Chapter 19: Thermodynamics: Entropy, Free Energy, and Equilibrium

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Chapter 19 Thermodynamics Entropy, Free Energy,
and Equilibrium
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Chapter 19 Outline

• Spontaneous Processes
• Entropy
• Second Law of Thermodynamics
• Molecular Interpretation
• Chemical Reactions
• Gibbs Free Energy
• Temperature
• Equilibrium Constant

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Review

• First Law of Thermodynamics energy is
  conserved.

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Spontaneous Processes

• Some classes of spontaneous processes
• Phase transitions (melting, freezing)
• Mixing
• Expansion
• Heat transfer
• Movement towards chemical equilibrium

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Spontaneous Processes
Can be Temperature Dependent!
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Spontaneous Processes

• Reversible and Irreversible
• A reversible process is one that can go back and
  forth between states along the same path
• Chemical systems in equilibrium are reversible
• In any spontaneous process, the path between
  reactants and products is irreversible.
• Thermodynamics gives us the direction of a
  process. It cannot predict the speed at which
  the process will occur.
• Why can endothermic reactions be spontaneous?

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Spontaneous Processes

• Some reactions are spontaneous, others never
  occur. Why?
• A system tries to minimize its ENERGY
• A system tries to maximize its ENTROPY
• How can we predict whether a reaction will occur
  over time?
• Thermodynamics!

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Kinetics and Thermodynamics
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Exothermic Spontaneous Processes

• In general, product-favored reactions are
  exothermic and
• spontaneous
• E.g. thermite reaction
• Fe2O3(s) 2 Al(s)
• ? 2 Fe(s) Al2O3(s)
• ?H - 848 kJ

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Non-Exothermic Spontaneous Processes

• But many spontaneous reactions or processes are
  endothermic . . .

NH4NO3(s) heat ? NH4 (aq) NO3-
(aq) ?Hsol 25.7 kJ/mol Or have ? H 0 .
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Expansion of a gas

• When there are many molecules, it is much more
  probable that the molecules will distribute among
  to the two flasks than all remain in only one
  flask.

Processes in which the disorder increases tend
to occur spontaneously
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Entropy

• Entropy, S, is a measure of the disorder of a
  system.
• Spontaneous reactions proceed to lower energy or
  higher entropy.
• In ice, the molecules are very well ordered
  because of the H-bonds.
• Therefore, ice has a low entropy.

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Entropy Dissolution of salts
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The Second Law of Thermodynamics

• The second law of thermodynamics explains why
  spontaneous processes have a direction.
• In any spontaneous process, the entropy of the
  universe increases.
• ?Suniv ?Ssys ?Ssurr
• Entropy is not conserved ?Suniv is increasing.

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The Second Law of Thermodynamics

• For a reversible process
• ?Suniv 0
• For a spontaneous process (irreversible)
• ?Suniv gt 0
• Note the second law states that the entropy of
  the universe must increase in a spontaneous
  process. It is possible for the entropy of a
  system to decrease as long as the entropy of the
  surroundings increases.

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The Molecular Interpretation of Entropy

• There are three atomic modes of motion
• translation (the moving of a molecule from one
  point in space to another),
• vibration (the shortening and lengthening of
  bonds, including the change in bond angles),
• rotation (the spinning of a molecule about some
  axis).

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The Molecular Interpretation of Entropy
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The Molecular Interpretation of Entropy

• Third Law of Thermodynamics the entropy of a
  perfect crystal at 0 K is zero.
• Entropy changes dramatically at a phase change.
• As we heat a substance from absolute zero, the
  entropy must increase.

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Conceptual Question

• Which of the following processes produces a
  decrease in the entropy of the system?
• A. Boiling water to form steam
• B. Dissolution of solid KCl in water
• C. Mixing of two gases into one container
• D. Freezing water to form ice
• E. Melting ice to form water

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Conceptual Question

• Consider a pure crystalline solid that is heated
  from absolute zero to a temperature above the
  boiling point of the liquid. Which of the
  following processes produces the greatest
  increase in the entropy of the substance?
• A. melting the solid
• B. heating the liquid
• C. heating the gas
• D. heating the solid
• E. vaporizing the liquid

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Recap

• Do you agree with the following statements?
• A. Spontaneous reactions are always fast.
• B. In any spontaneous process, the entropy of the
  system always increases.
• C. An endothermic reaction is always
  non-spontaneous.

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Entropy Changes in Chemical Reactions

• Standard molar entropies of elements are not
  zero.
• S? greater for gases than liquids and solids
• S? generally increases with increasing molar mass
• S? generally increases with increasing number of
  atoms in a molecule

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Conceptual Question

• Which substances in each of the following pairs
  would you expect to have the higher standard
  molar entropy? Why?
• C2H2 (g) or C2H6 (g)
• b. CO2 (g) or CO (g)
• c. I2 (s) or I2 (g)
• d. CH3OH (g) or CH3OH (l)

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Entropy Changes in Chemical Reactions

• Can Calculate ?S for chemical reactions
• Calculate ?S? for the dissolution of ammonium
  nitrate, given the following entropy values
• NH4NO3 (s) NH4 (aq) NO3- (aq)
• 151.04 J/molK 112.8 146.4

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Gibbs Free Energy

• For a spontaneous reaction the entropy of the
  universe must increase.
• Reactions with large negative ?H values are
  spontaneous.
• How do we balance ?S and ?H to predict whether a
  reaction is spontaneous?
• Gibbs free energy, G, of a state is
• For a process occurring at constant temperature

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Gibbs Free Energy
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Gibbs Free Energy a closer lookIs the melting
of ice spontaneous above 0ºC?
Summary
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Gibbs Free Energy
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Gibbs Free Energy

• Consider the formation of ammonia from nitrogen
  and hydrogen
• Initially ammonia will be produced spontaneously
  (Q lt Keq).
• After some time, the ammonia will spontaneously
  react to form N2 and H2 (Q gt Keq).
• At equilibrium, ?G 0 and Q Keq.

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Gibbs Free Energy

• Standard Free-Energy Changes
• We can tabulate standard free-energies of
  formation, ?G?f
• ?G? 0 for elements
• ?G? for a process is given by
• The quantity ?G? for a reaction tells us whether
  a mixture of substances will spontaneously react
  to produce more reactants (?G? gt 0) or products
  (?G? lt 0).

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Gibbs Free Energy and the Equilibrium Constant

• Recall that ?G? and K (equilibrium constant)
  apply to standard conditions
• Recall that ?G and Q (equilibrium quotient) apply
  to any conditions.
• It is useful to determine whether substances
  under any conditions will react

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Gibbs Free Energy and the Equilibrium Constant

• At equilibrium, Q K and ?G 0, so
• From the above we can conclude
• If ?G? lt 0, then K gt 1.
• If ?G? 0, then K 1.
• If ?G? gt 0, then K lt 1.

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Relationship Summary
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Temperature Dependence of K
DG? -RT ln(K) DH ? - TDS?

• y mx b
• (?H? and S? ? independent of temperature over a
  small temperature range)