Entropy and Free Energy

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Entropy and Free Energy

• Chapter 18

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Learning Objectives

• Students understand
• The concept of entropy and its relationship to
  reaction spontaneity.
• The relationship between enthalpy, entropy, and
  free energy changes for a reaction.

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Learning Objectives

• Students will be able to
• Calculate the change in entropy to determine
  spontaneity
• Use the change in Gibbs free energy to predict
  spontaneity
• Calculate standard free energy change from data
• Calculate an equilibrium constant for a process
  from free energy

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Spontaneous Change and Equilibrium

• reactions proceed until equilibrium is reached
• some favor reactants, some favor products
• spontaneous changes occur without outside
  intervention in the direction that leads to
  equilibrium
• doesnt mean quickly!

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18.1 Heat and Spontaneity

• many exothermic reactions are product-favored,
  but heat release alone does not determine
  spontaneity
• gas fills available space (energy neutral)
• ice melts (endothermic) above 0oC
• energy transfer as heat

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18.2 Dispersal of Energy Entropy

• Entropy, S, measures disorder or chaos and
  quantifies the dispersal of energy
• positional entropy describes positions in a given
  state (more positional entropy increases from
  solid? liquid? gas)
• energy goes from being more concentration to
  being more dispersed

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Second Law of Thermodynamics

• In any spontaneous process there is always an
  increase in the entropy of the universe.

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Entropy

• Thermal energy is caused by the random motion of
  particles.
• Potential energy is dispersed when it is
  converted to thermal energy (when energy is
  transferred as heat).

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Calculating Entropy

• ?S qrev/T
• where qrev is heat transfer under reversible
  conditions and T is the Kelvin temp at which
  change occurs
• Reversible process after carrying out a change
  along a given path, it must be possible to return
  to the starting point by the same path without
  altering surroundings.

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18.3 Dispersal of Energy

• Boltzmann proposed that the entropy of a system
  (dispersal of energy at a given temperature)
  results from the number of microstates (ways to
  distribute energy) available.
• As the number of microstates increases, so does
  the entropy of the system.

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Dispersal of Matter

• Gas expansion (dispersion of matter) leads to the
  dispersal of energy. If O2 and N2 are connected
  by a valve, they diffuse together leading to an
  even distribution. The mixture will never
  separate into separate samples on its own!

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Homework

• After reading sections 18.1-18.3, you should be
  able to do the following problems
• P. 711 (1-8)

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18.4 Entropy Measurements and Values

• For any substance under certain conditions, a
  numerical value for entropy can be determined
• The Third Law of Thermodynamics states that there
  is no disorder in a perfect crystal at 0 K S
  0.

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Entropy

• Entropy of a substance will increase in going
  from a solid to a liquid to a gas.
• Larger and more complex molecules have higher
  entropies than smaller and more simple molecules.
• Entropy increases as temperature is raised.
• Entropy of a gas increases with an increase in
  volume.

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Third Law of Thermodynamics

• ?Ssurr -?Hsys/T
• Sign is positive when exothermic heat flows to
  surroundings
• Sign is negative when endothermic

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Standard Entropy Values, So

• Change can also be calculated from tables
• ?Sorxn SSoproducts - SSoreactants

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Practice Problem

• Calculate the standard entropy changes for the
  following processes using entropy values in
  Appendix L. Do the calculated values of ?So
  match predictions?
• Dissolving 1.0 mol of NH4Cl(s) in water NH4Cl(s)
  ? NH4Cl(aq)
• The formation of 2.0 mol of NH3(g) from N2(g) and
  H2(g) N2(g) 3H2(g) ?
  2NH3(g)

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18.5 Entropy Changes

• Change in entropy is equal to the change in the
  entropy of the system AND the change in entropy
  of surroundings.
• ?Souniv ?Sosys ?Sosurr
• Spontaneous when ?Suniv gt 0, positive
• Not spontaneous when ?Suniv lt 0, negative

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Calculating ?So

• ?Sosys SSoproducts SSoreactants
• ?Ssurr - ?Hosys/T
• ?Souniv ?Sosys ?Sosurr

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Practice Problem

• Predict whether these reactions are spontaneous
  see table 18.1 p. 694
• CH4(g) 2O2(g) ? H2O(l) CO2(g) ?Hrxn
  -890.6kJ ?Ssys -242.8J/K
• 2Fe2O3(s) 3C(graphite) ? 4Fe(s) 3CO2(g)
• ?Hrxn 467.9kJ ?Ssys 560.7J/K
• C(graphite) O2(g) ? CO2(g)
• ?Hrxn -393.5kJ ?Ssys 3.1J/K
• N2(g) 3F2(g) ? 2NF3(g)
• ?Hrxn -264.2kJ ?Ssys -277.8J/K

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Practice Problem

• Is the reaction of hydrogen and chlorine to give
  hydrogen chloride gas predicted to be
  spontaneous?
• H2(g) Cl2(g) ? 2HCl(g)
• Calculate the values for ?Ssys and ?Ssurr

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Practice Problem

• 2Fe2O3(s) 3C(graphite) ? 4Fe(s) 3CO2(g)
• ?Hrxn 467.9 kJ and ?Srxn 560.7 J/K
• Show that it is necessary that this reaction be
  carried out at high temperatures.

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Homework

• After reading sections 18.4 and 18.5, you should
  be able to do the following
• P. 711 (9-14)

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18.6 Free Energy

• Free energy, G, describes whether or not a
  reaction is spontaneous. Gibbs free energy is
  dependent on change in enthalpy, change in
  entropy, and temperature of the system.
• ?G ?H T?S
• where T is Kelvin

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?Go and Spontaneity

• If the value of ?Grxn is negative, a reaction is
  spontaneous.
• If ?Grxn 0, the reaction is at equilibrium.
• If the value of ?Grxn is positive, the reaction
  is not spontaneous.

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Free Energy and Equilibrium

• At equilibrium, no net change in concentration of
  reactants and products occur, so free energy and
  the equilibrium constant have the following
  relationship ?G -RTlnK

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Free Energy and Equilibrium

• When ?G is negative, K is greater than 1 and the
  reaction is product favored. KgtQ
• When ?G is positive, K is less than 1 and the
  reaction is reactant favored. KltQ
• When ?G 0, the reaction is at equilibrium. Q K

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What is Free Energy?

• The free energy is the sum of the energies
  available from the enthalpy term (dispersal of
  energy) and the entropy term (dispersal of
  matter).

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Dependence of Spontaneity on Temperature
?S ?H ?G
- Spontaneous at all temps
Spontaneous at high temps
- - Spontaneous at low temps
- Process not spontaneous at any temp
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18.7 Free Energy and Chemical Reactions

• Standard free energy change can be calculated
  (free energy under standard conditions)
• ?Go ?Ho T?So

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Standard Free Energy

• The standard free energy of formation of a
  compound is the free energy change when forming
  one mole of the compound from the component
  elements. (element in standard state is zero)
• ?Grxno S?Gfo(products) S?Gfo(reactants)

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Practice Problem

• Using values of ?Hfo and So to find ?Hrxno and
  ?Srxno respectively, calculate the free energy
  change, ?Go, for the formation of 2 mol of NH3(g)
  from the elements at standard conditions.
• N2(g) 3H2(g) ? 2NH3(g)

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Practice Problem

• Calculate the standard free energy change for the
  oxidation of 1.00 mol of SO2(g) to form SO3(g).

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Homework

• After reading sections 19.6-19.7, you should be
  able to do the following
• P. 711b (15-16,21-24,29-32)