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Spontaneity, entropy and free energy

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50 % chance of finding the left empty. 4 possible arrangements ... Products - reactants to find DS (a state function) More complex molecules higher S . ... – PowerPoint PPT presentation

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Title: 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.

9
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.

10
  • 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

12
DSsurr
DSuniv
Spontaneous?
DSsys
-
-
-
No, Reverse



Yes

-
?
At High temp.
At Low temp.
13
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.

14
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.

15
DGDH-TDS

-
At all Temperatures
At high temperatures, entropy driven


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

-
16
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.

17
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.

18
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.

19
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

24
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

25
DGº K
  • 0 1
  • lt0 gt0
  • gt0 lt0

26
Temperature dependence of K
  • DGº -RTlnK DHº - TDSº
  • ln(K) DHº/R(1/T) DSº/R
  • A straight line of lnK vs 1/T

27
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.
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