Thermodynamics: Spontaneity, Entropy, and Free Energy

1
Thermodynamics Spontaneity,Entropy, and Free
Energy
Chapter Seventeen
2
Introduction

• Thermodynamics examines the relationship between
  heat and work.
• Spontaneity is the notion of whether or not a
  process can take place unassisted.
• Entropy is a mathematical concept describing the
  distribution of energy within a system.
• Free energy is a thermodynamic function that
  relates enthalpy and entropy to spontaneity, and
  can also be related to equilibrium constants.

3
Why Study Thermodynamics?

• With a knowledge of thermodynamics and by making
  a few calculations before embarking on a new
  venture, scientists and engineers can save
  themselves a great deal of time, money, and
  frustration.
• To the manufacturing chemist thermodynamics
  gives information concerning the stability of his
  substances, the yield which he may hope to
  attain, the methods of avoiding undesirable
  substances, the optimum range of temperature and
  pressure, the proper choice of solvent. - from
  the introduction to Thermodynamics and the Free
  Energy of Chemical Substances by G. N. Lewis and
  M. Randall
• Thermodynamics tells us what processes are
  possible.
• (Kinetics tells us whether the process is
  practical.)

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Spontaneous Change

• A spontaneous process is one that can occur in a
  system left to itself no action from outside the
  system is necessary to bring it about.
• A nonspontaneous process is one that cannot take
  place in a system left to itself.
• If a process is spontaneous, the reverse process
  is nonspontaneous, and vice versa.
• Example gasoline combines spontaneously with
  oxygen.
• However, spontaneous signifies nothing about
  how fast a process occurs.
• A mixture of gasoline and oxygen may remain
  unreacted for years, or may ignite instantly with
  a spark.

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Spontaneous Change (contd)

• Thermodynamics determines the equilibrium state
  of a system.
• Thermodynamics is used to predict the proportions
  of products and reactants at equilibrium.
• Kinetics determines the pathway by which
  equilibrium is reached.
• A high activation energy can effectively block a
  reaction that is thermodynamically favored.
• Example combustion reactions are
  thermodynamically favored, but (fortunately for
  life on Earth!) most such reactions also have a
  high activation energy.

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• Example 17.1
• Indicate whether each of the following processes
  is spontaneous or nonspontaneous. Comment on
  cases where a clear determination cannot be made.
• The action of toilet bowl cleaner, HCl(aq), on
  lime deposits, CaCO3(s).
• The boiling of water at normal atmospheric
  pressure and 65 C.
• The reaction of N2(g) and O2(g) to form NO(g) at
  room temperature.
• The melting of an ice cube.

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Spontaneous Change (contd)

• Early chemists proposed that spontaneous chemical
  reactions should occur in the direction of
  decreasing energy.
• It is true that many exothermic processes are
  spontaneous and that many endothermic reactions
  are nonspontaneous.
• However, enthalpy change is not a sufficient
  criterion for predicting spontaneous change

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Spontaneous Change (contd)
Water falling (higher to lower potential energy)
is a spontaneous process.
Conclusion enthalpy alone is not a sufficient
criterion for prediction of spontaneity.
H2 and O2 combine spontaneously to form water
(exothermic) BUT
liquid water vaporizes spontaneously at room
temperature an endothermic process.
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The Concept of Entropy
When the valve is opened
the gases mix spontaneously.

• There is no significant enthalpy change.
• Intermolecular forces are negligible.
• So why do the gases mix?

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The Concept of Entropy (contd)

• The other factor that drives reactions is a
  thermodynamic quantity called entropy.
• Entropy is a mathematical concept that is
  difficult to portray visually.
• The total energy of the system remains unchanged
  in the mixing of the gases

• but the number of possibilities for the
  distribution of that energy increases.

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Formation of an Ideal Solution
Benzene and toluene have similar intermolecular
forces, so there is no enthalpy change when they
are mixed.
They mix completely because entropy of the
mixture is higher than the entropies of the two
substances separated.
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Increase in Entropy in theVaporization of Water
Evaporation is spontaneous because of the
increase in entropy.
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The Concept of Entropy

• The spreading of the energy among states, and
  increase of entropy, often correspond to a
  greater physical disorder at the microscopic
  level (however, entropy is not disorder).
• There are two driving forces behind spontaneous
  processes the tendency to achieve a lower energy
  state (enthalpy change) and the tendency for
  energy to be distributed among states (entropy).
• In many cases, however, the two factors work in
  opposition. One may increase and the other
  decrease or vice versa. In these cases, we must
  determine which factor predominates.

