Matter and Measurement

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The Gibbs Free Energy Function and Phase
Transitions
H2O(l) --gt H2O(s) Normal freezing point of H2O
273.15K The change in enthalpy is the enthalpy of
freezing - enthalpy change associated when one
mole of liquid water freezes at 1atm and
273.15K DH -6007J Entropy change
DG DH - TDS -6007J - (273.15K)(-21.99J/K)
0J gt at 273.15K and 1 atm, liquid and solid
water are at equilibrium
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As water is cooled by 10K below 273.15K to
263.15K
Assume that DH and DS do not change with T DG
DH - TDS -6007J - (263.15K)(-21.99J/K)
-220J Since DG lt 0 water spontaneously freezes
At 10K above the freezing point, 283.15K DG
DH - TDS -6007J - (283.15K)(-21.99J/K)
219J DG gt 0 water does not spontaneously freeze
at 283.15K, 10K above the normal freezing point
of water Above 273.15K, the reverse process is
spontaneous - ice melts to liquid water.
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H2O(l) --gt H2O(s)
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For phase transitions, at the transition
temperature, the system is at equilibrium between
the two phases. Above or below the transition
temperature, the phase that is the more stable
phase is determined by thermodynamics - DG of the
phase transition.
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Reaction Free Energy DGr SnGm(products) -
SnGm(reactants) Standard Reaction Free
Energy DGor SnGom (products) -
SnGom(reactants) Difference in free energy of the
pure products in their standard states and pure
reactants in their standard states.
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• Standard Free-Energy of Formation
• The standard free energy of formation, DGfo, of a
  substance is the standard reaction free energy
  per mole for the formation of a compound from its
  elements in their most stable form

1/2N2 (g) 3/2 H2 (g) --gt NH3(g) DGfo -16 kJ
O2 (g) --gt O2 (g) DGfo 0
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DGfo is an indication of a compounds stability
relative to its elements Thermodynamically stable
compound DGfo lt 0 Thermodynamically unstable
compound DGfo gt 0
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• Standard Reaction Free Energy
• For a reaction aA bB --gt cC dD
• DGro c DGfo (C) d DGfo(D) - a DGfo(A) -b
  DGfo(B)
• The standard free energy of formation of elements
  in their most stable form at 298.15K is zero.

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• Problem Calculate the standard free-energy
  change for the following reaction at 298K
• N2(g) 3H2 (g) --gt 2NH3(g)
• Given that DGfoNH3(g) -16.66 kJ/mol.
• What is the DGo for the reverse reaction?

Since the reactants N2(g) and H2(g) are in their
standard state at 298 K their standard free
energies of formation are defined to be zero.
DGro 2 DGfoNH3(g) - DGfoN2(g) - 3
DGfoH2(g) 2 x -16.66 -33.32 kJ/mol For
the reverse reaction 2NH3(g) --gt N2(g) 3H2 (g)
DGro 33.32 kJ/mol
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C3H8(g) 5O2(g) --gt 3CO2 (g) 4H2O(l) DHo
- 2220 kJ a) Without using the information from
the tables of thermodynamic quantities predict
whether DGo for this reaction will be less
negative or more negative than DHo. b) Use data
from App. D to calculate DGro for this reaction.
Whether DGro is more negative or less negative
than DHo depends on the sign of DSo since DGro
DHo - T DSo The reaction involves 6 moles of
gaseous reactants and produces 3 moles of gaseous
product gt DSo lt 0 (since fewer moles of
gaseous products than reactants) Since DSo lt 0
and DHo lt 0 and DGro DHo - T DSo gt DGro is
less negative than DHo
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DGro 3DGfo(CO2 (g))4DGfo(H2O(l)-DGfo(C3H8(g))-5
DGfo(O2(g)) 3(-394.4) 4(-237.13) -
(-23.47) - 5(0) -2108 kJ
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• Effect of temperature on DGo
• Values of DGro calculated using the tabulated
  values of DGfo apply only at 298.15K.
• For other temperatures the relation
• DGro DHo - T DSo
• can be used, assuming DHo and DSo do not vary
  significantly with temperature.

