An investigation of the equilibrium of the reaction {l-aspartate(aq) + 2-oxoglutarate(aq) = oxaloacetate(aq) + l-glutamate(aq)}

Article abstract of DOI:10.1006/jcht.1998.0404

Apparent equilibrium constants have been measured for the following biochemical reaction: L-aspartate(aq) + 2-oxoglutarate(aq) = oxaloacetate(aq) + L-glutamate(aq). This reaction, catalysed by aspartate transaminase, was studied over the ranges 283.15 ≤ T/K ≤ 303.15, 6.94 ≤ pH ≤ 7.13, and 0.163 ≤ I_m/(mol·kg^-1) ≤ 0.167, where T is temperature and I_m is ionic strength. The instability of the oxaloacetate in solution required the use of an experimental procedure that was brief. Thus, the procedure used was to measure the change in the chromatographic response ΔR of the oxaloacetate chromatographic peak that accompanied the reaction. Values of ΔR were measured for several solutions under near equilibrium conditions. The chromatographic response ΔR is expected to be zero for a solution that is at equilibrium with regard to the above reaction and prior to the addition of the enzyme. The results were used to calculate the standard molar Gibbs energy change Δ_rG^o_m = (4.82 ± 0.21) kJ·mol^-1, the equilibrium constant K = (0.143 ± 0.012), the standard molar enthalpy change Δ_rH^o_m = (1.9 ± 2.9) kJ±mol^-1, and the standard molar entropy change Δ_rS^o_m = -(10 ± 10) J·K^-1·mol^-1 for the following chemical reference reaction at T = 298.15 K and I_m = 0: L-aspartate^-(aq) + 2-oxoglutarate^2-(aq) = oxaloacetate^2-(aq) + L-glutamate^-(aq). Under near physiological conditions (T = 311.15 K, pH = 7.0, I_m = 0.25 mol·kg^-1) the apparent equilibrium constant K′ for the overall biochemical reaction is calculated to have the value 0.147; the standard transformed Gibbs energy change Δ_rG′^o_m = 4.96 kJ·mol^-1 under these conditions.

Full text of DOI:10.1006/jcht.1998.0404

J. Chem. Thermodynamics 1998, 30, 1373᎐1384
Article No. ct980404
An investigation of the equilibrium of the
reaction L-aspartate aq H 2-oxoglutarate
H L-glutamate
{
(
)
(
aq
)
s oxaloacetate
(
aq
)
( aq) }
a
b
Nand Kishore, Yadu B. Tewari, and Robert N. Goldberg
Biotechnology Di¨ision, National Institute of Standards and Technology,
Gaithersburg, MD 20899, U.S.A.
Apparent equilibrium constants have been measured for the following biochemical reaction:
L-aspartateŽaq. q 2-oxoglutarateŽaq. s oxaloacetateŽaq. q L-glutamateŽaq..
This reaction, catalysed by aspartate transaminase, was studied over the ranges 283.15 F
TrK F 303.15, 6.94 F pH F 7.13, and 0.163 F I rŽmol.kgy1 . F 0.167, where
T
is
m
temperature and I is ionic strength. The instability of the oxaloacetate in solution required
m
the use of an experimental procedure that was brief. Thus, the procedure used was to
measure the change in the chromatographic response ⌬ R of the oxaloacetate chromatographic
peak that accompanied the reaction. Values of ⌬ R were measured for several solutions
under near equilibrium conditions. The chromatographic response ⌬ R is expected to be zero
for a solution that is at equilibrium with regard to the above reaction and prior to the
addition of the enzyme. The results were used to calculate the standard molar Gibbs energy
T
m
y1
change ⌬ G s Ž4.82 " 0.21. kJ .mol , the equilibrium constant K s Ž0.143 " 0.012., the
r
T
y1
standard molar enthalpy change ⌬ H s Ž1.9 " 2.9. kJ .mol , and the standard molar
r
m
T
m
y1
y1
entropy change ⌬ S s yŽ10 " 10. J .K .mol
for the following chemical reference
r
reaction at T s 298.15 K and Im s 0:
L-aspartate Žaq. q 2-oxoglutarate Žaq. s oxaloacetate2y Žaq. q L-glutamate Žaq..
Under near physiological conditions ŽT s 311.15 K, pH s 7.0, Im s 0.25 mol.kgy1 . the
apparent equilibrium constant KЈ for the overall biochemical reaction is calculated to have
y
2y
y
XT
y1
.
the value 0.147; the standard transformed Gibbs energy change ⌬ G s 4.96 kJ mol
r
m
under these conditions.
᭧ 1998 Academic Press
KEYWORDS: aspartate transaminase; enthalpy; equilibrium constant; L-glutamate;
oxaloacetate; 2-oxoglutarate
1
. Introduction
Aspartate transaminase ŽEC 2.6.2.1. catalyses the reaction:
L-aspartate aq q 2-oxoglutarate aq s oxaloacetate aq
Ž
.
Ž
.
Ž
.
q L-glutamate
Ž
aq .
.
1
Ž .
This reaction Žsee figure 1 for the structures of these substances. plays an
important metabolic role in the malate᎐aspartate shuttle, gluconeogenesis, and the
a
Guest researcher from the Department of Chemistry, Indian Institute of Technology, Bombay,
India.
bŽE-mail: robert.goldberg@nist.gov..
0021᎐9614r98r111373 q 12 $30.00r0
᭧ 1998 Academic Press