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Assessing Entropy Change

• The difference in entropy (S) between two states
  is the entropy change (DS).
• The greater the number of configurations of the
  microscopic particles (atoms, ions, molecules)
  among the energy levels in a particular state of
  a system, the greater is the entropy of the
  system.
• Entropy generally increases when
• Solids melt to form liquids.
• Solids or liquids vaporize to form gases.
• Solids or liquids dissolve in a solvent to form
  nonelectrolyte solutions.
• A chemical reaction produces an increase in the
  number of molecules of gases.
• A substance is heated.

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• Example 17.2
• Predict whether each of the following leads to an
  increase or decrease in the entropy of a system.
  If in doubt, explain why.
• (a) The synthesis of ammonia
• N2(g) 3 H2(g) ? 2 NH3(g)
• (b) Preparation of a sucrose solution
• C12H22O11(s) C12H22O11(aq)
• (c) Evaporation to dryness of a solution of urea,
  CO(NH2)2, in water
• CO(NH2)2(aq) ? CO(NH2)2(s)

H2O(l)
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Entropy Change

• Sometimes it is necessary to obtain quantitative
  values of entropy changes.
• DS qrxn/T
• where qrxn is reversible heat, a state function.

The expansion can be reversed by allowing the
sand to return, one grain at a time.
A reversible process can be reversed by a very
small change, as in the expansion of this gas. A
reversible process is never more than a tiny step
from equilibrium.
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Entropy as a Function of Temperature
and it increases dramatically during a phase
change.
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Standard Molar Entropies

• According to the Third Law of Thermodynamics, the
  entropy of a pure, perfect crystal can be taken
  to be zero at 0 K.
• The standard molar entropy, S, is the entropy of
  one mole of a substance in its standard state.
• Since entropy increases with temperature,
  standard molar entropies are positiveeven for
  elements.
• DS Svp S(products) Svr S(reactants)

Does the form of this equation look familiar?
(remember calculating enthalpy change from ?Hf?)
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• Example 17.3
• Use data from Appendix C to calculate the
  standard entropy change at 25 C for the Deacon
  process, a high-temperature, catalyzed reaction
  used to convert hydrogen chloride (a by-product
  from organic chlorination reactions) into
  chlorine
• 4 HCl(g) O2(g) ? 2 Cl2(g) 2 H2O(g)

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The Second Law of Thermodynamics

• Entropy can be used as a sole criterion for
  spontaneous change
• but the entropy change of both the system and
  its surroundings must be considered.
• The Second Law of Thermodynamics establishes that
  all spontaneous processes increase the entropy of
  the universe (system and surroundings).
• If entropy increases in both the system and the
  surroundings, the process is spontaneous.
• Is it possible for a spontaneous process to
  exhibit a decrease in entropy? Yes, if the
  surroundings ____________________.

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The Second Law of Thermodynamics
?Stotal ?Suniverse ?Ssystem
?Ssurroundings
For a spontaneous process
?Suniverse gt 0
Since heat is exchanged with the surroundings
qsurr qp ?Hsys
qsurr ?Hsys ?Ssurr
T
T
and
?Hsys ?Suniv
?Ssys
T

• Therefore

Multiply by T
T?Suniv ?Hsys T?Ssys
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Free Energy and Free Energy Change

• What is the significance of T?Suniv ?Hsys
  T?Ssys ?
• The entropy change of the universeour criterion
  for spontaneityhas now been defined entirely in
  terms of the system.
• The quantity T?Suniv is called the free energy
  change (DG).
• For a process at constant temperature and
  pressure
• DGsys DHsys TDSsys

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Free Energy and Free Energy Change

• If DG lt 0 (negative), a process is spontaneous.
• If DG gt 0 (positive), a process is
  nonspontaneous.
• If DG 0, neither the forward nor the reverse
  process is favored there is no net change, and
  the process is at equilibrium.

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Case 3 illustrated
At high T, the size of T?S is large, and T?S
predominates.
?H is () and is more-or-less constant with T.
At low T, the size of T?S is small, and ?H ()
predominates.
Since ?S is (), the slope T?S is also ().
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• Example 17.4
• Predict which of the four cases in Table 17.1 you
  expect to apply to the following reactions.
• (a) C6H12O6(s) 6 O2(g) ? 6 CO2(g) 6
  H2O(g)
• ?H 2540 kJ
• (b) Cl2(g) ? 2 Cl(g)
• Example 17.5 A Conceptual Example
• Molecules exist from 0 K to a few thousand
  kelvins. At elevated temperatures, they
  dissociate into atoms. Use the relationship
  between enthalpy and entropy to explain why this
  is to be expected.

