Advances
in Molecular
Relaxation
Processes
Elsevier Publishing Company, Amsterdam.
RELAXATION
TECHNIQUES
235
Printed in the Netherlands
IN FAST
REACTION
KINETICS
H. STREHLOW
Max-Planck-Institut
(West Germany)
fiir biophysikalische
Chemie
(Karl-Friedrich-Bonhoeffer-Institut),
CGttingen
CONTENTS
I. Introduction
................................
II. Chemical relaxation .............................
A. Temperature-, pressure- and field-jump techniques ..............
1. Temperature-jump technique ......................
2. Pressure-jump technique
........................
3. Field-jump technique ..........................
III. Stationary methods .............................
IV. The evaluation of relaxation times. ......................
V. Mean life times as obtained from NMR line broadening and chemical relaxation times
A.NMR ..................................
1. Advantages ..............................
2. Disadvantages .............................
B. Chemical relaxation
...........................
1. Advantages ..............................
2. Disadvantages .............................
VI. A practical comparison of NMR line broadening and a relaxation technique applied to
the same chemical reaction ..........................
References ...................................
235
236
236
238
239
239
240
240
241
243
243
246
246
246
246
246
248
I. INTRODUCTION
In the early nineteen-fifties,
two different kinds of relaxation techniques were
developed which both proved to be very useful in the investigation
of rapid chemical
reactions. One of these techniques
is nuclear magnetic
relaxation
in systems
with rapidly exchanging
magnetic nuclei. It was first introduced
by Gutowsky
et al.’ and has since been used in many laboratories.
The other relaxation
method has been called chemical relaxation.
It was mainly developed by Eigen
et al.’ and also has found widespread application.
Chemical relaxation will mainly
be covered in this review. The advantages and drawbacks of both techniques will
be compared and a specific example will shortly be given of a chemical reaction
which has been investigated
by NMR line broadening3
and by the pressure-jump
relaxation
method4.
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249
236
H. STREHLOW
II. CHEMICAL
RELAXATION
Chemical
equilibrium
temperature,
pressure
changed, momentarily
constants
depend
on external
parameters
such as
or electric field strength. If such parameters
are rapidly
the system will not be in equilibrium.
Therefore, a chemical
reaction occurs which re-establishes equilibrium conditions. As long as the relative
change in the equilibrium
constant is small - and in practice this is always the
case - the re-adjustment
of the concentrations
to their new equilibrium
values
occurs at a rate which is proportional
to the deviation of the momentary
concentration from its equilibrium
value. By measuring the change of concentration
as a
function of time, the rate constants
of the chemical reaction may be obtained.
Aside from these transient methods, the stationary state of a reacting system under
the influence of a periodically
changing external parameter is also changed by
chemical relaxation and may be used for the investigation
of fast chemical reactions (ultrasonic
absorption,
dielectric
relaxation).
A. Temperature-, pressure- andfield-jump techniques
The most simple situation prevails if the external parameter is changed as
quickly as possible from one constant value to another. Ideally, the parameter,
e.g. the pressure
system
%c
kz
A+B
will be subjected
Fig. 1. Principle
The equilibrium
din
on the reacting
(1)
to a step function
of pressure-jump
constant
in time (Fig. l(a)).
relaxation.
is changed
according
K __g,-_AE
dp
Advan. Mol. Relaxation
cpp RT
Processes,
2 (1972) 235-249
to
RELAXATION
TECHNIQUES
(where K is the equilibrium
IN
FAST
constant,
REACTION
AV the volume
KINETICS
of reaction,
237
a the coefficient
of thermal expansion, c,, the specific heat, p the density, and AH the enthalpy of
the reaction) and the concentrations
will approach their new equilibrium
values
(Fig. l(b)). We shall now evaluate the rate law for this approach assuming a reaction of type (1).