1
374
N. Kishore, Y. B. Tewari, and R. N. Goldberg
FIGURE 1. Structures of the substances in reaction Ž1..
glyoxylate pathway.Ž1. There have been several studiesŽ2 ᎐ 8. in which an apparent
equilibrium constant has been reported for reaction Ž1.. However, the reported
values of the apparent equilibrium constant vary from Ž0.13 to 0.3.. Additionally,
information on the temperature dependency of this reaction is sparse and there is
no report of the enthalpy change. An experimental difficulty in the study of this
reaction is the instability of the oxaloacetate in aqueous solution. This problem
makes the accuracy of some of the earlier studies suspect. For these reasons it was
decided to undertake an investigation of the thermodynamics of this reaction.
2
. Experimental
a
Pertinent information on the substances used in this study is given in table 1. The
purities of the biochemical substances were also examined by using the
chromatographic procedures described below and found to be consistent with the
values given in table 1. The mass fractions of water in these substances Žsee column
5
in table 1. were measured with a Metrohm Model 633 automatic Karl Fischer
Ž9.
titrator, which was calibrated with a water-saturated octanol solution. These
mass fractions of water were used in all subsequent calculations that involved the
amounts of these substances.
Oxaloacetate is known to decompose in aqueous solutions to pyruvate and
Ž6.
carbon dioxide. This instability was assessed by dissolving a sample of oxalo-
y1
Ä
Na HPO Žm s 0.050 mol.kg . q H PO Žm s
acetate in phosphate buffer
2
4
3
4
y1
.
.
4
0
2
.006 mol kg , pH s 7.18 and placing it in a thermostat set at the temperature
98.15 K. The amount of pyruvate formed was measured by using the
chromatographic procedure described below. During the first hour, the mole
fraction of the oxaloacetate that underwent decomposition was f0.024.
A Hewlett-Packard 1100 h.p.l.c. equipped with a u.v. detector set at the
wavelength ␭ s 215 nm and a Hewlett-Packard C-18 column Ž4 mm i.d., 250 mm
long. thermostatted at T s 318 K were used in this study. The mobile phase was
a
Certain commercial equipment, or instruments, or materials are identified in this paper to specify
the experimental procedures adequately. Such identification is not intended to imply recommendation
or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that
the materials, or equipment identified are necessarily the best available for the purpose.

