Thermodynamics and Equilibrium

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Chapter 20

• Thermodynamics and Equilibrium

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Overview

• First Law of Thermodynamics
• Spontaneous Processes and Entropy
• Entropy and the Second Law of Thermodynamics
• Standard Entropies and the Third Law of
  Thermodynamics

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• Free Energy Concept
• Free Energy and Spontaneity
• Interpretation of Free Energy
• Free Energy and Equilibrium Constants
• Relating DG to the Equilibrium Constant
• Change of Free Energy with Temperature

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Definitions

• Spontaneous or Product-favored reaction reaction
  in which most of the reactants can eventually be
  converted to products, given sufficient time
• Nonspontaneous or Reactant-favored reaction
  misleading - does not mean that it does not occur
  at all, rather, it means that when equilibrium is
  achieved, not many reactant molecules have been
  converted into products.

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Definitions Continued

• Thermodynamics the science of energy transfer,
  it helps us to predict whether a reaction can
  occur given enough time. Thermodynamics tells us
  nothing about the speed of the reactions.

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Reaction Probability

• After an exothermic reaction, energy is
  distributed more randomly - dispersed over a much
  larger number of atoms and molecules - than it
  was before. Energy dispersal is favored because
  it is much more probable that energy will be
  dispersed than that it will be concentrated.
• Just as there is a tendency for highly
  concentrated energy to disperse, highly
  concentrated matter also tends to disperse.

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There are two ways that the final state of a
system can be more probable than the initial one

• 1. Having energy dispersed over a greater number
  of atoms and molecules and
• 2. Having the atoms and molecules themselves
  more disordered

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Entropy A Measure of Matter Dispersal or
Disorder

• The dispersal or disorder in sample of matter can
  be measured with a calorimeter, the same
  instrument needed to measure the enthalpy change
  when a reaction occurs.
• The result is a thermodynamic function called
  entropy and symbolized by S.

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Entropy and the Third Law

• Measurement of entropy depends on the assumption
  that in a perfect crystal at the absolute zero
  temperature all translational motion ceases and
  there is not any disorder.

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Calculating Entropy Change

• When energy is transferred to matter in very
  small increments, so that the temperature change
  is very small, the entropy change can be
  calculated as DS q/T, the heat absorbed divided
  by the absolute temperature at which the change
  occurs.

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Standard Molar Entropies

• Applies to one mole of a substance at standard
  pressure. Expressed in units of joules per
  molekelvin.
• DS Sproducts Sreactants

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Example 1

• Calculate the standard molar entropy change for
  the formation of gaseous propane.
• Soc 6 J/K
• SoH 131 J/K
• SoC3H8 207 J/K

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Generalizations About Entropy

• 1. When comparing the same or very similar
  substances, entropies of gases are much larger
  than those of liquids, which are larger than for
  solids.
• 2. Entropies of more complex molecules are
  larger than those of simpler molecules,
  especially in a series of closely related
  compounds.
• 3. Entropies of ionic solids become larger as
  the attractions among the ions become weaker.
• 4. Entropy usually increases when a pure liquid
  or solid dissolves in a solution.
• 5. Entropy increases when a dissolved gas
  escapes from a solution.

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Example 2

• Indicate whether the entropy increases or
  decreases in each of the following processes.
• Moisture condenses on the outside of cold glass
• Gasoline vaporizes in the carburetor of an
  automobile engine
• Sugar dissolves in coffee
• Iron rusts

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Example 3

• Predict the sign of DS for the following
• AgCl(s) ? Ag(aq) Cl-(aq)
• 2H2(g) O2(g) ? 2H2O(l)
• H2O(l) ? H2O(g)
• N2(g) 3H2 (g) ? 2NH3(g)

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Entropy and the Second Law of Thermodynamics

• In a product-favored process there is a net
  increase in the entropy of the system and the
  surroundings.
• In other words when a product favored reaction
  occurs the entropy (disorder) of the universe
  increases. This means that even if the entropy
  of a particular system decreases in a product
  favored process, the total change in the entropy
  of the universe (the system and all its
  surroundings) must be positive.

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Entropy of the Surroundings

• The sign of DSsurr depends on the direction of
  heat flow (q).

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• A positive DSsurr occurs when heat flows out of
  the system into the surroundings and increases
  thermal motion. This should make sense to you
  because heat is a form of energy and when the
  energy increases the molecular motion increases
  which causes more randomness.

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• A negative DSsurr occurs when heat flows into the
  system from the surroundings, decreasing the
  thermal motion of the surroundings and therefore
  decreasing the entropy.

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DSsurr and absolute temperature

• If the surroundings are at a high temperature,
  the various types of molecular motion are already
  sufficiently energetic.
• Therefore, the absorption of heat from an
  exothermic process in the system will have
  relatively little impact on molecular motions and
  the resulting increase in entropy will be small.

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• If the temperature of the surroundings is low,
  then the addition of the same amount of heat will
  cause a more drastic increase in molecular
  motions and hence a larger increase in entropy.
• So, the entropy change produced when a given
  amount of heat is transferred is greater at low
  temperatures than at high temperatures.

