Download Lecture 22 - Chemistry at Winthrop University

Chap 7: The 2nd and 3rd Laws
Entropy and Gibbs Free Energy
• Why do things fall apart?
• Why doe some things happen
spontaneously?
• Why does anything worthwhile take work?
–
I’m not sure that our discussions will completely answer this, but we’ll give it a go.
7.1 Spontaneous Change
• Last chapter, we learned about work,
heat and enthalpy
• We learned that all energy in the
universe is conserved and constant
(at least I hope we did, it will be on the final…)
– But that’s not really very useful
– We want to predict the behaviour of the
universe around us.
Spontaneous Changes
We know from our own
experiences that some
things will happen
spontaneously
We can make the
reverse happen
(heat a metal
cube up, partition
a gas), but that
takes work
(energy)
Metal cools
Gas expands
Spontaneity in Processes
• A process is spontaneous if it has the
tendency to occur without being driven
by an external influence
– Don’t confuse ‘spontaneous’ with ‘speedy’
or ‘rapid’!
7.2: Entropy and Disorder
• If we think about the universe around us and look
at all of the spontaneous changes we have
observed over our lifetimes, one thing is certain:
Energy and Matter tend to disperse in a
disorderly fashion
• Gas molecules don’t pile up on one side of a
flask
• Buildings fall apart
• Thing left untended will get worse
The 2nd Law of Thermodynamics
The entropy of an isolated system
increases in the course of any
spontaneous change
• We can summarize this law
mathematically as:
q
S 
T
The 2nd Law
q
S 
T
• What does this mean?
– If a lot of heat energy is transferred, there is a
large increase in entropy
– This
 change in entropy is more noticeable at
lower temperatures than higher temperatures
(relatively)
• Temperature must be in Kelvin and heat must be
in Joules

Entropy
• Entropy is a measure of disorder,
according to the second law of
thermodynamics
• The entropy of an isolated system
increases in any spontaneous reaction
• Entropy is a state function
Changes in Entropy
• The equation we obtained from the
second law
S 
q
T
is valid for isothermal situations (change
of state,gas expansion) but we
frequently want to be able to determine
the entropy as temperature changes…

Entropy Change as a Function of
Temperature at Constant Volume
T2 
S = C ln 
T1 
• If T2 > T1, then the logarithm is ‘+’ and entropy
increases
 sense since we are raising the temperature
– Makes
and thermal motion will increase
• The greater (higher) the heat capacity, the
higher the entropy change
Entropy Change as a Function of
Changing Volume
• We can use a similar logic to derive the
change in entropy when the volume changes:
V2 
S = nR ln  
V1 
• When V2 > V1, the entropy increases
• Note: 
Units are still J/K

Entropy Change as a Function of
Pressure
• Remember Boyle’s Law?
• We can substitute this relationship into
the equation for entropy change as a
function of volume to get:
P1 
S = nR ln  
P2 
Entropy decreases
for a sample that has
been compressed
isothermally (P1>P2)

Entropy Changes Occurring as a Function
of Physical State Changes
• What happens to the entropy of a
system as we change state?
• Remember: Melting point temp = Tf
Boiling Point temp = Tb
• Temperature doesn’t change as we heat
a sample to cause a phase change
• Let’s look at liquid water --> water vapor
Boiling Water and Entropy
Let’s get 3 facts straight:
1. At a transition temperature (Tf or Tb), the temperature remains
constant until the phase change is complete
2. At the transition temperature, the transfer of heat is reversible
3. Because we are at constant pressure, the heat supplied is equal to the
enthalpy
Water Boiling and Entropy
S =
H vap
(at the boiling temperature)
Tb
• We use the ‘ º ’ superscript to denote
the standard
entropy

(the entropy at 1 bar of pressure)
S =
H vap
Tb
Ice Melting and Entropy
• We use the same logic to determine the
entropy of fusion, Sfus
Sfus

H fus
=
Tb
Sfus =

H fus
Tb
Trouton’s Rule
• Because the entropy increases so much
in going from liquid to a gas, many
liquids have similar S°vap values
Trouton’s Rule
• Why is this?
– Positional disorder of a gas versus a solid
or liquid (which are pretty close to the
same thing)
• Exceptions: Molecules with very weak
or very strong intermolecular forces
– Helium, Water and Methanol
7.5: A Molecular Interpretation of Entropy
• We’ve looked at the changes to the entropy of
a system, but now let’s look at the absolute
entropy of the system itself
• If we had a perfect crystal, the positional
disorder would be ____
• If the temperature was 0K, the would be ___
thermal disorder, so the entropy would be ___
The 3rd Law
The entropies of all perfect crystals
approach zero as the absolute
temperature approaches zero.
The Boltzmann Formula
Where:
k = Boltzmann’s constant
S = k lnW
= 1.381 x10-23 J/K
W=# of ways atoms or molecules in
the system can be arranged and still
give the same total energy
• W is a reflection of the ensemble, the
collection of molecules in the system
• This entropy value is called the
statistical entropy
The Boltzmann Formula
• Let’s think about W (Wahrscheinlichkeit) for a
moment
– Word translates as “probability” or “likelihood”
• If we could only arrange the atoms/molecules
in the system one way, there would be ___
entropy since ln(1) = __
• As we start to increase the population of the
system, we can arrange the members of the
system in different ways and still have the
same total energy, so W increases.
The Boltzmann Formula
Example 7.7
Each molecule can be oriented 2 ways
W = 2 x 2 x 2 x 2 = 16
Residual Entropy
• We know Boltzmann’s concept of the
ensemble is correct from observations of
molecules at low temperature (and using
logic with some cynicism)
• As we get near absolute zero, the entropy
within the crystal becomes increasingly a
function of the positional entropy within the
ensemble cause by the packing of the
components
• Let’s think about this for a minute…
Residual Entropy
The entropy of 1 mole
of FClO3 at T = 0 K is
10.1 J/K. Suggest and
interpretation.
•How many molecules
do we have?
•How many ways can
each molecule be
arranged?
•What is the residual
entropy?
•Pretty close!