Aspartate transaminase reaction
1375

1
376
N. Kishore, Y. B. Tewari, and R. N. Goldberg
y3
formed from: ŽI.
Ä
tetrabutyl ammonium hydroxide Žc s 0.02 mol.dm . q
y3
ammonium phosphate Žc s 0.025 mol.dm
.4
adjusted to pH s 5.3 with H PO
3
4
and ŽII. acetonitrile. The following gradients of these two mobile phases were
formed: volume fraction ␾ŽI. s 0.90 and ␾ŽII. s 0.10 at time t s 0; ␾ŽI. s 0.85
and ␾ŽII. s 0.15 at t s 10 min; ␾ŽI. s 0.80 and ␾ŽII. s 0.20 at t s 20 min. The
3
y1
.
flow rate was 0.0133 cm s . Typical retention times of the substrates were:
L-aspartate, 4.6 min; L-glutamate, 4.6 min; pyridoxal 5-phosphate, 15.8 min; 2-
oxoglutarate, 16.8 min; and oxaloacetate, 18.9 min. Since the peaks attributable to
the L-aspartate and the L-glutamate overlapped it was not possible to use this
method to measure the molalities of these two substances. Also, the pyridoxal
5
-phosphate and 2-oxoglutarate peaks showed some overlap. Therefore, the
measurement of the apparent equilibrium constant for reaction Ž1. was based upon
the well-resolved oxaloacetate peak.
The method used for the equilibrium measurements is now described. First, a
solution containing all four reactants ŽL-aspartate, 2-oxoglutarate, oxaloacetate,
and L-glutamate. in phosphate buffer containing pyridoxal 5-phosphate was
prepared in a Teflon stoppered glass bottle. The oxaloacetate was the last substance
added to the reaction mixture. This was done to minimize decomposition of the
oxaloacetate in solution. The molalities of the reactants were selected so as to
result in a value of the apparent reaction quotient QЈ in the vicinity of the
estimated value of the apparent equilibrium constant KЈ for reaction Ž1.. A small
portion of this reaction mixture was immediately injected into the h.p.l.c. Aspartate
aminotransferase was then added to the remaining reaction mixture. This solution
was then allowed to equilibrate in a thermostat set at the desired temperature for
the 15 min required to obtain the chromatogram of the just-injected reaction
mixture Ži.e. without the enzyme.. Immediately after completion of this
chromatogram, the reaction mixture with enzyme was injected into the h.p.l.c. and
its chromatogram was obtained. The change in the chromatographic response ⌬ R
of the peak corresponding to oxaloacetate was the critical information obtained
from both chromatograms. Neglecting the very small mole fraction Ž x f 0.006. of
oxaloacetate that has decomposed in 15 min, ⌬ R is expected to be zero for a
solution that is already at equilibrium with regard to reaction Ž1. prior to the
addition of the enzyme. This procedure was then repeated several times so that
results were obtained for several solutions having a range of values of the reaction
quotient QЈ. All solutions were prepared gravimetrically so as to permit the
accurate calculation of the molalities of all substances in these solutions.
An attempt was made to measure calorimetrically the enthalpy change for
reaction Ž1.. The calorimetric procedures were similar to those previously
Ž10.
described.
In these experiments, the initial solution consisted of a mixture of
L-aspartate and 2-oxoglutarate, with the 2-oxoglutarate being the limiting reagent.
y1
Both substances were in phosphate buffer
Ä
Na HPO Žm s 0.098 mol.kg . q
2
4
y1
H PO Žm s 0.0073 mol.kg ., pH s 7.50
4
. Following f20 min of reaction in the
3
4
microcalorimeter, the contents of the reaction vessels were analysed using the
h.p.l.c. procedure described above. Thus, it was found that the mole fraction of
oxaloacetate converted to Žpyruvate q carbon dioxide. was f0.013. However,