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• The result is that DSsurr qsurr/T where qsurr
  is the heat flow into the surroundings at the
  absolute (Kelvin) temperature, T.
• For a constant-pressure processes DH was defined
  as being equal to the qsystem which would be
  equal to -qsurr.
• So this means that DSsurr -DH/T

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DS and DH

• For a product-favored process
• DSsystem - DH/T gt 0 or
• TDS - DH gt 0

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Second Law of Thermodynamics

• To be product favored a reaction must lead to an
  increase in the entropy of the universe.
• For a product favored process TDS - DH gt 0 or if
  we multiply the equation throughout by -1 DH -
  TDS lt 0.
• Now we have a criterion for a product-favored
  reaction that is expressed only in terms of the
  properties of the system and we no longer need be
  concerned with the surroundings.

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Gibbs Free Energy

• A new thermodynamic function can now be
  introduced, its called the Gibbs Free Energy, or
  simply Free Energy, as follows
• G H - TS
• G has the units of energy and, like H and S, it
  is a state function. (State Function A
  quantity whose value is determined only by the
  state of the system)

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DG

• The change in free energy (DG) of a system (which
  if what we're interested in) for a process at
  constant temperature is given by DG DH - TDS

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Example 4

• Given the values of DH and DS, which of the
  following changes will be spontaneous at constant
  T and P?
• DH 25KJ DS 5.0 J/K T 300 K
• DH 25 KJ DS 100J/K T 300 K
• DH -10 KJ DS 5.0 J/K T 298 K
• DH -10 KJ DS -40.0 J/K T 200 K

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Standard Free Energies of Formation

• The standard free energy of formation, Gf, of
  a substance is defined similarly to the standard
  enthalpy of formation. That is, DGf is the
  free-energy change that occurs when 1 mol of a
  substance is formed from its elements in their
  most stable states at 1 atm and at a specified
  temperature (usually 25 C)

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• By tabulating DGf for substances we can easily
  calculate DG for any reaction involving those
  substances using the following formula
• DG DGf (products) - DGf (reactants)
• NOTE If you are confused about the two
  different ways to calculate the DG - this last
  one can only be used when the temperature is that
  of the tabulated values - usually 25 C.

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Example 5

• For the following reaction at 298 K, determine
  the value of the Gibbs Free Energy
• 4PH3(g) 8O2(g) ? P4O10(s) 6H2O(l)
• DGf PH3 13 KJ/mol
• DGf O2 0 KJ/mol
• DGf P4O10 -2698 KJ/mol
• DGf H2O -237 KJ/mol

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Product-Favored or Reactant-Favored?

• Reactions at constant temperature and pressure go
  in such a direction as to decrease the free
  energy of the system.
• DG lt 0 Product-Favored Reaction
• DG gt 0 Reactant-Favored.
• DG 0 The system is at equilibrium. There
  is no net change.

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Free Energy and Temperature

• The value of G and consequently the
  directionality of the reaction change with
  temperature.

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Free-Energy and Temperature

• DH DS Low Temperature High Temperature
• reactant-favored product-favored
• - reactant-favored reactant-favored
• - product-favored product-favored
• - - product-favored reactant-favored

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?G Temperature Dependence

• Spontaneity Reaction becomes spontaneous when ?G
  goes from to ?. We use ?G 0 to tell us when
  reaction just becomes spontaneous or 0 ?H ? T?S
  or T ?H/?S.

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Example 6

• Determine the temperature at which the synthesis
  of HI(g) becomes spontaneous.
• ?Ho 52.96 kJ and ?So 166.4 J/mol
• H2(g) I2(g) ? 2HI(g)

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EQUILIBRIUM CONSTANTS AND ?G

• Equilibrium constant for a reaction
• aA bB ... ? mM nN
• ... is defined as
• Tells how far to right reaction proceeds.
• Large value ? mostly products.
• Small value ? mostly reactants.
• At equilibrium this equation must always be
  obeyed no matter what relative amount of reactant
  and was started with.

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Thermodynamics and the Equilibrium Constant

• DG DGo RT lnQ
• At equilibrium Q K and DG 0
• DGo -RT lnK where R is 8.31 J/mol K

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Example 7

• Chloroform, formerly used as an anesthetic, and
  now believed to be a carcinogen has a heat of
  vaporization of 31.4 KJ/mol. The entropy of
  vaporization is 94.2 J/molK. At what
  temperature would you expect chloroform to boil
  (i.e. at what temperature will the liquid and
  vapor be in equilibrium)?

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Thermodynamics

• First Law The total energy of the universe is
  constant
• Second Law The total entropy of the universe is
  always increasing
• Third Law The entropy of a pure, perfectly
  formed crystalline substance at absolute zero is
  zero

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• Neither of the first two laws of thermodynamics
  has ever been or can be proven. However, there
  has never been a single, concrete example showing
  otherwise.