Spontaneity, entropy and free energy

1
Chapter 16

• Spontaneity, entropy and free energy

2
Spontaneous

• A reaction that will occur without outside
  intervention.
• We cant determine how fast.
• We need both thermodynamics and kinetics to
  describe a reaction completely.
• Thermodynamics compares initial and final states.
• Kinetics describes pathway between.

3
Thermodynamics

• 1st Law- the energy of the universe is constant.
• Keeps track of thermodynamics doesnt correctly
  predict spontaneity.
• Entropy (S) is disorder or randomness
• 2nd Law the entropy of the universe increases.

4
Entropy

• Defined in terms of probability.
• Substances take the arrangement that is most
  likely.
• The most likely is the most random.
• Calculate the number of arrangements for a system.

5

• 2 possible arrangements
• 50 chance of finding the left empty

6

• 4 possible arrangements
• 25 chance of finding the left empty
• 50 chance of them being evenly dispersed

7

• 4 possible arrangements
• 8 chance of finding the left empty
• 50 chance of them being evenly dispersed

8
Gases

• Gases completely fill their chamber because there
  are many more ways to do that than to leave half
  empty.
• Ssolid ltSliquid ltltSgas
• there are many more ways for the molecules to be
  arranged as a liquid than a solid.
• Gases have a huge number of positions possible.

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Entropy

• Solutions form because there are many more
  possible arrangements of dissolved pieces than if
  they stay separate.
• 2nd Law
• DSuniv DSsys DSsurr
• If DSuniv is positive the process is spontaneous.
• If DSuniv is negative the process is spontaneous
  in the opposite direction.

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• For exothermic processes DSsurr is positive.
• For endothermic processes DSsurr is negative.
• Consider this process H2O(l) H2O(g)
• DSsys is positive
• DSsurr is negative
• DSuniv depends on temperature.

11
Temperature and Spontaneity

• Entropy changes in the surroundings are
  determined by the heat flow.
• An exothermic process is favored because by
  giving up heat the entropy of the surroundings
  increases.
• The size of DSsurr depends on temperature
• DSsurr -DH/T

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DSsurr
DSuniv
Spontaneous?
DSsys
-
-
-
No, Reverse



Yes

-
?
At High temp.
At Low temp.
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Gibb's Free Energy

• GH-TS
• Never used this way.
• DGDH-TDS at constant temperature
• Divide by -T
• -DG/T -DH/T-DS
• -DG/T DSsurr DS
• -DG/T DSuniv
• If DG is negative at constant T and P, the
  Process is spontaneous.

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Lets Check

• For the reaction H2O(s) H2O(l)
• DSº 22.1 J/K mol DHº 6030 J/mol
• Calculate DG at 10ºC and -10ºC
• Look at the equation DGDH-TDS
• Spontaneity can be predicted from the sign of DH
  and DS.

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DGDH-TDS

-
At all Temperatures
At high temperatures, entropy driven


At low temperatures, enthalpy driven
-
-
Not at any temperature, Reverse is spontaneous

-
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Third Law of Thermo

• The entropy of a pure crystal at 0 K is 0.
• Gives us a starting point.
• All others must begt0.
• Standard Entropies Sº ( at 298 K and 1 atm) of
  substances are listed.
• Products - reactants to find DSº (a state
  function).
• More complex molecules higher Sº.

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Free Energy in Reactions

• DGº standard free energy change.
• Free energy change that will occur if reactants
  in their standard state turn to products in their
  standard state.
• Cant be measured directly, can be calculated
  from other measurements.
• DGºDHº-TDSº
• Use Hesss Law with known reactions.

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Free Energy in Reactions

• There are tables of DGºf .
• Products-reactants because it is a state
  function.
• The standard free energy of formation for any
  element in its standard state is 0.
• Remember- Spontaneity tells us nothing about rate.

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DGDH-TDS

-
At all Temperatures
At high temperatures, entropy driven


At low temperatures, enthalpy driven
-
-
Not at any temperature, Reverse is spontaneous

-
20
Third Law of Thermo

• The entropy of a pure crystal at 0 K is 0.
• Gives us a starting point.
• All others must begt0.
• Standard Entropies Sº ( at 298 K and 1 atm) of
  substances are listed.
• Products - reactants to find DSº (a state
  function)
• More complex molecules higher Sº.

21
Free Energy in Reactions

• DGº standard free energy change.
• Free energy change that will occur if reactants
  in their standard state turn to products in their
  standard state.
• Cant be measured directly, can be calculated
  from other measurements.
• DGºDHº-TDSº
• Use Hesss Law with known reactions.

22
Free Energy in Reactions

• There are tables of DGºf
• Products-reactants because it is a state
  function.
• The standard free energy of formation for any
  element in its standard state is 0.
• Remember- Spontaneity tells us nothing about rate.

23
Free energy and Pressure

• DG DGº RTln(Q) where Q is the reaction
  quotients (P of the products /P of the
  reactants).
• CO(g) 2H2(g) CH3OH(l)
• Would the reaction be spontaneous at 25ºC with
  the H2 pressure of 5.0 atm and the CO pressure of
  3.0 atm?
• DGºf CH3OH(l) -166 kJ
• DGºf CO(g) -137 kJ DGºf H2(g) 0 kJ

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How far?

• DG tells us spontaneity at current conditions.
  When will it stop?
• It will go to the lowest possible free energy
  which may be an equilibrium.
• At equilibrium DG 0, Q K
• DGº -RTlnK

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DGº K

• 0 1
• lt0 gt0
• gt0 lt0

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Temperature dependence of K

• DGº -RTlnK DHº - TDSº
• ln(K) DHº/R(1/T) DSº/R
• A straight line of lnK vs 1/T

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Free energy And Work

• Free energy is that energy free to do work.
• The maximum amount of work possible at a given
  temperature and pressure.
• Never really achieved because some of the free
  energy is changed to heat during a change, so it
  cant be used to do work.