Aspartate transaminase reaction
1377
y1
.
see Appendix ,
Ž .
since the enthalpy change for this reaction is fy615 kJ mol
the correction for this small amount of reaction is in fact quite large. In our
calorimetric experiments, the correction for oxaloacetate decomposition amounted
to 2.4 times the calorimetrically determined enthalpy of reaction. Consideration of
the uncertainties inherent in the measurement of this very small amount of
pyruvate led us to the conclusion that the direct calorimetric measurement of the
enthalpy of reaction Ž1. required a substantially improved analysis for the amount
of pyruvate formed and thus was not a suitable experimental approach for the
determination of the enthalpy change for reaction Ž1..
Measurement of pH was done with an Orion Model 811 pH meter and a
Radiometer combination glass micro-electrode. The pH meter was calibrated with
Radiometer standard buffers and with a standard phosphate buffer ŽpH s 7.42 at
T s 298.15 K.. This latter buffer was prepared from KH PO and Na HPO ,
2
4
2
4
standard reference materials 186-Id and 186-IId, respectively, from the National
Institute of Standards and Technology.
3
. Results and discussion
The apparent equilibrium constantŽ11. for reaction Ž1. is:
KЈ s L-glutamate
Ä
m
Ž
oxaloacetate. . L-aspartate. .
m
Ž
.
4
r
Ä
m
Ž
m
Ž
2-oxoglutarate
.
4
.
2
Ž .
The molalities m in the above equation are the total molalities of the various
charged and uncharged species that are formed from the dissociation of the various
substances in solution. The oxaloacetate exists as a mixture of the enol and keto
Ž12.
forms. The keto form is the active substrate in this enzyme-catalysed reaction
Ž13.
and is also the predominant form Žmole fraction x f 0.90. for 5 - pH - 10.
Ž14.
Since the solid oxaloacetic acid exists as the enol form
and since the Žpartial.
conversion to the keto form in solution is extremely rapid,Ž13. it will be understood
that we are considering the equilibrium mixture of the enol and keto forms of
oxaloacetate under the specified solution conditions. A reference reaction that
pertains to specific ionic forms is now introduced:
L-aspartatey
aq
q 2-oxoglutarate2y
oxaloacetate
aq
Ž
.
Ž
.
s
2
y
q L-glutamatey
Ž
aq
.
Ž
aq
.
.
3
Ž .
While the choice of reference reaction is not unique,Ž11. it will be seen that the one
selected is the predominant reaction under the experimental conditions used in
this study. The equilibrium constant for reaction Ž3. is:
2
y
L-glutamatey
m
Ž
oxaloacetate . .
L-aspartatey. .
m
Ž
.
.
K s
.
4
Ž .
2y
m
Ž
m
Ž
2-oxoglutarate

1
378
N. Kishore, Y. B. Tewari, and R. N. Goldberg

Aspartate transaminase reaction
1379
Since both reactions Ž1. and Ž3. are symmetrical, the apparent equilibrium constant
for reaction Ž1. and the equilibrium constant for reaction Ž3. are independent of
the choice of standard state.
The results of the equilibrium measurements are given in table 2. In these
measurements, the apparent reaction quotients QЈ were selected so that
QЈŽmin.. - KЈ - QЈŽmax.., where KЈ is the presumed value of the apparent
equilibrium constant, and QЈŽmin.. and QЈŽmax.. are, respectively, the minimum
and maximum values of the apparent equilibrium quotient used in the experiments.
As pointed out above, ⌬ R is expected to be zero for a solution that is already at
equilibrium with regard to reaction Ž1.. Therefore, a fit of QЈ against ⌬ R was
performed for each set of results and, from this fit, we obtain the value of QЈ
corresponding to ⌬ R s 0 which is also equal to KЈ. Thus, the following results
were obtained: KЈ s Ž0.133 " 0.008. at T s 283.15 K; KЈ s Ž0.144 " 0.015. at
T s 288.15 K; KЈ s Ž0.133 " 0.010. at T s 292.65 K; KЈ s Ž0.143 " 0.009. at T s
2
98.15 K; and KЈ s Ž0.145 " 0.016. at T s 303.15 K. Quadratic fits were used for
all sets of results with the exception of that at T s 293.15 K, where a linear fit was
found to adequately represent the results.
The above uncertainties are equal to two estimated standard deviations of the
mean, and they are a measure of the random errors in the results. However, there
are several possible sources of experimental error in our measurements. We judge
Ž15.
that reasonable estimates of the standard uncertainties
due to these possible
systematic errors in the values of KЈ are: decomposition of the oxaloacetate,
.
Ž
.01 KЈ; impurities in the various substances used in this study including the
0
moisture contents., 0.03.KЈ; and chromatography, 0.02.KЈ. These estimates of
possible systematic error are combined in quadrature together with the statistical
T
TABLE 3. The p K values and standard molar enthalpy changes ⌬ H for the aqueous proton
r
m
dissociation reactions of substances pertinent to this study at T s 298.15 K and Im s 0
T
⌬r Hm
Reaction
p K
.
y1
kJ mol
y
2y
q
L-aspartic acid s L-aspartic acid q H
3.90
10.00
4.1
38
y
q
L-aspartic acid s L-aspartic acid q H
q
q
q
L-glutamic acid s L-glutamic acid q H
2.16
4.30
9.96
3.0
3.0
40.0
y
L-glutamic acid s L-glutamic acid q H
y
2y
q
L-glutamic acid s L-glutamic acid q H
y
q
oxaloacetic acid s oxaloacetic acid q H
2.56
4.37
16
4
y
2y
q
oxaloacetic acid s oxaloacetic acid q H
y
2y
q
14 a
2
2
-oxoglutaric acid s 2-oxoglutaric acid q H
2.24
5.12
y
q
a
-oxoglutaric acid s 2-oxoglutaric acid q H
8
y
2y
q
pyridoxal 5-phosphate s pyridoxal 5-phosphate q H
3.72
6.46
8.89
16.4
y5.8
23.1
y
q
pyridoxal 5-phosphate s pyridoxal 5-phosphate q H
q
2
y
3y
pyridoxal 5-phosphate s pyridoxal 5-phosphate q H
H PO s HPO 2yq Hq
y
7.21
4.2
2
4
4
a
These values are estimated.

