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UNDERSTANDING THERMODYNAMIC RELATIONSHIPS
Let’s look at how DH (enthalpy change
or heat of reaction) and DS (entropy change
of a reaction) fit together with DG to explain
the behavior of a chemical reaction. Consider the thermodynamic equation:
It is clear that the value of DG (positive
or negative) depends on the values of DH
and DS as well as the temperature of the
reaction. Another way to think about it is that the DG,
or maximum potential usable energy of the reaction, is distributed between the
two terms, DH and TDS.
The DH (enthalpy) term represents energy that can
be measured as the evolution or absorption of heat during the course of the
reaction. The TDS (entropy) term indicates
energy associated with the change of entropy, or disorder, of the system during
the course of the reaction. This is the energy that increases the random motion
or orientation of molecules involved in the reaction and is thus lost to the
system, because it cannot be utilized productively.
|
Enthalpy, and Entropy |
| Enthalpy (DH) |
| |
positive (+) |
Heat absorbed |
| |
negative (–) |
Heat released |
| Entropy (DS)
|
| |
positive (+) |
Increase in disorder |
| |
negative (–) |
Decrease in disorder |
|
| DG |
= |
DH |
– |
TDS |
|
Maximum usable
potential energy
of a reaction
|
|
Heat
energy |
|
Energy gained or
lost due to changes in
thermal and positional
disorder of molecules |
|
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Understanding spontaneity in terms of enthalpy and entropy
There is only so much potential energy associated with a chemical reaction,
and any energy that is involved in increasing entropy cannot be made to do useful
work. Let’s look at a concrete example. The hydrolysis of ATP, a common
biochemical reaction in our bodies, provides energy for physiological processes:
ATP 
ADP + Pi DG = –30.5
kJ/mol at 25°C |
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Measurements of enthalpy show that DH for
this reaction is only – 16.7 kJ/mol at 25°C. In other words, although
the Gibbs Free Energy of the reaction is –30.5 kJ/mol, meaning it has the
potential to release 30.5 kJ/mol of usable energy when hydrolyzed, only 16.7 kJ/mol
of heat energy was actually released. What happened to the other 13.8 kJ/mol of
energy? Look once again at Willard Gibbs’ equation and plug in the values
for DG and DH:
DG = DH
– TDS
–30.5 kJ/mol = –16.7 kJ/mol – TDS
–13.8 kJ/mol = – TDS
TDS = 13.8 kJ/mol |
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The rest of the energy is accounted for by the TDS
term. The TDS term is positive, indicating
an increase in the entropy of the system. This energy that increases the entropy
of the system cannot be recovered to do useful work.
Thus, in the Gibbs equation, the enthalpy and entropy terms are in competition
with each other. Experiment with the following interactive element to gain a better
understanding of the interplay between enthalpy and entropy. Notice that the temperature
of a reaction is also a factor in the entropic term of the equation. Move the
sliders to experiment with different thermodynamic scenarios.
Example 5: Protein folding
Polypeptide chains fold spontaneously into defined patterns to make functional
proteins. This process involves the polypeptide chain going from a disordered,
random structure to a highly ordered one. How is this not a violation of the
Second Law of Thermodynamics?
Answer
The ordering of the protein from a free-swinging peptide chain involves a
variety of physical forces, some that favor the unfolded peptide chain, and some
that favor the neatly folded protein. When assessing entropic contributions to
Gibbs Free Energy for the purpose of determining spontaneity, you must not look
only at the system, but also at the surroundings. It is true that the entropy
of the protein decreases when it is folded because the chain is arranged in a
more orderly fashion. However, there are other entropic considerations in the
surroundings of the protein. In an unfolded protein, all of the hydrophobic portions
of the polypeptide are exposed to the aqueous environment, and the water molecules
order themselves around the hydrophobic residues in ordered structures called
hydration spheres. As a protein is folded, these hydrophobic residues initially
exposed to the aqueous environment are buried in the interior of the protein,
hidden away from contact with water molecules, and the entropy of the water molecules
increases as the need for hydration spheres diminishes, in effect overcoming the
entropy decrease for the protein alone. In other words, while the entropy of the
system (the protein) decreases, the entropy of the surroundings increases to a
greater degree, leading to an overall increase in entropy for the universe.
The folding of a protein also provides an example of the "DH"
and "–TDS" terms competing
with one another to determine the DG of
the folding process. As described above, the change in entropy of the protein
as it folds is negative, so the "–TDS"
term is positive. However, in addition to entropic effects there are enthalpic
contributions to protein folding. These include hydrogen bonding, ionic salt
bridges, and Van der Waals forces. An input of thermal (heat) energy is required
to disrupt these forces, and conversely when these interactions form during
protein folding they release heat (the DH
is negative). When all of these entropic and enthalpic contributions are weighed,
the enthalpy term wins out over the entropy term. Therefore the free energy
of protein folding is negative, and protein folding is a spontaneous process.
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