When DGro 0,
Use this expression to determine temperature
above or below which reaction becomes spontaneous.
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Problem The normal boiling point is the
temperature at which a pure liquid is in
equilibrium with its vapor at 1 atm. a) write the
chemical equation that defines the normal boiling
point of liquid CCl4 b) what is the value of DGo
at equilibrium? c) Use thermodynamic data to
estimate the boiling point of CCl4.
b) At equilibrium DG 0. In any equilibrium for
a normal boiling point, both the liquid and gas
are in their standard states. Hence, for this
process DG is DGo.
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c)
where for this reaction T is the boiling
point Note To determine the boiling point
accurately we need the values of DHo and DSo for
the vaporization process at the boiling point of
CCl4
DHo (1mol)(-106.7 kJ/mol) - (1mol)(-139.3kJ/mol)
32.6 kJ DSo (1mol)(309.4 J/mol-K)
-(1mol)(214.4 J/mol-K) 95.0 J/K
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• The Gibbs Function and the Equilibrium Constant
• DG DGro R T ln Q
• Q - reaction quotient
• Under standard conditions the concentrations of
  all reactants and products are set to 1
• (standard pressure of gases 1 atm
• Standard pressure of solutions 1 M)
• Under standard conditions, ln Q 0
• gt DG DGro

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At equilibrium DG 0 and Q K At
equilibrium DGro - R T ln K or K e- DGro
/RT DGro lt 0 gt K gt 1 DGro gt 0 gt K lt 1 DG
DGro R T ln Q - RT ln K RT ln Q
when Q K gt DG 0 equilibrium
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If the reaction mixture has too much N2 or H2
relative to NH3, Q lt K, and reaction moves
spontaneously in the direction to form NH3 till
equilibrium is established Q K. If there is
too much NH3 in the mixture, Q gt K, decomposition
of NH3 is spontaneous, till equilibrium is
established Q K
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• Temperature Dependence of K
• The temperature dependence of K can be used to
  determine DHo and DSo of a reaction

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• If the equilibrium constant of a reaction is
  known at one temperature and the value of DHo is
  known, then the equilibrium constant at another
  temperature can be calculated

If DHo is negative (exothermic), an increase in T
reduces K if it is positive (endothermic), an
increase in T increases K
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For the equilibrium between a pure liquid and its
vapor, the equilibrium constant is simply the
equilibrium vapor pressure (since pure liquids do
not appear in the equilibrium expression)
Hence
The Clausius-Clapeyron equation indicates the
variation of vapor pressure of a liquid with
temperature
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Driving Non-spontaneous Reactions The magnitude
of DG is a useful tool for evaluating
reactions. For a spontaneous process at constant
pressure and temperature, the change in free
energy for a process equals the maximum amount of
work that can be done by the system on its
surroundings wmax DGr For non-spontaneous
reactions (DGr gt 0), the magnitude of DGr is a
measure of the minimum amount of work that must
be done on the system to cause the process to
occur. A reaction for which DGr is large and
negative (like the combustion of gasoline), is
much more capable of doing work on the
surroundings than a reaction for which DGr is
small and negative (like the melting of ice).
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Many chemical reactions, including a large
number that are central to biological systems,
are non-spontaneous. For example Cu can be
extracted from the mineral chalcolite which
contains Cu2S. The decomposition of Cu2S is
non-spontaneous Cu2S --gt 2Cu(s) S(s) DGro
86.2 kJ Since this reaction is not spontaneous
Cu cannot be directly obtained from the above
reaction. Instead, work needs to be done on this
reaction, and this is done by coupling this
non-spontaneous reaction with a spontaneous
reaction so that the overall reaction is
spontaneous.
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Consider the following reaction S(s) O2(g)
--gt SO2 (g) DGro -300.4kJ Coupling this
reaction with the extraction of Cu from
Cu2S Cu2S --gt 2Cu(s) S(s) DGro 86.2
kJ S(s) O2(g) --gt SO2 (g) DGro
-300.4kJ Net Cu2S(s) O2 (g) --gt 2Cu(s)
SO2(g) DGro -214.2kJ
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Biological systems employ the same principle by
using spontaneous reactions to drive
non-spontaneous reactions. Many biochemical
reactions are not spontaneous. These reactions
are made to occur by coupling them with
spontaneous reactions which release heat. The
metabolism of food is the usual source of free
energy needed to do the work to maintain
biological systems. C6H12O6(s) 6O2 (g) --gt 6CO2
(g) 6H2O(l) DHo -2803 kJ
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A means of transporting the energy released by
glucose metabolism to the reactions that require
energy is needed. The free energy released by
the metabolism of glucose is used to convert
lower-energy ADP (adenine diphosphate) to higher
energy ATP (adenine triphosphate). The energy
stored in the ATP molecule is then available to a
biochemical reaction that requires energy and in
the process ATP is converted to ADP.
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