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Chemical thermodynamics
Reading: Chapter 19
As you read ask yourself …
Why do reactions that occur in nature have a specific direction? What ultimately
drives physical and chemical changes in matter?
What is entropy, why does it matter and what does it measure?
Why can we know the absolute values of entropy when we can’t know
the absolute value of enthalpy?
How can we predict which direction (forward or reverse) is spontaneous
for
f a reaction?
What thermodynamic quantity helps us predict the spontaneous direction
for a reaction, how is this related to our understanding of equilibria?
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Chemical thermodynamics
How fast is the reaction?
How far does it proceed?
How does the energy involved in the reaction affect the extent of
reaction?
first law of thermodynamics:
i used
d iin
energy is
process
energy is lost to
surroundings
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To reverse the process, have add more energy than was produced
because some energy was lost in heat to the surroundings.
“nature’s heat tax”
efficient processes have the smallest number of transactions
(pay the tax the smallest number of times)
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Spontaneous processes
first law balances the books but doesn’t tell us the extent of the process
some processes have directional character a spontaneous process
processes that are spontaneous in one direction are nonspontaneous in the
other direction
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spontaneity of a reaction is
a nonspontaneous process is
NOT
impossible
spontaneity
p
y can depend
p
on temperature
p
ice
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reversible processes
a change that can be reversed by an
infinitely small change in a variable
Heat flows reversibly
when T is changed by an
infinitely small amount
T + ΔT
T - ΔT
irreversible process
the system and the
surroundings cannot be
returned to their original
state
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What makes a process spontaneous?
possibly system goes to lowest enthalpy?
evaporation, melting ice at T = 20 °C, dissolving of NH4NO3 in water
need to develop a “chemical potential” that
predicts spontaneity
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define a new thermodynamic quantity to evaluate disorder or randomness
Entropy – a thermodynamic function that increases with the number of
symbol for entropy = S
associated
associated
i t d with
ith th
the extent
t t th
thatt th
the energy iis di
distributed
t ib t d or di
dispersed
d
if randomness increases in a spontaneous process,
then entropy must increase
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What is meant by “energetically equivalent ways”?
consider a gas expansion into a vacuum
expansion is at constant
temperature
vacuum
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some of the possible external
arrangements
omitting the 3 to 1 and 1 to 3
arrangements
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internal arrangements that give the same
external arrangement
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Entropy
Entropy is a state function
entropy depends on measurable quantities
for an isothermal process
qrev is the heat for the reversible isothermal path
Since S is a state function, we can use this equation for any
isothermal process even an irreversible process
phase changes are isothermal changes
solid  liquid
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Second law of thermodynamics
in any spontaneous process, the total entropy of the
universe always increases
to make predictions about spontaneity, we have to consider both the system
and the surroundings
calculate ΔS surroundings for 1 mole of ice melts in a hand at 37 °C
∆Sfusion 
(1mole)(-6.01x10 3 J/mol)
310K
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to reduce randomness in the system (ΔSsystem < 0)
Consider condensing steam at 80 °C
∆Svap 
(1mole)(-41x103 J/mol)
373K
∆Ssurr 
(1mole)(41 x103 J/mol)
353K
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Molecular interpretation of entropy
why does entropy depend of number of possible energetically
equivalent states ?
perfectly
f tl ordered
d d CO
crystal
k = R/NA = 1.38 X 10-23 J/K
one random
d
arrangement
out of 220
W is the number of energetically
g
y
equivalent ways to arrange
the components of the system
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Which of the following has a positive value for ΔS?
A.
B.
C.
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for molecules, energetically equivalent ways involve considering all of the
energies of all of the molecules in the system
each molecule has a certain kinetic energy made
up of
g p
possible
microstate: a single
arrangement of the positions
and kinetic (motional) energy
of each molecule in the
system
W is the number of
microstates
inc. size
inc. T
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entropy
randomness (entropy)
increases with greater degrees of
freedom
How does ΔS change in these reactions?
2 SO2(g) + O2(g)  2 SO3(g)
H2O(ℓ) → H2O(g)
CaCO3(s) → CaO(s) + CO2(g)
Ag+(aq) + Cl-(aq) → AgCl(s)
S[C(g)] = 158.0 J/mol K
S[CO(g)] = 197.9 J/mol K
S[CO2(g)] = 213.6 J/mol K
4Fe(s) + 3O2(g) → 2Fe2O3(s)
A.