If cA, c, and cc are the instantaneous
concentrations
of A, B and C, re-spectively, which change with time to their equilibrium
values c,, , cB, and cc after
the pressure jump, we have the equation
The deviations
designated
of the actual
concentrations
from their equilibrium
Aci E ci-c
(4)
With the mass balance
Ac,+Ac,
equation
= 0
and the stoichiometric
(9
equation
AC, = AC, = AC
we obtain
values will be
as
(6)
from eqn. (3)
dAc
- kl(G+QAc+k2A
c+k,(Ac)2+k,
CACB-k2C,
dt
(7)
k, (AC)” is small compared with the other terms, as long as the shifts in concentration are much smaller than the concentrations.
This term may, therefore, be
neglected. The last two terms vanish, since the 5 refer to equilibrium
conditions.
Therefore, we are left with a linear differential equation, the solution of which is
AC = Ac(t = 0) exp (-t/z)
(8)
1
- = k,(c,+c,)+k,
r
(9
with
r is the relaxation time for the reaction, which may be determined experimentally
by measuring the change of the concentrations
as a function of time.
If the outlined principle is to be realized for the measurement
of fast chemical
reactions, three problems have to be solved.
(I) How to effect a very sudden jump in temperature,
pressure or electric
field.
(2) How to measure the fast-changing,
very small concentration
differences.
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249
238
H. STREHLOW
(3) How is the measured
relaxation
time connected
with the rate constants
and concentrations
of the reactants? (Equation (9) is only a special case referring
to system (l).)
The first two experimental problems will be discussed with the description of
different chemical relaxation apparatus. The theoretical question of the dependence
of r on the reaction mechanism,
the concentrations,
and the equilibrium
values
involved will then follow.
I. Temperature-jump technique
Fast temperature jumps have been realized by two different techniques, the
first of which has been used very extensively in the investigation
of chemical relaxations. A high-voltage
condenser is discharged through a solution containing
the
chemical system to be investigated.
The switching of the circuit is performed by a
spark gap. The temperature jump thus obtained is given by
AT=g [I-exp(-&)I
(10)
with C the capacity of the capacitor, U the voltage, R the resistance, cP the specific
heat, p the density, and V the volume of the solution. Typical values are U = 50
kV, C = 0.1 yF, p = 1 g cmP3, V = 5 cm3, cP = 4.19 joule/grad,
R = 40 R.
Under these conditions
temperature
jumps of 5 “C can be achieved in about
RCj2 = 2 psec. With temperature jumps as high as this, relatively large shifts of
the equilibrium
constants
AInK=-
AH AT
RT2
result and optical detection methods with their inherent advantages may be used.
Absorption
spectrometry
is the technique most often used for the detection
of the concentration
changes with time. If the reacting species involved in the
chemical reaction to be measured do not change the absorption of light sufficiently,
it is possible to couple another chemical reaction to the system which does absorb
light and is fast enough not to be rate-determining.
pH indicators are often used as
coupled systems, since in many reactions proton transfer occurs.
Besides light absorption,
optical rotation
and fluorescence
spectrometry
have been used, though less frequently, for the detection of concentration
changes
in temperature-jump
relaxation equipment.
Another way to perform fast temperature jumps is the absorption
of light
either from a fast flash light6 or from a giant pulse laser7. Values of AT of roughly
1 “C in 2 psec have thus been obtained. A similar technique is the absorption
of
intense microwave pulses (AT - 0.7 “C in 2 psec)*.
Aduan. MO!. Relaxation
Processes,
2 (1972) 235-249
RELAXATION
TECHNIQUES
With these techniques,
IN
FAST
electrical
REACTION
conductance
KINETICS
239
has been used as a monitor
of the concentration
changes after the temperature jump. However, detection by
optical absorption
has also been used in combination
with the microwave pulse
technique’.
2. Pressure-jump
technique
Different kinds of pressure-jump
apparatus have been described in the literature. In the most often used version, pressure (of the order of 100 atm) is applied
to the system to be investigated
in an autoclave”.
The autoclave is closed by a
metal membrane
which bursts spontaneously
at this pressure. In about 50 psec
the pressure falls to 1 atm. Thus, relaxation times 2 100 psec can be measured.
The concentration
changes are followed by conductivity
measurements.
