Biology Reference
In-Depth Information
“quantization” here means that the energy levels are not continuous but are
separated into discrete states.
n
Just as electrons have their energy levels within an atom (which can be depicted
diagrammatically as shown in the left panel in Fig.
11.28
), it is postulated here that
energy levels (or more accurately “partial molar free energies,” also known as
“chemical potentials” [Wall 1958, p. 192]) within a living cell. The partial molar
free energy of the ith chemical,
m
i
, including biopolymers, can be calculated as:
m
i
¼ð@
G
=@
n
i
Þ
T
;
P
;
n1
;
n2
;:::
(12.30)
which states that the chemical potential of the ith chemical in a system consisting of
components labeled as 1, 2, 3,
, is equal to the partial derivative of Gibbs free
energy of the system with the temperature, pressure, and the concentrations of all
the components held constant except the ith component.
If the ith chemical, say, A, interacts with at least one another chemical, B, to
produce two products, C and D, i.e., A + B
...
C + D, the Gibbs free energy
change,
D
G, experienced by the system under consideration is given by:
$
G
Initial
¼ D
G
þ
D
G
¼
G
Final
RT ln C
ð
½
½
D
=
½
A
½
B
Þ
(12.31)
where G
Final
and G
Initial
are the Gibbs free energy content of the system in the final
(or product) and initial (or reactant) state, respectively, R is the universal gas constant,
ln is the natural logarithm, and
D
G˚ is the change in the standard Gibbs free energy of
the system, namely, the Gibbs free energy change per mole of the system at the
standard state characterized by the standard T and P, and the unit concentrations
(or more accurately activities) of all the chemicals in the system. At equilibrium
nothing can change and hence
D
G
0, and the quotient, ([C][D]/[A][B]) assumes a
unique numerical value known as the
equilibrium constant
denoted as K, leading to
the following equation:
¼
D
G
¼
RT ln K
(12.32)
K=e
D
G
RT
=
(12.33)
As Eqs.
12.31
and
12.32
indicate, the standard Gibbs free energy change,
D
G˚,
can be determined by measuring the equilibrium constant, K, of the chemical
reaction system under the standard condition.
Gibbs free energy has the interesting property that it
minimizes
when spontane-
ous processes occur under the environmental conditions of constant temperature (T)
and pressure (P) (Callen 1985; Kondepudi and Prigogine 1998; Kondepudi 2008).
In other words, Gibbs free energy is a quantitative measure of the tendency of a
physical system to change spontaneously, for whatever reasons, given the right
environmental conditions to overcome kinetic barriers. Under constant T and P, all
spontaneous processes occur with a net decrease in Gibbs free energy, indicating
