Download Entropy, a statistical approach

The Laws of Thermodynamics
No one breaks the Laws…
You can’t win…
you can’t break even…
and you can’t even get out of the game.
Wouldn’t it be nice to know if a reaction has a chance of
working before you even try it?
What makes reactions go?
Reactions tend to a position of minimum energy, that is…
So this must be what makes reactions go.
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In thermodynamics, we define the System as that part of the
universe in which we are interested.
That which is not the System constitutes the Surroundings.
Taken together the System and the Surroundings constitute
the…
But First…
The First Law of Thermodynamics:
The (internal) energy (U) of an isolated system is constant.
An isolated system has a fixed volume and is thermally
insulated from the surroundings. Any change to the energy
of a system must take place by a transfer of heat (q) or work
(w) to/from the surroundings.
U  q  w
•
Heat and work are path functions (not state functions).
•
Heat at a constant pressure is called enthalpy. By definition, at constant
pressure:
q  H
•
Imagine a reaction done in a balloon. The volume of the balloon may change
over the course of the reaction.
– If the balloon shrinks, work has been done on the system.
– If the balloon expands, the system has done work (can be restated as
“negative work has been done on the system”).
– The amount of work done on the system depends on the pressure and on
the change in volume. At constant pressure:
w  PV
1st Law: Heat and Work
• Recalling that U  q  w and that q  H at constant
pressure, we can relate enthalpy and internal energy:
q  U  w
H  U  PV
This is the strict definition of enthalpy - a state function. And
we have pointed out the correlation between enthalpy and the
whether reactions go.
The Second Law of Thermodynamics…
For any spontaneous process, the entropy of the universe increases.
Suniverse  0
This is a truly profound observation with
important implications.

S univ erse  S sy stem  S surroundin gs
The macrostate of a system has macroscopic
properties such as temperature, volume, density
and pressure.
To try to get a handle on Entropy and to quantitate
it, we must consider the system and its
microstates.
Macroscopic versus microscopic states
We can describe the system’s microscopic state, or its microstate as a specific
ensemble of particles and their states:
1 atom gas
It is also:
2. Moving (translation)
3. Rotating
4. Vibrating
Every time it hits another atom
or the wall of the balloon it
changes to a new microstate.
Each microstate has the same total energy.
1 mol gas
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Macroscopic versus microscopic states
The system’s microstate is described by:
o Positions of all particles
o Momenta of all particles (p = mv)
o Occupied energy levels for each particle
This would be a lot of variables if each particle was considered independently. A
system with a mass of ~1 mg will contain millions of millions of millions of particles
to consider.
We can take advantage of the large number of particles in a system by taking a
statistical approach. The system as a whole should behave as though it consisted of
“average” particles.
This statistical approach allows us to relate the macroscopic and microscopic states
of a system.
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Entropy, a statistical approach
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Entropy, a statistical approach
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Each set of particle locations represents a
different microstate. When the volume
increases (stopcock opens), the number of
microstates is 2n, where n is the number of
particles.
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Entropy, a statistical approach
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Entropy, a statistical approach
Properties of entropy
o For any given macroscopic state, there is a fixed number of microscopic
states that could apply. Thus, the value for the entropy of a given
macroscopic state is fixed. As such, entropy is a state function. It
depends only on the macroscopic state of the system.
o The change in entropy of a system depends only on the initial and final
states – not on the path taken from one to the other. This is true for any
state function.
o If a system has  possible microstates then doubling the size of the
system will double the entropy (by increasing the number of possible
microstates to 2). Thus, entropy is an extensive property. It depends on
sample size.
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Entropy, a thermodynamic approach
The entropy of a perfect crystal approaches zero as the temperature
approaches absolute zero.
Therefore, we define an absolute entropy scale by defining the entropy
of perfect crystal at 0 K as:
S = 0 J/mol K
We can measure entropies for substances by looking at the relationship
between the amount of heat absorbed and the change in T.
S 

dqrev
T
For an isothermal process, this simplifies to:

qrev
S 
T
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Entropy change during a phase transition
In essence, the entropy of a
substance is the amount of heat
required to increase its
temperature by a given amount.
Unlike enthalpies (where only
changes are measured),
entropies are absolute.
As reflected in this graph, the
entropy, S, of O2 at 298 K is
205.1 J/mol K.
Tables of entropies at 298 K for
a wide range of materials are
available in this fashion as
standard entropies, S°.
Figure 18.7 The increase in entropy of O2 during phase changes from solid to
liquid to gas.
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The third law of thermodynamics
And since entropy is a state function, the entropy change for a process is:
 r S   S( products)  S(reac tan ts)
Example: Propane (C3H8) is burned near room temperature so that the water
produced is liquid rather than vapor. Calculate the entropy change for
this reaction.

C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(l)
J
mol  K
J
S(O2(g))  205.0
mol  K
J
S(CO2(g))  213.7
mol  K
J
S(H2O(l) )  69.940
mol  K
S(C3H8(g))  269.9
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Generalities about entropy changes:
• the entropy of gases > liquids > solids
(reactions in which gases are formed from condensed phases tend to
have positive entropy changes)
• reactions in solution or in the same phase which produce more product
molecules than reactant molecules tend to have positive entropy changes
(a matter of stoichiometry)
• dissolution of a solid into solution is normally associated with a positive
entropy change, but there are exceptions.
The third law of thermodynamics
Figure 18.8
The entropy of a salt solution is usually greater
than the entropy of the solid and the entropy of
the water, but it is affected by water molecules
becoming organized around each ion.
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The third law of thermodynamics
J
mol  K
J

S(Mg 2(aq)
)  138.1
mol  K
J

S(F(aq)
)  13.8
mol  K
S(MgF2(s) )  57.24
• The ions organize the solvent due to ion-dipole forces,
the water has less entropy with MgF2 dissolved in it.
• Powerful ion-ion forces, increase in microstates of
MgF2 is not as large as one might suppose.
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