0 K can be
  taken to be zero.
• The direction of spontaneous change is that in
  which total entropy increases.
• The free energy change, ?G, is equal to -T?S, and
  it applies just to the system itself, without
  regard for the surroundings.

42
Summary (Continued)

• The standard free energy change, ?Go, can be
  calculated by substituting standard enthalpies
  and entropies of reaction and a Kelvin
  temperature into the Gibbs equation, or, by
  combining standard free energies of formation.
• The condition of equilibrium is one for which ?G
  0.
• The value of ?Go is by itself often sufficient to
  determine how a reaction will proceed.
• Values of ?Gof, ?Hof, and So are generally
  tabulated for 25oC.