Transcript Petrucci ch_17

General Chemistry:
An Integrated Approach
Hill, Petrucci, 4th Edition
Chapter 17
Thermodynamics: Spontaneity,
Entropy, and Free Energy
Mark P. Heitz
State University of New York at Brockport
© 2005, Prentice Hall, Inc.
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.
Chapter 17: Thermodynamics
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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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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
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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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Chapter Seventeen
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Spontaneous Change (cont’d)
• 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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Chapter Seventeen
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Spontaneous Change (cont’d)
• 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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Chapter Seventeen
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Spontaneous Change (cont’d)
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 …
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… liquid water vaporizes
spontaneously at room
temperature; an
endothermic process.
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
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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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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
The Concept of Entropy
Consider mixing two gases: this occurs
spontaneously, and the gases form a homogeneous
mixture.
There is essentially
no enthalpy change
involved, so why is
the process
spontaneous?
The driving force is a thermodynamic quantity called
entropy, a mathematical concept that is difficult to
portray visually
EOS
Chapter 17: Thermodynamics
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Entropy
The total energy of a system remains unchanged in
the mixing of the gases but the number of
possibilities for the distribution of that energy
increases
This spreading of the
energy and increase of
entropy correspond to a
greater physical disorder
at the microscopic level
EOS
Chapter 17: Thermodynamics
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Entropy
There are two natural tendencies behind
spontaneous processes: the tendency to achieve a
lower energy state and the tendency toward a more
disordered state
EOS
Chapter 17: Thermodynamics
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Increase in Entropy in the
Vaporization of Water
Evaporation is
spontaneous because of
the increase in entropy.
Chapter 17: Thermodynamics
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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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Chapter Seventeen
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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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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
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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) H2O(l)
C12H22O11(aq)
(c) Evaporation to dryness of a solution of urea,
CO(NH2)2, in water:
CO(NH2)2(aq)  CO(NH2)2(s)
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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
Entropy (S)
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 the entropy of the system
Entropy (S) is a state function:
it is path independent
 Sfinal – Sinit = DS
DS = qrev/T
EOS
Chapter 17: Thermodynamics
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Entropy Change
• Sometimes it is necessary to obtain quantitative values of
entropy changes.
The expansion
DS = qrxn/T
can be reversed
• where qrxn is reversible heat, a state function.
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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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
Standard Molar Entropies
The standard molar entropy, So, is the entropy of
one mole of a substance in its standard state.
DS = SvpSo(products) – SvrSo(reactants)
According to the Third Law of Thermodynamics,
the entropy of a pure, perfect crystal can be taken to
be zero at 0 K
EOS
Chapter 17: Thermodynamics
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Standard Molar Entropies
In general, the more atoms in its molecules, the
greater is the entropy of a substance
Entropy is a function of temperature
EOS
Chapter 17: Thermodynamics
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The Second Law
of Thermodynamics
The Second Law of Thermodynamics establishes
that all spontaneous or natural processes increase
the entropy of the universe
DStotal = DSuniverse = DSsystem + DSsurroundings
In a process, if entropy increases in both the
system and the surroundings, the process is surely
spontaneous
EOS
Chapter 17: Thermodynamics
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Free Energy and Free Energy Change
• What is the significance of: –TΔSuniv = ΔHsys – TΔSsys ?
• The entropy change of the universe—our criterion for
spontaneity—has now been defined entirely in terms of the
system.
• The quantity –TΔSuniv is called the free energy change
(DG).
• For a process at constant temperature and pressure:
DGsys = DHsys – TDSsys
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Chapter Seventeen
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Free Energy and Free Energy Change
• If DG < 0 (negative), a process is spontaneous.
• If DG > 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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Chapter Seventeen
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Case 3 illustrated
At high T, the size of
TΔS is large, and –TΔS
predominates.
ΔH is (+) and is moreor-less constant with T.
At low T, the size of
TΔS is small, and ΔH
(+) predominates.
Since ΔS is (+), the
slope TΔS is also (+).
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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
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.
Analysis and Conclusions
To cause a molecule to dissociate into its atoms, we must supply the molecule with
enough energy to induce such vigorous vibrations that its atoms fly apart, an
endothermic process (∆H > 0). To assess the entropy change, we first note that a
molecule has a greater number of available energy levels than does any one of its
constituent atoms taken alone. However, because two or more atoms are produced
for every molecule dissociated, we find a greater number of available energy levels
in a system of individual atoms than if the same atoms are united into molecules (∆S
> 0). The key factor, then, is the temperature, T. At low temperatures, ∆H is the
determining factor, dissociation into atoms is a nonspontaneous process, and
therefore molecules are generally stable with respect to uncombined atoms.
However, no matter how large the value of ∆H, eventually a temperature is reached
at which the magnitude of T∆S exceeds that of ∆H. Then ∆G is negative, and the
dissociation becomes a spontaneous process. For all known molecules, this high
temperature limit is no more than a few thousand kelvins.
Chapter 17: Thermodynamics
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Standard Free Energy Change
The standard free energy change, DGo, of a
reaction is the free energy change when reactants
and products are in their standard states
e.g., O2 is a gas, Br2 is liquid, etc. ...
DGo = DHo – TDSo
Be mindful of units; H is usually in kJ
and S is in J K–1
EOS
Chapter 17: Thermodynamics
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Standard Free Energy Change
The standard free energy of formation, DGof, is
the free energy change that occurs in the formation
of 1 mol of a substance in its standard state from
the reference forms of its elements in their standard
states
DGo = Svp DGof(products) – Svr DGof(reactants)
EOS
Chapter 17: Thermodynamics
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Free Energy Change
and Equilibrium
At equilibrium, DG = 0. Therefore, at the
equilibrium temperature, the free energy change
expression becomes
DH = TDS and DS = DH/T
Entropy and enthalpy of vaporization can be
related to normal boiling point
EOS
Chapter 17: Thermodynamics
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Vaporization Energies
Trouton’s rule implies that about the same
amount of disorder is generated in the passage of
one mole of substance from liquid to vapor when
comparisons are made at the normal boiling point
DS°vapn = DH°vapn/Tbp  87 J mol–1 K–1
EOS
Chapter 17: Thermodynamics
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Illustrating Trouton’s 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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Chapter Seventeen
30
Raoult’s 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 volume—lower 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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General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Seventeen
Relationship of DGo and Keq
DG = 0 is a criterion for equilibrium at a single
temperature, the one temperature at which the
equilibrium state has all reactants and products in
their standard states
DG and DGo are related through the reaction
quotient, Q
DG = DGo + RT ln Q
Under the conditions of DG = 0 and DGo = -RT ln K
eq
Q = Keq, the equation above becomes
EOS
Chapter 17: Thermodynamics
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The Equilibrium Constant, Keq
Activities are the dimensionless quantities needed
in the equilibrium constant expression Keq
For pure solid and liquid phases: activity, 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: Assume
intermolecular or interionic attractions are
negligible and replace solute activity by the
numerical value of the solute molarity
Chapter 17: Thermodynamics
EOS
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The Significance of the Sign and
Magnitude of DGo
DGprod << DGreac
DGo is a large, negative
quantity and equilibrium is
very far to the right
(towards products)
EOS
Chapter 17: Thermodynamics
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The Significance of the Sign and
Magnitude of DGo
DGprod >> DGreac
DGo is a large, positive
quantity and equilibrium is
very far to the left (towards
reactants)
EOS
Chapter 17: Thermodynamics
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The Significance of the Sign and
Magnitude of DGo
DGprod  DGreac
the equilibrium lies more
toward the center of the
reaction profile
EOS
Chapter 17: Thermodynamics
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The Dependence of
DGo and Keq on Temperature
To obtain equilibrium constants at different
temperatures, it will be assumed that DH and DS
do not change much with temperature
the 25 oC values of DHo
and DSo along with the
desired temperature are
substituted
DGo = DHo – TDSo
EOS
Chapter 17: Thermodynamics
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The Dependence of
DGo and Keq on Temperature
To obtain Keq at the desired temperature, the
following equation is used …
ln K eq





