The Second Law of Thermodynamics

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The Second Law of Thermodynamics In any physical
process, the entropy of the universe shall tend
to increase. Formal definition of the entropy
(You must be aware of the Second Law of
Thermodynamics. It is essential.)
The subject matter below is usually covered in
introductory physical chemistry courses. You do
NOT need to commit this to memory, although you
may find it useful in improving your
understanding.
Example The Carnot (Theoretical) Heat Engine. 1
? 2 Use heat Q1 to expand a gas. (Temperature of
gas constant.) 2 ? 3 Expand more gas cools. 3 ?
4 Compress gas. (Temperature of gas constant.) 4
? 1 Compress gas gas warms. Because of entropy,
you never warm back up to 1 unless you add heat.
1
Q1
2
T1
T2
4
Q2
3
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The Boltzmann Definition1 of Entropy is
Particularly Useful in Biochemistry
In which kB is the Boltzmann constant, kB
1.381 X 10-23 J/Kelvin and W is the number of
microstates consistent with the observed
macrostate. The Boltzmann definition
corresponds to the number of ways a system may be
organized to produce indistinguishable
macrostates. The more ways there are to produce
indistinguishable macrostates, the more
randomness, or entropy. Note R 8.3144
J/(Kelvin mol) NA kB

• It is well beyond the scope of our purposes to
  prove, however, the Boltzmann definition of
  entropy
• is identical to the definition of entropy given
  on the previous slide. The interested person
  should consult a
• standard physical chemistry text.

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Dave Morgans Statements of the Second Law of
Thermodynamics Entropy especially in
biochemistry is randomness in the system. The
total energy of the universe remains constant but
it declines in quality as it tends to turn into
vibrational, electronic, rotational, etc., modes
(heat). Entropy is that fraction of a systems
internal energy which occurs essentially in
the modes described above and which can not be
harnessed to do work. Theoretically you can
take a certain amount of heat and turn it in to
an equivalent amount of work. (The Carnot Heat
Engine.) Practically this is impossible. There
are fundamental (theoretical!) limits to the
efficiency with which any form of energy may be
harnessed to do something useful. Perpetual
motion machines are impossible.
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The world is running out of oil. The world will
run out of oil. The economy runs on
oil. Alternative fuels (and energy sources) are
necessary. Implications of the Second Law For
the Future of Energy Hydrogen (for combustion)
will (probably) never be a good replacement for
fossil fuels. Good fuels are low entropy.
oil, coal, biodiesel, fat, uranium, plutonium,
hydrogen (for nuclear fusion) are good fuels
you get a big bang for the buck. Renewable
sources solar, wind, fuel cells arent good
energy sources you only get a bit of a pop for
the buck.
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The Third Law of Thermodynamics
A perfectly ordered crystal will exhibit zero
entropy at zero Kelvin.
This crystal is perfectly ordered, and (at 0
K) exhibits an entropy of 0.
This crystal is imperfectly ordered, and (at 0
K) exhibits an entropy gt 0.
Regrettably, perfectly ordered crystals appear to
be impossible to prepare. Regrettably, achieving
a temperature of 0 Kelvin also appears to be
impossible. (The coldest temperature ever
produced in a lab is approximately 1 X 10-10 K.)
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The Laws of Thermodynamics Have Been Humourously
Summarized
THE FIRST LAW The energy of the universe is
constant. You cant get something from
nothing. TANSTAAFL1 THE SECOND LAW The entropy
of the universe tends to increase. You cant
win. THE THIRD LAW The entropy of a perfect
crystal is 0 at 0 Kelvin. You cant get perfect
crystals. You cant get to 0 Kelvin. You cant
get out of the game.
Humourously expressed or not, the Laws of
Thermodynamics are fundamental statements about
the nature of the universe in particular, they
establish the impossibility of certain (otherwise
desirable) things.
1 See Robert A. Heinleins science fiction
masterpiece The Moon is a Harsh Mistress.
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Problem If the Second Law of Thermodynamics is
valid
In any physical process, the entropy of the
universe tends to increase, Why dont we (and
everything else) just decompose into random,
disordered, high entropy states? Answer The
Gibbs Free Energy
Implication Even if a process leads to a lower
entropy state (i.e., it is expected not to be
favourable) the process may still occur if a
sufficient amount of enthalpy (essentially heat)
is liberated in it.
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Even if a process leads to a lower entropy state
(i.e., it is expected not to be favourable) the
process may still occur if a sufficient amount of
enthalpy (essentially heat) is liberated by it.
Is the Gibbs Free Energy Consistent with the
Second Law of Thermodynamics?
Sure. We measure free energies on isolated
systems. Processes in isolated systems can lead
to more ordered states and well see examples
in this course (e.g., protein folding) but the
point is even if entropy declines in an isolated
system it will still have increased (indeed, to a
larger extent) in the universe as a whole.
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The Gibbs Free Energy and Spontaneity
Consider an arbitrary chemical reaction
A
B
If DG lt 0 the reaction is spontaneous in the left
to right direction.
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Spontaneity and Rate
Spontaneous refers to whether or not a process
will occur in a system left to its own devices
without the input of energy. Spontaneity bears
no necessary relationship to rate. Some
spontaneous reactions (e.g., the explosion of a
bomb) occur very rapidly. Some spontaneous
reactions (e.g., the conversion of graphite to
diamond) occur very slowly.
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A Look at the Nature of Equilibrium (I)
Consider an arbitrary chemical reaction
kf
A
B
kr
The rate law for the time dependence of A is
The rate law for the time dependence of B is
At equilibrium, neither the concentration of A
nor the concentration of B changes, with time.
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A Look at the Nature of Equilibrium (II)
At equilibrium, the rate at which A is converted
into B is equal to the rate at which B is
converted into A. No net change in either
concentration occurs. But the reaction is still
occurring.
And look closely here. Note that the equilibrium
concentrations of B and A are a ratio of rate
constants
What is the punch line?
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The Equilibrium Constant
Consider an arbitrary chemical reaction
a A b B
c C d D
The equilibrium constant for this reaction is
Meaning At equilibrium, and only at
equilibrium, the expression above relates the
equilibrium constant Keq and the equilibrium
concentrations of the species in the reaction.
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The Relationship Between the Gibbs Free Energy
and the Equilibrium Constant
In a chemical process, the position of
equilibrium is related to the free energy of the
process
In which DG is the free energy change for the
process, R is the gas constant R 8.3144 J /
(Kelvin mol) R 1.9891 cal / (Kelvin mol), and T
is the absolute temperature at which the process
takes place. The calorie1 is a common unit in
biochemistry (and is less common in other
branches of chemistry) 1 calorie 4.18 J

• One calorie is the amount of energy required to
  raise the temperature of one gram of
• water by one degree Celsius (or Kelvin).

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When Two Equations are Equal to the Same
Quantity They are Equal to Each Other
We are now equipped with two equations for the
free energy change of a process
Therefore
This is called the vant Hoff Relationship. If a
series of data is taken at different temperatures,
and, at each, an equilibrium constant is
determined, the enthalpy and the entropy of the
process may be estimated.
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A Common Problem in Biochemistry Binding Between
Two Species to Make a Complex
The protein myoglobin (Mb) binds Oxygen (O2)
Mb O2
MbO2
Do not be concerned by the p here. It means
pressure, and is used because O2 is a gas. This
is a perfectly normal equilibrium statement for
cases involving a gas.
By convention in biochemistry, equilibrium
constants are usually expressed as dissociation
constants, KD. Dissociation constants are the
equilibrium constants for the reverse reaction
not complex formation but complex
dissociation. Note, therefore, that
and
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