Chapter 19 Chemical Thermodynamics

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Chapter 19Chemical Thermodynamics
Chemistry, The Central Science, 10th
edition Theodore L. Brown H. Eugene LeMay, Jr.
and Bruce E. Bursten
John D. Bookstaver St. Charles Community
College St. Peters, MO ? 2006, Prentice Hall, Inc.
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Thermodynamics

• Thermodynamics is concerned with the question
  can a reaction occur?
• HW Work problems in the chapter as we finish
  each section. For tomorrow 19.7 to 19.17 odd
• BE PREPARE TO PRESENT YOUR EXAMPLES AT THE
  BEGINNING OF THE CLASS!!!

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First Law of Thermodynamics-Energy is conserved-.

• Energy cannot be created nor destroyed.
• Therefore, the total energy of the universe is a
  constant.
• Energy can, however, be converted from one form
  to another or transferred from a system to the
  surroundings or vice versa.

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Spontaneous Processes

• Spontaneous processes are those that can proceed
  without any outside intervention.
• The gas in vessel B will spontaneously effuse
  into vessel A, but once the gas is in both
  vessels, it will not spontaneously separate again.

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Spontaneous Processes

• Processes that are spontaneous in one direction
  are nonspontaneous in the reverse direction.

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Spontaneous Processes

• Processes that are spontaneous at one temperature
  may be non-spontaneous at other temperatures.
• Above 0?C it is spontaneous for ice to melt.
• Below 0?C the reverse process is spontaneous.

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Reversible Processes

• In a reversible process the system changes in
  such a way that the system and surroundings can
  be put back in their original states by exactly
  reversing the process.

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Irreversible Processes

• Irreversible processes cannot be undone by
  exactly reversing the change to the system.
• The system can go back but the surroundings are
  changed.
• Spontaneous processes are irreversible.

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Entropy

• Entropy (S) is a term coined by Rudolph Clausius
  in the 19th century.
• Clausius was convinced of the significance of the
  ratio of heat delivered and the temperature at
  which it is delivered,

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Entropy

• Entropy can be thought of as a measure of the
  randomness of a system.
• It is related to the various modes of motion in
  molecules.

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Entropy

• Like total energy, E, and enthalpy, H, entropy is
  a state function.
• Therefore,
• ?S Sfinal ? Sinitial

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Entropy

• For a process occurring at constant temperature
  (an isothermal process), the change in entropy is
  equal to the heat that would be transferred if
  the process were reversible divided by the
  temperature

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Second Law of Thermodynamics

• The total entropy of the universe increases for
  any spontaneous (irreversible) processes, and
  does not change for reversible processes.

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Second Law of Thermodynamics

• In other words
• For reversible processes
• ?Suniv ?Ssystem ?Ssurroundings 0
• For irreversible processes
• ?Suniv ?Ssystem ?Ssurroundings gt 0

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• Entropy is not conserved ?Suniv is increasing!
• For a reversible process ?Suniv 0.
• For a spontaneous process (i.e. 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.
• For an isolated system, ?Ssys 0 for a
  reversible process and ?Ssys gt 0 for a
  spontaneous process.

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• Entropy
• Suppose a system changes reversibly between state
  1 and state 2. Then, the change in entropy is
  given by
• at constant T where qrev is the amount of heat
  added reversibly to the system. (Example a
  phase change occurs at constant T with the
  reversible addition of heat.)

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Calculating entropies for phase changes

• Q rev D H
• Then D S D H / T

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Entropy and the Second Law of Thermodynamics

• The Spontaneous Expansion of a Gas
• Why do spontaneous processes occur?
• Consider an initial state two flasks connected
  by a closed stopcock. One flask is evacuated and
  the other contains 1 atm of gas.
• The final state two flasks connected by an open
  stopcock. Each flask contains gas at 0.5 atm.
• The expansion of the gas is isothermal (i.e.
  constant temperature). Therefore the gas does no
  work and heat is not transferred.

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• The Spontaneous Expansion of a Gas
• Why does the gas expand?

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• The Spontaneous Expansion of a Gas
• Consider the simple case where there are two gas
  molecules in the flasks.
• Before the stopcock is open, both gas molecules
  will be in one flask.
• Once the stopcock is open, there is a higher
  probability that one molecule will be in each
  flask that both molecules being in the same flask.

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• The Spontaneous Expansion of a Gas
• When there are many molecules, it is much more
  probable that the molecules will distribute among
  the two flasks than all remain in only one flask.

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Entropy on the Molecular Scale

• Ludwig Boltzmann described the concept of entropy
  on the molecular level. He used statistical
  thermodynamics statistics and probability are
  used to link macro and micro world.
• Temperature is a measure of the average kinetic
  energy of the molecules in a sample.

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Entropy on the Molecular Scale

• Molecules exhibit several types of motion
• Translational Movement of the entire molecule
  from one place to another.
• Vibrational Periodic motion of atoms within a
  molecule.
• Rotational Rotation of the molecule on about an
  axis or rotation about ? bonds.

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Entropy on the Molecular Scale

• Boltzmann envisioned the motions of a sample of
  molecules at a particular instant in time.
• This would be akin to taking a snapshot of all
  the molecules.
• He referred to this sampling as a microstate of
  the thermodynamic system.

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Entropy on the Molecular Scale

• Each thermodynamic state has a specific number of
  microstates, W, associated with it.
• Entropy is
• S k lnW
• where k is the Boltzmann constant, 1.38 ? 10?23
  J/K.