A relative
change of resistance of 10e5 is about the limit of detectability.
However, a general
drawback of conductivity
measurements
in relaxation techniques is the appreciable
loss in sensitivity if the solution contains non-relaxing
electrolytes e.g. buffers.
Another version of the pressure-jump
apparatus”
follows the course of
the reaction by measuring
the temperature
with a rapidly indicating
thermistor
(NTC resistor), thus taking advantage of the heat of reaction. The range of relaxation times which can thus be measured is about 10-2-100 sec.
A third type of pressure-jump
apparatus works with an increasing pressure
step12. As in gas shock wave technique, a shock wave may be produced in liquids
resulting in a very sudden pressure jump (N 1 psec) at the end of the shock tube.
This jump is much sharper than in the normal pressure-jump
apparatus.
The time available for measurement
is 21/v, where 1 is the length of the tube
and v the velocity of sound. 21/v is of the order of 14 msec. This version of the
pressure-jump
technique is, therefore, a useful tool for measuring reactions which
are too fast for the more conventional
pressure-jump
apparatus. The concentration
changes are either followed by conductivity
or - with a pressure jump of the order
lo3 atm - with absorption
spectrophotometry13.
3. Field-jump
technique
If, during a reaction, the electric moment changes, e.g. in the dissociation of
a weak electrolyte, the equilibrium constant is shifted by the application ofan electric
field jump, E, according to
d In K
dE
AEVE
(11)
=E
where AE is the change of the dielectric constant due to the chemical reaction.
Rather high electrical fields, of the order of 104-lo5 V cm-‘, are necessary to cause
a detectable shift in equilibrium.
Therefore, only solutions with a low conductivity
may thus be investigated,
because otherwise, in highly conducting
media, the
Adoan. Mol. Relaxation
Processes,
2 (1972) 235-249
H. STREHLOW
240
electric field collapses
from a large condenser
discharge of a coaxial
thus be studied, either
concentration
III.
too soon. The electric
with a switch-on and
high voltage cable into
with conductivity
or
field is applied in pulse form either
a switch-off spark gap14, or from the
the celli’. Rather fast reactions can
with absorption
spectrometry
as the
monitor.
STATIONARY
METHODS
Instead of a stepwise perturbation
of the chemical equilibrium,
as discussed
in Section II, a periodical perturbation
may also be applied as in an ultrasonic wave
or in an alternating
electric field. If the reaction is very fast compared with the
frequency (l/z >> w) the system will respond in phase and no energy absorption
will occur. The energy
next half-wave of the
phase shift of 90” but
reaction cannot follow
absorbed in a half-wave by the system is dissipated in the
oscillation.
With very slow reaction (l/r << 0) there is a
again no energy absorption,
since the response of the slow
the excitation and its amplitude therefore vanishes. With
l/r = w a maximum of energy is absorbed with a phase shift of 45”. Therefore,
chemical relaxation adds to the absorption
of energy in ultrasonic16
and electric
high-frequency
fields l4 the maximum effect occurring at a frequency o = l/z. In
the case of the chemical contribution
to dielectric relaxation, eqn. (11) shows that
AlnKA(,!?‘). Therefore, the equilibrium
is shifted only sufficiently if the high
frequency field is superimposed
with a high, constant electric field. With periodica
perturbation
techniques, relaxation times as short as lo- lo set may be determined
IV.
THE EVALUATION
OF RELAXATION
TIMES
As demonstrated
above (eqn. (9)) an expression for the relaxation rate may
be derived for a given reaction. In more complicated
types of reaction systems,
more than one relaxation time will be observed. Without derivation, some expressions for relaxation times for some practically important reactions are given below.
