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### Negative Entropy in Chemical Reactions

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Date: 08/20/2001 at 12:45:32
From: Joseph
Subject: Negative entropy in chemical reactions...

Hello!

I am doing some research on entropy and the Second Law of
Thermodynamics. Perhaps you can help me with a question that I have?

The Second Law of Thermodynamics states that entropy (disorder) in
the universe must always either increase or remain constant. However,
although UNIVERSAL entropy cannot decrease, INDIVIDUAL entropy can.
There are many examples of this; one would be the freezing of water.
This process causes water to go from a "less ordered" state to
a "more ordered" state. Thus, there has been a decrease of entropy in
the water. HOWEVER, during the freezing process, water also gives
off energy into its surroundings, warming them and causing them to
INCREASE in disorder. Consequently, there is no change in UNIVERSAL
entropy; just a move from disorder in the water to disorder in the
surroundings; and the Second Law of Thermodynamics is not broken.

Now, to my question...

Could you name some more chemical reactions in which the disorder of
the chemicals involved decreases as a result of the reaction?

Thanks so much!
Sincerely,
Joseph Dugan
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Date: 08/21/2001 at 11:44:31
From: Doctor Achilles
Subject: Re: Negative entropy in chemical reactions...

Hi Joseph,

Thanks for writing to Dr. Math.

There are countless examples of reactions that give off heat in
exchange for decreasing local entropy. Rather than just listing some
of them, I'll give you a couple of main CLASSES (types) of reactions
and you can figure out specific examples:

1) Phase changes. Water freezing is an example. Matter basically
exists in three states: solid, liquid, and gas. As things move from
gas to liquid or from liquid to solid, they lose entropy and give off
heat. Even without changing phase, cooling things down decreases their
local entropy and necessarily heats their surroundings. The reason is
that molecules are moving faster (and thus have more randomness or
entropy) when they are warmer. A phase change is just a dramatic
example of this: gas molecules bounce around freely, liquid molecules
are stuck together but move around one another, solid molecules just
vibrate in place but don't move around.

2) Phase changes are often considered PHYSICAL reactions, because no
molecules actually change; they just associate in different ways.
Chemical reactions (where molecules interact and become other
molecules) have entropy changes associated with them as well. There
are published tables of the relative entropy of different molecules.
So for example if you have two molecule A's reacting with one molecule
B to make two molecule X's:

2A + B -> 2X

Then you can find the change in entropy by adding the entropy of the
products (2X) and subtracting the entropy of the reactants (2A+B).
Fortunately, you don't HAVE to look relative entropies to make a good
guess. In the reaction above, we started with three molecules and
ended up with two. As a general rule, if you end up with fewer
molecules than you started with, then entropy decreased (you've
crammed the same number of atoms into a smaller number of molecules,
so they are more ordered). HOWEVER, if there are phase changes
involved, for example three liquid molecules becoming two gas
molecules, then the general rule about counting molecules is no longer
valid.

Most general chemistry will focus on simple chemical reactions, such
as the generation of water vapor from hydrogen and oxygen gas. My
favorite subset of chemical reactions (and the topic of much chemical
research these days) is biomolecules: proteins, fats, sugars, etc.
Building proteins out of amino acids and building fats out of simple
carbon compounds are processes that decrease local entropy
substantially: many of these large biomolecules (especially proteins)
are very carefully ordered to achieve a specific function. Cells
expend a lot of energy and generate a lot of heat in the process of
making these large molecules. When plants make sugar, they take the
energy neatly packaged in individual particles of light and turn it
into heat. Life is very highly structured, and living things are
constantly fighting against the second law of thermodynamics to stay
structured. In the process, they must use a lot of energy, which is
released as heat.

Hope this is helpful. Good luck coming up with examples, if you'd like
write back.

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Physics/Chemistry

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