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Entropy on the Molecular Scale

• The change in entropy for a process, then, is
• ?S k lnWfinal ? k lnWinitial

• Entropy increases with the number of microstates
  in the system.

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Entropy on the Molecular Scale

• The number of microstates and, therefore, the
  entropy tends to increase with increases in
• Temperature.
• Volume.
• The number of independently moving molecules.

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Entropy and Physical States

• Entropy increases with the freedom of motion of
  molecules.
• Therefore,
• S(g) gt S(l) gt S(s)

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Solutions

• Generally, when a solid is dissolved in a
  solvent, entropy increases.

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• There is a balance between energy and entropy
  considerations.
• When an ionic solid is placed in water two things
  happen
• the water organizes into hydrates about the ions
  (so the entropy decreases), and
• the ions in the crystal dissociate (the hydrated
  ions are less ordered than the crystal, so the
  entropy increases).

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The Molecular Interpretation of Entropy

• A gas is less ordered than a liquid that is less
  ordered than a solid.
• Aqueous ions are less ordered than pure solids
  and liquids, but more ordered than gases
• Any process that increases the number of gas
  molecules leads to an increase in entropy.
• When NO(g) reacts with O2(g) to form NO2(g), the
  total number of gas molecules decreases, and the
  entropy decreases.

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Entropy Changes

• In general, entropy increases when
• Gases are formed from liquids and solids.
• Liquids or solutions are formed from solids.
• The number of gas molecules increases.
• The number of moles increases.

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• Examples Determine the sign of ?S for each of
  the following
• Na (s) ½ Cl2 (g) ? NaCl (s)
• N2 (g) 3 H2 (g) ? 2 NH3 (g)
• 2 H2 (g) O2 (g) ? 2 H2O (l)
• H2O (l) ? H2O (g)
• NaCl (s) ? Na (aq) Cl- (aq)

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Third Law of Thermodynamics

• The entropy of a pure crystalline substance at
  absolute zero is 0.

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• Energy is required to get a molecule to
  translate, vibrate or rotate.
• The more energy stored in translation, vibration
  and rotation, the greater the degrees of freedom
  and the higher the entropy.
• In a perfect crystal at 0 K there is no
  translation, rotation or vibration of molecules.
  Therefore, this is a state of perfect order (zero
  entropy).

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• Boiling corresponds to a much greater change in
  entropy than melting.
• Entropy will increase when
• liquids or solutions are formed from solids,
• gases are formed from solids or liquids,
• the number of gas molecules increase,
• the is temperature increased.

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Entropy Changes in Chemical Reactions

• Absolute entropy can be determined from
  complicated measurements.
• Standard molar entropy, S? entropy of a
  substance in its standard state. Similar in
  concept to ?H?.
• Units J mol-1 K-1. Note units of ?H kJ mol-1.
• Standard molar entropies of elements are not
  zero.
• For a chemical reaction which produces n moles of
  products from m moles of reactants

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Standard Entropies

• These are molar entropy values of substances in
  their standard states.
• Standard entropies tend to increase with
  increasing molar mass.

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Standard Entropies

• Larger and more complex molecules have greater
  entropies. More atoms in the molecule allow for a
  greater degree of freedom.

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• Examples Calculate ?S for each of the following
  reactions
• CH4 (g) 2 O2 (g) ? CO2 (g) 2 H2O (g)
• N2 (g) 3 H2 (g) ? 2 NH3 (g)
• 2 SO3 (g) ? 2 SO2 (g) O2 (g)
• HCl (g) ? H (aq) Cl- (aq)

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Entropy Changes in Surroundings

• Heat that flows into or out of the system changes
  the entropy of the surroundings.
• For an isothermal process

• At constant pressure, qsys is simply ?H? for the
  system.

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Entropy Change in the Universe

• The universe is composed of the system and the
  surroundings.
• Therefore,
• ?Suniverse ?Ssystem ?Ssurroundings
• For spontaneous processes
• ?Suniverse gt 0

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Entropy Change in the Universe

• This becomes
• ?Suniverse ?Ssystem
• Multiplying both sides by ?T,
• ?T?Suniverse ?Hsystem ? T?Ssystem

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Gibbs Free Energy

• ?TDSuniverse is defined as the Gibbs free energy,
  ?G.
• When ?Suniverse is positive, ?G is negative.
• Therefore, when ?G is negative, a process is
  spontaneous.

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Gibbs Free Energy

1. If DG is negative, the forward reaction is
   spontaneous.
2. If DG is 0, the system is at equilibrium.
3. If ?G is positive, the reaction is spontaneous in
   the reverse direction.

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Standard Free Energy Changes

• Analogous to standard enthalpies of formation
  are standard free energies of formation, ?G?.

f
where n and m are the stoichiometric coefficients.
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Free Energy Changes

• At temperatures other than 25C,
• DG DH? ? T?S?
• How does ?G? change with temperature?

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Free Energy and Temperature

• There are two parts to the free energy equation
• ?H? the enthalpy term
• T?S? the entropy term
• The temperature dependence of free energy, then
  comes from the entropy term.

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Free Energy and Temperature
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Free Energy and Equilibrium

• Under any conditions, standard or nonstandard,
  the free energy change can be found this way
• ?G ?G? RT lnQ
• (Under standard conditions, all concentrations
  are 1 M, so Q 1 and lnQ 0 the last term
  drops out.)

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Free Energy and Equilibrium

• At equilibrium, Q K, and ?G 0.
• The equation becomes
• 0 ?G? RT lnK
• Rearranging, this becomes
• ?G? ?RT lnK
• or,
• K e??G?/RT