Thermodynamics of Bioreactions
115
(15)
The maximum value for z is equal to the theoretical P/O ratio, i.e. 3 for oxidation of NADH if all
constituents of the respiratory system are present, and it is 2 for oxidation of some FADH3. When
q<
1, z is a
complicated function of the rates of the proton flows that exist in parallel with the main proton flow through
the protein F0. Hence the experimentally derived effective P/O ratios in the range 1.2-1.3 are not at all
improbable.
The thermodynamic efficiency of the process is (-0.696)
(-0.75), or only slightly above 50%. It is close to
the optimal value
i f
= -0.72 and
= 0.529) obtained by Eq. (13). The decrease of thermodynamic
efficiency by a factor 2 when
q
decreases from 1 to 0.95 is quite dramatic. It may be interesting to speculate
why
q
is less than 1. Roels (1983) proposed an answer: The less-than-perfect coupling between oxidation
and phosphorylation is due to the extraneous processes driven by the proton gradient across the membrane.
Looking at the total process of cell growth, some of the thermodynamic efficiency lost in the oxidative
phosphorylation is regained since, e.g., membrane energetization is maintained (no ATP is needed for this),
as is sugar transport by secondary active transport. This yields an intracellular phosphorylated sugar which
unloads its internal free energy in further cell processes.___________________________________________
PROBLEMS
Problem 4.1 Thermodynamic properties of
N H 3
and of
NH4OH.
From a table of thermodynamic data one obtains
5° = 45.77 cal mol*1
K'1
forN2
5° = 46.01 for NHj
&H? =
- 11.04 kcalm ol1
forNH3
all at standard conditions (298 K) and gaseous NH3. Other data are to be taken from the examples in this
a.
Calculate (A Gf° ) for (NH3)g at standard conditions.
b.
Calculate the heat of combustion and the free energy of combustion for (NH3)g at the standard
state. Compare with table 4.3 for A
Hc°,
The following relation holds for x < 4 wt
%
aqueous solutions of NH3:
chapter.
;
7
V
jh
3
(mm Hg) =
8.24 x
(1)
The heat of absorption of NH3 in water is 446 cal g‘!.
c.
Calculate A
Hr,
A
HK
,
AGf and A
Gc
for a 1 M solution of NH3 in water.
d.
Assume that
NH4OH
is fully dissociated to NHi+ and
OH\