Thermodynamics of Bioreactions
97
4.1.1
Changes in Free Energy and Enthalpy
The change of Gibbs free energy by a chemical reaction is calculated from
( A G )ra tio n = ( £
Yp,A G f j
) product, -
( 2
Y S j
A G / J ) , Ubsdttt«
( 4 .2 )
where
YP
.
and
Ys
are the absolute values of stoichiometric coefficients for products and substrates
respectively. In eq. (4.2) A Gy is the free energy of formation of the reactants at the state at which
they are present in the reaction. Conventionally elements in their stable form at 25°C and 1
atm are
defined to have zero free energy. A
G}
is then the standard free energy of formation of the
compound from its constituent elements at the reference temperature; here chosen as 25°C, and
1
atm.
In analogy with eq. (4.2) the enthalpy of reaction
(AH)
can be found by using Ajfy instead
of A Gy where
AHf is
the enthalpy of formation of the reactant. Similarly the entropy change
AS
that accompanies the reaction can be calculated. All chemical compounds are defined to have zero
entropy at
T
= 0 K = - 273°C. At standard conditions 298 K, 1
atm the entropy 5° is consequently
positive for all compounds, reflecting the increase of “disorder” which accompanies the change in
reference temperature for
S
from 0 to 298K.
Extensive tables of A G }, A
H}
and 5° are available, and using data from these tables AG° and
A H
for the reaction can be calculated using (4.1). When calculating AG° and A
H
at
temperatures in the vicinity of 25°C the change in Aand in 5° from
(AH°f,2n , S\n
) can often
be neglected while A G / is a stronger function of
T.
Example 4.1 Thermodynamic data for H20
In Handbook of Chemistry and Physics one obtains the following standard values for 0 2, H2 and H20 - all
in the gas phase
A G /
AH}
0 2
0
0
49
H2
0
0
31.21
H,0
-54640
-57800
45.11
A G / and A
H°r
are in cal mole’1, 5° is in cal (mole K.)'1. Since eq. (4.1) is a relation between A G .
A H
and
A S
we can use two of these quantities to calculate the third. Thus, for water
A H / = -54640 + (45.11 - 31.21 - 0.5 ■
49) ■
298 = -57800 cal mole’1
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