1
380
N. Kishore, Y. B. Tewari, and R. N. Goldberg
uncertainties in the measured value of KЈ, expressed as one estimated standaŽr15d.
deviation of the mean, to obtain a set of combined standard uncertainties.
These combined standard uncertainties are then doubled to arrive at the final
set of expanded uncertainties. Thus, our final results for the apparent
equilibrium constant for reaction Ž1. are: KЈ s Ž0.133 " 0.013. at T s 283.15 K;
KЈ s Ž0.144 " 0.019. at T s 288.15 K; KЈ s Ž0.133 " 0.015. at T s 292.65 K;
KЈ s Ž0.143 " 0.015. at T s 298.15 K; and KЈ s Ž0.145 " 0.020. at T s 303.15 K.
We now wish to relate the experimental results for reaction Ž1. to thermodynamic
quantities for the reference reaction Ž3.. This requires the p K values and standard
T
molar enthalpies ⌬ H for the proton dissociation reactions of the reactants and
r
m
T
m
of the other solutes in solution. These p K and ⌬ H values are given in table 3.
Where necessary, the values of the p K and ⌬ H were adjusted to I s 0 by
using an ‘‘ion-size’’ parameter of 1.6 kg
equation to estimate the activity coefficients of the aqueous species in solution.
The values for the p K and ⌬ H for the ionization of H PO Žaq. were taken
from Wagman et al.;
r
T
m
r
m
1
r2
y1r2
.
mol
in the extended Debye᎐H ¨u ckel
T
m
y
r
2
4
Ž16.
the remaining values in table 3 were taken from Martell et
Ž17.
T
m
al. In the absence of values for the ⌬ H for the ionizations of the 2-oxoglutaric
r
acid species, we have estimated values for these quantities by assuming that the
values of the standard molar entropy changes were the same as those of the
respective oxaloacetic acid reactions.
The equilibrium model used for the calculation of equilibrium constants and
standard molar enthalpies for the reference reactions has been described
Ž18.
previously.
This model has been modified recently so that it now utilizes the
Ž19.
computer code of Alberty and KrambeckŽ20. to solve the
Mathematica
simultaneous non-linear equations that describe the various equilibria. This
Mathematica code has been extended so as to include corrections for non-ideality
Ž18.
and so that the calculations are made self-consistent
with regard to the ionic
strength I . The non-ideality corrections are based on the extended Debye᎐H ¨u ckel
m
1
r2
y1r2
.
equation in which the ion-size parameter has been set at 1.6 kg
mol
. Thus,
by applying this model and by using both the experimental values of KЈ and the
thermodynamic quantities given in table 3, we obtain the following values of K for
the reference reaction Ž3. at I s 0: T s 283.15 K, K s Ž0.134 " 0.013.; T s
m
2
88.15 K, K s Ž0.145 " 0.019.; T s 292.65 K, K s Ž0.142 " 0.015.; T s 298.15 K,
K s Ž0.139 " 0.015.; and T s 303.15 K, K s Ž0.146 " 0.020.. The uncertainties
given here are the same expanded uncertainties obtained above. Note that the
differences between the values of KЈ and K are relatively small. A principal reason
for this is that the measurements were performed at pH values that were well
removed Ž<pH y p K < ) 2.6. from the p K values of the reactants. Additionally, the
reference reaction Ž3., which is the predominant reaction under the experimental
conditions used, is charge symmetric. Thus, in terms of the Debye᎐H ¨u ckel model
employed to treat the results, the equilibrium constant for reaction Ž3. is
independent of the ionic strength.
We now use the model of Clarke and GlewŽ21. with these values of the
equilibrium constant as a function of temperature to calculate values of the
standard molar Gibbs energy and standard molar enthalpies of reaction. In these

