At this point we need to bring a couple of important qualifications
into the discussion. In thermodynamics is important to remember that
we are not just concerned with entropy, but with the spontaneity of a
reaction. Both energy and entropy are important. The DG term is
very useful for predicting spontaneity at conditions of constant
pressure. The equation DG = DH - TDS has the additional advantage of
putting all quantities in terms of the system, so we don't have to
worry about measuring the surroundings. If the reaction is
exothermic (DH is negative), the reaction is favored. Likewise if DS
is positive (entropy increases) the reaction is favored. No problem.
For the opposite conditions (DH positive, DS negative), the reaction
is not favored. Again, no problem. But what if DH is negative and
DS is negative, or the reverse is true? Then it depends on which, DH
or DS, is the greater factor, and the temperature at which the
reaction takes place. It is important to remember this because some
reactions may be spontaneous and still result in a reduction of
entropy. A simple example of this (again, related to the third law)
is the freezing of water. Entropy is decreased in a spontaneous
process if the temperature is less than 0 oC. A mistake in
forgetting this seems to be made more often by creationists who seem
to assume that any reduction in entropy automatically creates a
problem for any reaction we might consider. A mistake that seems
more common to those who think thermodynamics presents no problem to
the origin of life is made when they equate examples of spontaneous
reductions of a system's entropy (such as the formation of O2 or the
freezing of water, snowflakes, etc.) with living systems where the
reduction is non-spontaneous. Spontaneous reactions that reduce
entropy are not the thermodynamic problem, so there is no need to
keep pointing them out. (As far as life is concerned, even many
spontaneous reactions present problems. But these are kinetic,
rather than thermodynamic, problems.)
A second qualification concerns
our use of the term entropy. Entropy as
discussed by some dealing with information is not always the
same concept as is often used by chemists for reactions. First, is the entropy
(S) of one mol of a given molecule at a given temperature, e.g. the
standard entropy, So (at 298 oK). A second way to refer to entropy
is as the change in entropy (DS) that is involved with the formation of a product in a
reaction. It is important to remember that entropy is an extensive
property, that is, entropy is directly related to how much of a
substance there is. In this sense, a polymer of five amino acids
(a-a-a-a-a) has less entropy (S) than a polymer of 10 amino acids
(a-a-a-a-a-a-a-a-a-a) simply because by having a greater number of
atoms, more conformations can be achieved resulting from a greater
number of vibrational and rotational motions, and the number of
arrangements possible in the sequence. The same would be true of a
DNA polymer. Most larger molecules will have a larger S value than
most smaller molecules. This concept of entropy (S) may be
important for biological information theory, but is *not* the chemical thermodynamic
problem. That concerns the change in entropy, DS. For the chemist
concerned with entropy changes associated with reactions, the problem
is not a comparison between the final state of any two different
molecules you happen to pick, but between the constituent reactants
and the final products. What has a lower entropy state, five
separate amino acids in solution (a + a + a + a + a) or five amino
acids as a single polymeric molecule (a-a-a-a-a) in solution? Again,
a polymer of five amino acids plus five separate amino acids in
solution (a-a-a-a-a + a + a + a + a + a) or a single polymer of 10
amino acids? Which systems have the greater number of possible
arrangements? A valid comparison is one only for a balanced
equation; that is, between equivalent numbers of atoms before and
after the thermodynamic states we are describing.
Lets illustrate several of the concepts from the previous two paragraphs by
considering states of oxygen, all as gases. The standard entropy
(So) of O is 161 J/K mol, O2 is 205 J/K mol, and O3 is 239 J/K mol.
Entropy (S) is greater as the number of atoms in the molecule
increases. However, if we wish to consider the change in entropy
(DS) between, say O and O2, the reaction 2 O --> O2 has an entropy
change of DS = 205 - 2(161) = -117 J/oK mol. The entropy change is
negative. Another way of saying this is that the entropy (DS ) is
reduced. But wait a minute, we just said the entropy (S) of O2 was
increased over O! I have seen many discussions (including, I think,
some on this list) where people talk past each other on this point. I
think we need to be careful with terms, and maybe some have just not
considered the difference in how the entropy term is being used. But
while 1 mol of O atoms may have less entropy than 1 mol of O2
molecules, the combined O2 molecule has less entropy than the 2 mols of O
atoms that react to form it. It is legitimate to say that a
biological DNA molecule has a high degree of entropy (S) and has more
entropy (S) than a couple of base pairs. It can be confusing to say
that a DNA polymer has increased entropy. An increased entropy
state from what? My natural tendency is to think that the implication
is of an increased entropy state from its reaction components, but then
is the statement accurate? It might be helpful to explicitly state
or make clear from the context what is meant.
The second feature we can note about our illustration is that the negative entropy (-DS)
from 2 O to O2 suggests a non-spontaneous reaction. But we must also
consider the energy (DH), which at 25 oC (standard temperature and
pressure) is -498000 J/mol. The overall DGrxn is -464000 J/mol. The
reaction is overwhelmingly spontaneous even though the entropy state
is reduced.
The question, of course, after considering the relative push and pull
of energy and entropy on a reaction, is whether the reaction is
expected to be spontaneous or not. If it is not, then chemical work
must be done to push the reaction product rock up the energy state
hill.
Regards, Paul
Paul D. Brown
Dept. of PSES, University of Idaho
Moscow, ID 83844