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ΔS > 0
B.
ΔS <0
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entropy and temperature
entropy
as T decreases,
energy decreases and
population of energy
l
levels
l d
decrease
Third law of thermodynamics:
The entropy of a perfectly ordered crystalline substance
at 0 K is zero
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Entropy changes in chemical reactions
∆Ssys can not be measured easily (in contrast to ∆H)
Absolute entropies, S, can be obtained for substances
because of third law
law, entropy on an absolute scale
S is a state function so can calculate ∆S
∆S = ∑ ni Si (products) - ∑ mj Sj (reactants)
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Standard molar entropy
defined for pure substances at 1 atm pressure and 25°C
– see Table 19.2 and Appendix C
S°[O2(g)] = 205.0 J/mol K
standard molar entropies of gases
S°[H2O(l)] = 69.91 J/ mol K
S°[H2O(g)] = 188.83 J/ mol K
standard molar entropies increase
S°[Na(s)] = 51.45 J/ mol K
76.78
S°[Rb(s)] = 76
78 J/ mol K
S°[K(s)] = 64.47 J/ mol K
standard molar entropies increase
S°[CH4(g)] = 186.3 J/ mol K
S°[C3H8(g)] = 269.0 J/ mol K
S°[C2H6(g)] = 229.5 J/ mol K
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The change in entropy for a reaction can be calculated from the standard molar
entropies by ∆S° = ∑ ni Si°(products) - ∑ mj Sj°(reactants)
example:
What is the change in entropy in the reaction:
Al2O3(s) + 3H2(g) → 2Al(s) + 3H2O(g)
Data from Appendix C:
Substance
Al2O3(s)
H2(g)
Al(s)
H2O(g)
S⁰ (Jmol-1K-1)
51.00
114.6
28.32
188.83
This method provides the ΔS for the system,
to predict spontaneity, we need
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Entropy of the surroundings
Entropy change for
surroundings
depends on the heat
change
h
off the
h system
f an isothermal
for
i th
l process,
and at constant P, qsys = ΔHsys
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Overall spontaneity depends on both ΔSsys and ΔSsurr
which is more important?
p Why
y is freezing
g water at -4°C spontaneous?
p
example:
ΔSsys is < 0 because going from liquid to solid, less motional energy
ΔSsurr = –ΔHfus/ T
ΔHfus from solid to liquid is +
for the process to be spontaneous
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How do we put the two ΔS calculations together?
Example:
CO(g) + 2H2(g) → CH3OH(l), all substances at 298 K
S° values: CH3OH(l) = 126.8 J K-1mol-1, CO(g) = 197.7 J K-1mol-1,
H2(g) = 130.7 J K-1mol-1
ΔH°f values: CH3OH(l) = -238.66 kJ mol-1, CO(g) = -110.52 kJ mol-1
What is ΔSsys?
How would we calculate ΔSsurr?
Is this reaction spontaneous?
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overall prediction of spontaneity depends on
ΔSuniv > 0
ΔSuniv = ΔSsys + ΔSsurr
Gibbs Free Energy
gy
G = H - TS
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ΔG = –TΔSuniv
when ΔSuniv is positive
Gibbs free energy ( or just free energy) is called the chemical potential
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Q<K
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pure reactants
equilibrium Q = K
ΔG = 0
Q>K
pure
products
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Which is more important ΔHsys/T or ΔSsys ?
ΔH
ΔS
+
–
+
+
–
+
–
–
ΔG = ΔH - TΔS
Rxn. Spontaneity
example: pure chromium is obtained by reducing Cr O with Al:
2 3
Cr2O3(s) + 2 Al(s) → 2 Cr(s) + Al2O3(s)
I the
Is
th reaction
ti spontaneous
t
att 25°C given
i
th
thatt ΔH° = –536
536 kJ/ moll and
d
ΔS° = -79.3 kJ/ mol?
Will changing the temperature, change the spontaneity?
(assuming that ΔH ° and ΔS° do not change with temperature)
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