Type of reaction
Relaxation time
A$B
kz
1
- = k,+k,
T
(12)
1
- = k,(c,+c,)+k,
r
(13)
A+B
SC
kz
ktz
A+B
kz1
Advan.
kz3
~
+AB+C
Mol. Relaxation
1
=$[~k&(~k)‘-4rrk]
Tl,Z
ksz
Processes,
2 (1972) 235-249
(14)
RELAXATION
TECHNIQUES
IN
FAST
REACTION
KINETICS
241
where
c k = k,,(G+c,)+k,,+k23+k32
and
nk = kl2(CA+~)(k23+k32)+k21
km
A+B+ABSC
k32
1
-=
r
k,,
kzs
_ G+G)
l+K(EJ4:+c,)
+k
(15)
32
(+ indicates that the equilibrium
A + B 4 AB is very fast compared with AB+C;
eqn. (15) is obtained from eqn. (14) with k,,, k,, >> k,,, k32; K E cAB/cAcB.
The following characteristics
of these equations are noteworthy.
The relaxation times depend on both the forward and backward rate constants in an additive
manner. In general, they are functions of the concentrations
which are different
for different types of reaction. Therefore, proposed mechanisms
may be tested by
the determination
of the concentration
dependence
of r. However, it should be
mentioned that only if the rate can be measured over a rather large range of concentration are the conclusions unambiguous,
A considerable
degree of experimental precision is required for that purpose. In many cases, modern equipment really
affords this precision provided that a careful evaluation
of z is performed18.
In
eqns. (12)-(15)
for the sake of simplicity, the influence of the activity coefficients
has been neglected. With higher concentrations
this is, of course, not permissible.
In principle, equilibrium
constants may also be evaluated from the concentration
dependence
of r. In most cases, however, more precise results are obtained
by
combining
relaxation measurements
with conventionally
determined
equilibrium
constants.
Another way of obtaining equilibrium
constants should be mentioned.
The
amplitude of the relaxation effect, i.e. Ac(t = 0) in eqn. (8), provides information
on equilibrium constants which are sometimes not easily obtained with other techniques. Though this method cannot be considered to be very precise, it may supply
important semi-quantitative
data on equilibrium constants in complicated chemical
systemsi9.
V.
MEAN LIFE TIMES AS OBTAINED
FROM NMR LINE BROADENING
AND CHEMICAL
RELAX-
ATION TIMES
For the sake of simplicity, we shall only compare the data for the most
simple reaction of type shown in eqn. (12) assuming that each of the species A and
B contains at least one nucleus with magnetic moment, e.g. a proton. Therefore,
we shall rewrite
AHSBH
kz
(12a)
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249
242
H. STREHLOW
This most simple case is sufficient to demonstrate
the differences in the two techniques. If the proton experiences a chemical shift v,--v, in the state AH with respect
to the state BH, chemical exchange manifests itself in increasing the line widths in
the NMR spectrum. If the mean life times of the proton in the states AH and BH,
rA and zn respectively, are very long compared with (v~-v~)-’ and with T,, two
lines of line widths ~/XT, are observed (assuming a magnet of ideal homogeneity).
The only kinetic information
provided in this case is an upper limit for the rate
of exchange. For T, > zA, zB > (v~-v~)-~, two broadened
lines are observed
with the additional line widths
(16)
It is this “slow case” with two broadened,
especially useful kinetic information.
not yet overlapping,
lines which supplies
If r-l E (zi 1 +z, ‘) is of the order vA-vB, a single broad line with a line
width of the order vA-vB is observed. With decreasing r, this line sharpens again
and an exchange broadening
of the coalesced single line is given by
Av+ exchange
=
4n(vA
-
vB)2it
&A+
zB)
(17)
where p, is the proton fraction in state AH andp, that in state BH. With extremely
fast reactions, the exchange broadening
vanishes (rA, zB + 0 in eqn. (17)). In this
latter case, only a lower limit for the exchange rate is supplied provided that the
chemical shift is known or can be estimated.
