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Chapter 16. Spontaneity, entropy and free energy. Spontaneous. A reaction that will occur without outside intervention. We can’t determine how fast. We need both thermodynamics and kinetics to describe a reaction completely. Thermodynamics compares initial and final states.

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chapter 16

Chapter 16

Spontaneity, entropy and free energy

spontaneous
Spontaneous
  • A reaction that will occur without outside intervention.
  • We can’t determine how fast.
  • We need both thermodynamics and kinetics to describe a reaction completely.
  • Thermodynamics compares initial and final states.
  • Kinetics describes pathway between.
thermodynamics
Thermodynamics
  • 1st Law- the energy of the universe is constant.
  • Keeps track of thermodynamics doesn’t correctly predict spontaneity.
  • Entropy (S) is disorder or randomness
  • 2nd Law the entropy of the universe increases.
entropy
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.
slide5
2 possible arrangements
  • 50 % chance of finding the left empty
slide6
4 possible arrangements
  • 25% chance of finding the left empty
  • 50 % chance of them being evenly dispersed
slide7
4 possible arrangements
  • 8% chance of finding the left empty
  • 50 % chance of them being evenly dispersed
gases
Gases
  • Gases completely fill their chamber because there are many more ways to do that than to leave half empty.
  • Ssolid
  • 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.
entropy1
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.
slide10
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.
temperature and spontaneity
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
slide12
-

+

?

DSsurr

DSuniv

Spontaneous?

DSsys

-

-

-

No, Reverse

+

+

+

Yes

+

-

?

At High temp.

At Low temp.

gibb s free energy
Gibb's Free Energy
  • G=H-TS
  • Never used this way.
  • DG=DH-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.
let s check
Let’s 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 DG=DH-TDS
  • Spontaneity can be predicted from the sign of DH and DS.
d g d h t d s
Spontaneous?

DS

DH

DG=DH-TDS

+

-

At all Temperatures

At high temperatures,

“entropy driven”

+

+

At low temperatures,

“enthalpy driven”

-

-

Not at any temperature,

Reverse is spontaneous

-

+

third law of thermo
Third Law of Thermo
  • The entropy of a pure crystal at 0 K is 0.
  • Gives us a starting point.
  • All others must be>0.
  • 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.
free energy in reactions
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.
  • Can’t be measured directly, can be calculated from other measurements.
  • DGº=DHº-TDSº
  • Use Hess’s Law with known reactions.
free energy in reactions1
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.
d g d h t d s1
Spontaneous?

DS

DH

DG=DH-TDS

+

-

At all Temperatures

At high temperatures,

“entropy driven”

+

+

At low temperatures,

“enthalpy driven”

-

-

Not at any temperature,

Reverse is spontaneous

-

+

third law of thermo1
Third Law of Thermo
  • The entropy of a pure crystal at 0 K is 0.
  • Gives us a starting point.
  • All others must be>0.
  • 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.
free energy in reactions2
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.
  • Can’t be measured directly, can be calculated from other measurements.
  • DGº=DHº-TDSº
  • Use Hess’s Law with known reactions.
free energy in reactions3
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.
free energy and pressure
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
how far
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
d g k
DGº K

=0 =1

<0 >0

>0 <0

temperature dependence of k
Temperature dependence of K
  • DGº= -RTlnK = DHº - TDSº
  • ln(K) = DHº/R(1/T)+ DSº/R
  • A straight line of lnK vs 1/T
free energy and work
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 can’t be used to do work.
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