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First
Law of Thermodynamics
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What is the law
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An
example in the body
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| The total energy
of a system and its surroundings remains constant. Energy
is neither created nor destroyed but may be used to
do useful work on the system or surroudings. |
The energy produced
by the digestion and breakdown of proteins may be used by
the organism to synthesize other molecules, or it may be used
to keep the temperature of the organism constant. |
First
Law Math in the Body
This law is
represented as:
DE= q - w
------
(1) where delta E is the
change in internal energy of the system, and
q is positive number when heat
is absorbed by the system from its surroundings and a negative
number when heat moves away from the system.
w is positive when work
done by the system and negative when the work is done by the
surroundings. NOTE: Since the concept of w
generally applies to gaseous systems (where partial pressure
or volume of the system may vary) it is generally ignored
for reaction in a solution. Cellular reactions occur in solutions.
In this case the equation may be written as: DE=
q
So: under these conditions, D
E is essentially a change in heat content of the system. Therefore DE
= DH
(the change in enthalpy of the system). |
Second
Law of Thermodynamics: Direction of Reactions
The first law is
essentially keeps track of energy produced and spent and these
must balance. The second law helps us understand
why certain processes can proceed in a reversible manner whereas
others essentilly are unidirectional. For example, it is
poosible to convert water to ice and vice versa but if
we burn a piece of cloth to carbon dioxide and water, it
is not reversible.
This concept can be understood if we realize
that not all the energy or heat content of the system (DH)
in solution may not be available for useful work. That is, some
of the energy may be lost in non-productive manner.
Thus delta H may be defined as:
DH
= DG
+ T DS ------
(2)
where DG is the free energy change in the system and is the energy
available to do useful work (convert a substrate to a product),
and
DS is the change in the entropy of the system (entropy is defined
as degree of randomness of the components of the system).
These are conditions of constant pressure,
volume, and absolute temperature in degrees Kelvin (T= 273 + degree
centigrade). This equation is generally written as:
DG = DH - T DS ------
(3)
It is
clear and logical to think that if the free energy of the product
is less than that of the reactants, then the reaction will be
inclined to go in a forward direction.
However,
if DG
is positive then the backward reaction will be favored. Negative
values of DG
can be achieved if dH is negative and dS is positive. Such reactions
are considered as Enthalpy Driven and/or
Entropy Driven.
- However,
depending upon the magnitude, it is possible to have negative
value for DG
even if DH
is positive or DS
is negative. An example is melting of ice to water. The DH
for this system is positive whereas dS is highly positive which
compensates for the positive dH.
- On
the other hand when water freezes to ice, DS
is negative (less randomness in the structure of water) but positive
TDS
value is compensated for by negative enthalpy change.
It
must be remembered that favorable reactions must have a negative value for dG. Such reactions
are called Exergonic. Reactions with positive DG are not favored in the forward direction and are called
Endergonic. See a site
showing endergonis
and exergonic reactions from the University of Central Arkansas.
Let
us see if thermodynamics can explain the cellular processes
Considering a cellular process: S ---->
P, the free energy of substrate and product can be described
as:
Gs = G0s+
RT ln {S} and
Gp = G0p
+ RT ln {P}
G0p and G0s
are standard free energy changes and represent the free
energy of product and substrate when they are present
at 1M concentrations. For biochemical reactions, standard
free energy changes are normalized to pH 7 because many
of the biochemical reactions involve {H+} as one of the
components of the reaction and it is simpler not to have
to include {H+} as one of the components of
the reaction. Thus G0 are represented as G0'.
Therefore, change in free energy of a reaction can be
represented by:
DG= (Gp-Gs)= (Gp0'-Gs0'
) + RT( ln {P}- ln {S})
DG= DG0'
+ RT ln {P}/{S}
(1)
When the reaction reaches equilibrium, there is no net
change in the concentrations of substrate and product;
therefore no useful work is done by the system and ![]() G
=0. Under these conditions:
0=DG0'
+ RT ln {P}e/{S}e or DG0'
= - RT ln {P}e/{S}e = -RT ln Keq or DG0'
= -RT ln Keq
Thus knowing standard free energy change for a reaction,
one can calculate the equilibrium constant. For these
calculations, R is 1.98 cal/mole/degree Kelvin and T is
(273 + Degree centigrade) (in recent literature, the heat
energy is represented by Joules or KiloJoules; it is easy
to convert calories or kilocalories to Joules: 1 cal =
4.184 joules). Based on these calculations, one can predict
the magnitude of Keq. Thus
DGo'
= 0 Keq
= 1
DGo' is negative Keq
> 1
DGo' is positive Keq
< 1
Keq values
also indicate whether the reaction is favored in a particular
direction. Keq =1 means that the reaction is equally favored
in both directions. Keq greater than one means that the
reaction is favored in the forward direction whereas Keq
of less than one means that the reaction is favored in
the backward direction.
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. For
additional descriptions of the 1st and 2nd Laws in the cell, see
the Protein
Chemistry page on the web site from the Natural Toxins Research
Center at Texas A&M, and a Thermodynamic
fundamentals web site from Xavier University of Louisiana.
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