K 2  D H o  1 1 
 ln

- 


K1 
R T1 T 2



This is the van’t Hoff equation
EOS
Chapter 17: Thermodynamics
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Equilibrium with Vapor
DHo for either sublimation or vaporization is used
depending on the other component
Partial pressures are exchanged for K’s
o
vap
 P2  D H
 
ln 
R
 P1 
1
1 
 
 T1 T 2 
This is the Clausius–Clapeyron equation
EOS
Chapter 17: Thermodynamics
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Temperature Dependence of Keq
EOS
Chapter 17: Thermodynamics
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Summary of Concepts
• A spontaneous change is one that occurs by itself
without outside intervention
• The third law of thermodynamics states that the
entropy of a pure, perfect crystal at 0 K can be
taken to be zero
• The direction of spontaneous change is that in
which total entropy increases
• The free energy change, DG, is equal to –TDS, and
it applies just to the system itself
EOS
Chapter 17: Thermodynamics
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Summary (cont’d)
• The standard free energy change, DGo, can be
calculated by substituting standard enthalpies and
entropies of reaction and a Kelvin temperature
into the Gibbs equation, or, by combining standard
free energies of formation
• The condition of equilibrium is one for which DG
=0
EOS
Chapter 17: Thermodynamics
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Summary (cont’d)
• The value of DGo is in itself often sufficient to
determine how a reaction will proceed
• Values of DGof, DHof, and DS are generally
tabulated for 25 oC. To obtain values of Keq at
other temperatures, the van’t Hoff equation must
be used
• The Clausius–Clapeyron equation connects
solid/vapor or liquid/vapor equilibria to varying
temperature
EOS
Chapter 17: Thermodynamics
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