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Standard Free Energy Change, ?G

• The standard free energy change, DG, of a
  reaction is the free energy change when reactants
  and products are in their standard states.
• The standard free energy of formation, DGf, is
  the free energy change for the formation of 1 mol
  of a substance in its standard state from the
  elements in their standard states.
• DG Svp DGf(products) Svr DGf(reactants)

The form of this equation should appear very
familiar by now!
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• Example 17.6
• Calculate ?G at 298 K for the reaction
• 4 HCl(g) O2(g) ? 2 Cl2(g) 2 H2O(g)
• ?H 114.4 kJ
• (a) using the Gibbs equation (17.8) and (b) from
  standard free energies of formation.

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Free Energy Change and Equilibrium

• At equilibrium, DG 0 (reaction is neither
  spontaneous nor nonspontaneous).
• Therefore, at the equilibrium temperature, the
  free energy change expression becomes
• DH TDS and DS DH/T
• Troutons rule states that the entropy change is
  about the same when one mole of a substance is
  converted from liquid to vapor (at the normal
  boiling point).
• DSvapn for many substances is about 87 J
  mol1 K1.
• This rule works best with nonpolar substances.
• It generally fails for liquids with a more
  ordered structure, such as those with extensive
  hydrogen bonding.

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Illustrating Troutons Rule
The three substances have different entropies and
different boiling points, but DS of vaporization
is about the same for all three.
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• Example 17.7
• At its normal boiling point, the enthalpy of
  vaporization of pentadecane, CH3(CH2)13CH3, is
  49.45 kJ/mol. What should its approximate normal
  boiling point temperature be?

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Raoults Law Revisited
higher entropy for the vapor from the solution
than from the pure solvent.
Entropy of a vapor increases if the vapor expands
into a larger volumelower vapor pressure.
Entropy of vaporization of the solvent is about
the same in each case, which means
A pure solvent has a lower entropy than a
solution containing the solvent.
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Relationship of DG to the Equilibrium Constant,
Keq

• DG 0 is a criterion for equilibrium at any
  temperature.
• DG 0 is a criterion for equilibrium at a
  single temperature, that temperature at which the
  equilibrium state has all reactants and products
  in their standard states.
• ?G and DGo are related through the reaction
  quotient, Q
• DG DG RT ln Q
• When DG 0, then Q Keq, and the equation
  becomes
• DG -RT ln Keq

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The Equilibrium Constant, Keq

• The concentrations and partial pressures we have
  used in Keq are approximations.
• Activities (a) are the correct variables for Keq.
  But activities are very difficult to determine.
  That is why we use approximations.
• For pure solid and liquid phases a 1.
• For gases Assume ideal gas behavior, and replace
  the activity by the numerical value of the gas
  partial pressure (in atm).
• For solutes in aqueous solution Replace solute
  activity by the numerical value of the solute
  molarity (M).

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• Example 17.8
• Write the equilibrium constant expression, Keq,
  for the oxidation of chloride ion by manganese
  dioxide in an acidic solution
• MnO2(s) 4 H(aq) 2 Cl(aq) ?
• Mn2(aq) Cl2(g) 2 H2O(l)

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Calculating Equilibrium Constants

• Rearranging Equation (17.12)

DG -RT ln Keq
DG ln Keq -
RT

• The units of DG and R must be consistent both
  must use kJ or both must use J.

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• Example 17.9
• Determine the value of Keq at 25 C for the
  reaction
• 2 NO2(g) N2O4(g)

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The Sign and Magnitude of DG
Intermediate DG equilibrium lies in
intermediate position.
Large, negative DG equilibrium lies far to
right.
Large, positive DG equilibrium lies far to left.
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Coupled Reactions

• A nonspontaneous reaction may be coupled with a
  spontaneous reaction.
• The decomposition of copper(I) oxide is quite
  nonspontaneous at room temperature

• By coupling this decomposition with the formation
  of CO from carbon,

we can reduce the nonspontaneity of Cu2O and make
the overall reaction occur slightly above room
temperature
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The Dependence of DG and Keq on Temperature

• To obtain equilibrium constants at different
  temperatures, it will be assumed that DH does
  not change much with temperature.
• To obtain Keq at the desired temperature, the
  vant Hoff equation is used

-DH ln Keq constant
or RT

• The form used depends on whether we have a single
  value of Keq available, or multiple values.

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• Example 17.10
• Consider this reaction at 298 K
• CO(g) H2O(g) CO2(g) H2(g)
  ?H298 41.2 kJ
• Determine Keq for the reaction at 725 K.

41

• Cumulative Example
• Waste silver from photographic solutions or
  laboratory operations can be recovered using an
  appropriate redox reaction. A 100.0-mL sample of
  silver waste is 0.200 M in Ag(aq) and 0.0200 M
  in Fe3(aq). Enough iron(II) sulfate is added to
  make the solution 0.200 M in Fe2(aq). When
  equilibrium is established at 25 C, how many
  moles of solid silver will be present?
• Ag(aq) Fe2(aq) ? Ag(s) Fe3(aq)