The proton fractions and the life times are connected by
PA~B
=
(18)
PB~A
The rate constants
dCm_
and the average life times are given by
k
dt
1
c
CAH
AH=TA
:
-_=
’
k1
(19
k2
(20)
TA
and
_
d%H_
-
k
c
2BH=-
dt
CBH
TB
: -_=
’
TB
are thus obtained
In the “slow case”, eqn. (16) the single rate constants
directly. In the case of chemical relaxation, only the sum of the two rate constants
is determined
1
- = k,+k,
r
= k,(l+K)
Only with additional information
about the equilibrium
the single rate constants be obtained. Correspondingly
Adoan. Mol. Relaxation
Processes,
2 (1972) 2?5-249
constant, K = kJk2, can
for the measurement
of
RELAXATION
activation
TECHNIQUES
parameters
IN
FAST
REACTION
not only the temperature
243
KINETICS
dependence
of z must be evaluated
in chemical relaxation but also that of K, i.e. the enthalpy of the reaction must be
known from equilibrium
measurements.
In the “slow case”, NMR measurements
of the area under the line of AH and
BH, respectively,
supplies the proton fractions pA and pB . Their ratio, pA/pB, is
independently
obtained from the ratio of the life times, r&n, so that the consistency of the measurement
may be contrclled.
From measurements
of zA and zs
as a function of temperature,
we obtain most directly the rate constants k, and
kz and the concentrations
pA andp,
at different temperatures
as well as the two
energies of activation and the enthalpy of the reaction. The latter can be obtained
independently
either from the temperature
dependence of the areas under the two
absorption
lines or from the difference between the two activation energies.
is more direct and more
Thus, in the “slow case”, the NMR information
abundant
than that obtained from chemical relaxation.
supplies less inHowever, in the “fast case”, eqn. (17) NMR line broadening
formation than chemical relaxation. Equation (17) contains the sum of z, and ze
and, furthermore,
the mole fractions pA and pB and the chemical shift (vA-vB)
which cannot be taken from a high resolution spectrum with coalesced absorption
lines. Therefore, as with chemical relaxation, additional information
on the equilibrium constant must be available and an estimation of the chemical shift has to be
made. The latter difficulty is overcome with a suitable application
of the spin-echo
technique”.
We are now in a position
two compared techniques.
A.
to list the advantages
and the drawbacks
of the
NMR
1. Advantages
In the “slow case”, very direct and precise information
is obtained on the
single rate constants,
on equilibria
and on activation
parameters.
In the “fast
case” with the application of the spin-echo technique the directness of information
is comparable
to that of chemical relaxation.
NMR technique
is the only method
which allows the measurement
of fast exchange reaction with no change in the
composition
of the system, e.g. of the reaction
NH;
+ NH3 5 NH, + NH;
k
or the kinetic measurement
of hindered molecular rotation. Of course, chemical
relaxation cannot be applied to such cases, since the equilibrium
constant is unity
under all conditions.
Another advantage of NMR is the need for only a fraction of a cm3 of solution,
the concentration
of which, however, should be as high as possible.
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249
244
TABLE
SURVEY
1
OF CHEMICAL
Technique
Temperature-jump
Pressure-jump
Field-jump
Stationary,
ultrasonic
Stationary,
dielectric
Advan.
RELAXATION
AT, Ap, AE
produced by
TFSHNIQUES
Detection
of Ac by
Time range
Zower limit
Upper limit
(see)
(set)
Volume of
solution
needed (cm3)
Discharge of
capacitor
Optical absorption
(rotation, fluorescence)
5 x 10-6
0.2
3-10
Flash light
Conductivity
2x10-5
2x10-2
0.3
Laser
Conductivity
2x10-6
2 x10-2
0.01
Microwave
Conductivity,
optical absorption
2x10-6
2 x 10-Z
0.1
Autoclave
with rupture
disc
Conductivity,
thermometry,
optical absorption
1o-4
lo-2
10-b
10
100
1
Shock wave
in liquids
Conductivity,
optical absorption
2 x 10-e
2 x 10-G
2x10-3
4x10-3
Capacitor
switch-on
switch-off
Conductivity
10-7
10-a
Cable
discharge
Optical absorption
5 x 10-a
5 x 10-S
Ultrasonic
wave
Dissipation of
acoustical energy
lo-‘0
10-S
Phase angle in
conductivity bridge
10-7
10-a
0.1
Dielectric loss
5 x10-9
10-e
1
High electric
field with
superimposed
high-frequency
field
Mol. Relaxation
Processes,
2 (1972) 235-249
0.3
50
5
0.1
5
10
2
2%1000
RELAXATION
TECHNIQUES
IN
FAST
REACTION
ReJ
Disadvantages
Type of reactions
Advantages
Biochemical
reactions,
complex formation,
proton transfer
Very widely
Ionic reactions
Fast, simple,
volumes
Ionic reactions
Very fast, extremely
small volumes
Not simple
Ionic reactions
Conductivity
and optical
absorption
possible,
gentle disturbance
of
equilibrium
Expensive
Ionic reactions,
biochemical reactions
Simple, small volume,
sensitive
Not very fast
Rather slow
Not very fast
Ionic reaction,
transfer
Fast,
Fast,
Time per experiment
Rates are measured
proton
245
KINETICS
concentration
5
of flash photolysis
6
High electrolyte
necessary
applicable
Possibility
small
small volume,
small volume
7
in application
equipment
8, 9
10
11
high
at high pressures
12
13
Dissociation
electrolytes,
transfer
of weak
proton
High dilution
very fast
possible,
High dilution
Sophisticated
necessary.