Aspartate transaminase reaction
1381
␮
␮

1
382
N. Kishore, Y. B. Tewari, and R. N. Goldberg
calculations, it was assumed that the standard molar heat capacity change
T
p, m
T
m
y1
T
m
s 0 for reaction Ž3.. Thus, ⌬ G s Ž4.82 " 0.21. kJ.mol
⌬r
C
and ⌬ H s
r
r
y1
Ž1.9 " 2.9. kJ.mol
for reaction Ž3. at T s 298.15 K and I s 0. These results
m
T
m
lead to K s Ž0.143 " 0.012. and to the standard molar entropy of reaction ⌬ S s
r
y1
y1
yŽ10 " 10. J .K .mol
at T s 298.15 K and I s 0. The uncertainties given
m
here are expanded uncertainties and include components for both the random
errors and possible systematic errors in the measurements Žsee above..
Previous results from the literature for the biochemical reaction Ž1. are
summarized in table 4. For each result we have used the aforementioned
T
equilibrium model with the value of ⌬ H for reaction Ž3. obtained in this study to
r
m
calculate values of KŽT s 298.15 K, I s 0. for reaction Ž3.. These values are
m
given in column 6 of table 4. It is seen that our result is in good agreement with
Ž5.
Ž8.
Ž5.
those of Krebs,
and Krebs and Stubbs.
Krebs’
results were based on
manometric measurements and were of a remarkably high precision. However,
Ž5.
neither he nor the other workers assigned uncertainties to their results. In any
Ž3.
case, it is likely that our results are also in agreement with those of Darling,
Ž6.
Ž7.
Nisonoff et al., and Henson and Cleland.
Ž22.
Miller and Smith-Magowan’s
extensive thermochemical network analysis of
the reactions in the Krebs cycle led to values of the standard molar Gibbs energies
T
m
y
2y
of formation ⌬ G of the aqueous species L-aspartate , 2-oxoglutarate
,
f
2
y
y
T
oxaloacetate , and L-glutamate . Combination of these ⌬ G values leads to
f
m
T
m
y1
.
Ž .
⌬r G s 4.68 kJ mol and K s 0.151 for reaction 3 . This result is based upon
T
m
Ž22.
the ⌬ G values in Miller and Smith-Magowan’s
table 10 for the ‘‘succinate q
f
T
acetate’’ pathway. An alternative set of ⌬ G values obtained by Miller and
f
m
Ž22.
T
m
y1
Žthe ‘‘all 3rd law’’ pathway. leads to ⌬ G s 4.48 kJ.mol and
Smith-Magowan
r
T
K s 0.164 for reaction Ž3.. The uncertainties in the ⌬ G values are large enough
f
m
T
T
to bring both calculated values of ⌬ G into agreement with our result ⌬ G s
f
m
r
m
y1
Ž4.82 " 0.21. kJ.mol and K s Ž0.143 " 0.012.. This agreement is not surprising
Ž22.
Ž5.
since Miller and Smith-Magowan
gave a high weight to the result of Krebs,
which, as noted above, is in agreement with the results obtained in this study. We
T
are unaware of any thermodynamic pathway that yields a value of ⌬ Hm for
r
reaction Ž3..
The value of KЈ for reaction Ž1. under near physiological conditionsŽ23. is also of
interest. With the equilibrium model and the values of the thermodynamic
quantities for the reference reaction, we calculate KЈ ŽT s 311.15 K, pH s 7.0,
y1
.
.
s 0.147. The standard transformed Gibbs energy change
I s 0.25 mol kg
m
⌬
XT
y1
for reaction Ž1. is 4.96 kJ.mol . This calculated value of KЈ is in good
agreement with the value KЈ s 0.151 obtained by Krebs and Stubbs under these
G
r
m
Ž8.
conditions.
Appendix
T
The aim is to obtain a value of ⌬ Hm for the reaction:
r
2
y
s pyruvatey
q HCOy3
oxaloacetate
Ž
aq
.
Ž
aq
.
Ž
aq
.
.
5
Ž .

