Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Negative Entropy in Chemical Reactions


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


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 
to talk about this some more, or if you have other questions, please 
write back.

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

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/