Aspartate transaminase reaction
1383
In the absence of an experimental result for this reaction, we use a thermochemical
cycle with the following reactions:
y
q oxaloacetate2y
q NADH 2y
H PO
Ž
aq
.
Ž
aq
.
Ž
aq
q NADy
-malate2y
aq
aq
s NADH 2y q Hq
aq aq .
s HPO 42 y q Hq
.
s
2
4
2
y
q HPO 42 y
Ž
S
.
-malate
Ž
aq
.
Ž
aq
.
Ž
aq
.
,
Ž
Ž
Ž
Ž
6
7
8
9
.
.
.
.
2
y
fumarate
Ž
aq
.
.
.
s
Ž
S
.
Ž
.
,
NADy
aq
q H 2
g
aq ,
Ž
.
Ž
Ž
.
Ž
.
y
H PO
Ž
aq
Ž
.
Ž
.
2
4
NAD and NADH are, respectively, the oxidized and reduced forms of ␤-
nicotinamide adenine dinucleotide. We have the following results ŽT s 298.15 K,
T
m
y1
I s 0. from the literature: ⌬ H s y85.7 kJ.mol
for reaction Ž6. from
m
r
Ž24.
T
y1
Ž25.
.
for reaction 7 from Gajewski et al.;
Ž .
Jespersen;
⌬ H s y15.7 kJ mol
r
m
T
y1
Ž22.
.
Ž .
⌬r H s y31.9 kJ mol for reaction 8 from Miller and Smith-Magowan;
and
m
T
y1
Ž16.
.
9 from Wagman et al.
Ž .
⌬r H s 4.2 kJ mol
for reaction
Thus, for the
m
reaction:
2
y
s fumarate2y
oxaloacetate
Ž
aq
.
q H 2
Ž
g
.
Ž
aq
.
,
Ž
10
.
T
m
T
m
T
m
T
m
T
m
y1
⌬r H Ž5. s ⌬ H Ž6. y ⌬ H Ž7. q ⌬ H Ž8. y ⌬ H Ž9. s y106.1 kJ.mol . Use
r
r
r
r
T
of this result with the value of the standard molar enthalpy of formation ⌬ H of
f
m
2
y
Ž26.
T
m
y1
fumarate Žaq. given by Wilhoit
leads to ⌬ H s y672.9 kJ.mol
for
f
2
y
Ž26.
T
y
oxaloacetate Žaq.. We then use Wilhoit’s
values of ⌬ H for pyruvate Žaq.
f m
y
T
m
y1
and HCO Žaq. to calculate ⌬ H s y615.3 kJ.mol for reaction Ž5..
3
r
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2
3
4
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6
7
8
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(Recei¨ed 31 March 1998; in final form 12 June 1998)
WA98r017