equipment
14
Dissociation
electrolytes,
transfer
of ueak
proton
High dilution possible,
very fast. Measurements
in non-aqueous
media
High dilution
Sophisticated
necessary.
equipment
15
Ionic reactions,
association
of uncharged molecules,
biochemical
reactions
Very fast
Not sensitive large volumes.
A series of apparatus
for a time
range 1O-9-1O-5
set
16
Ionic
Fast,
Cumbersome
21
reactions
Biochemical
reactions,
hydrogen
bonding
reactions
small volume
to use.
Experimentally
Very fast
Advan.
Mol. Relaxation
difficult
Processes,
17
2 (1972) 235-249
246
H. STREHLOW
2. Disadvantages
Only compounds with magnetic nuclei must be used. The sensitivity of NMR
is much inferior to that of chemical relaxation techniques. However, with modern
equipment this drawback of NMR will become much less serious. In the most
informative “slow case”, only a small range of average life times from about 1 set
to at most (depending on the chemical shift), 5 x lo- 3 set is accessible. In many
cases the time range is considerably smaller. The equipment is rather expensive
and the whole technique is more sophisticated than with chemical relaxation. This
is particularly true if spin coupling is involved or in cases where the chemical shifts
are small, or if the “intermediate case” (zAN (vA-va)- ‘) is investigated.
Another disadvantage is that the concentration ratio, pAlpa, should not
differ too much from unity. Similar arguments, however, apply also to chemical
relaxation.
B. Chemical relaxation
1. Advantages
These techniques are applicable over a larger time range (although only with
an arsenal of different relaxation apparatus; see Table 1). With many techniques,
solutions with small concentration may also be investigated. The apparatus is less
complicated and expensive than NMR equipment. For most reactions at least one
relaxation technique may be found which is especially suited for the problem
and supplies precise data.
2. Disadvantages
As with NMR, irreversible reactions cannot be investigated. Most equipment
is not available commercially. The exponential decay curves may often be disturbed
by heat exchange processes or other artefacts. Therefore, it is difficult to get a
relaxation time with a precision better than about f 5 %.
A definite advantage of both NMR line broadening and chemical relaxation
techniques is the simplicity of the mathematical treatment. All kinetic differential
equations are linearized. Therefore, advantage should be taken of chemical relaxation techniques also in the case of slow reactions, where conventional techniques
are applicable.The increased simplicity in evaluation of the rate laws oftenwill compensate for the change in experimental technique.
VI.
A PRACTICAL
NIQUE APPLIED
COMPARISON
OF NMR LINE BROADENING
TO THE SAME CHEMICAL
AND A RELAXATION
TECH-
REACTION
The kinetics of hydration of pyruvic acid were investigated by the pressureAduan. Mol. Relaxation
Processes,
2 (1972) 235-249
RELAXATION
TECHNIQUES
IN
FAST
REACTION
247
KINETICS
jump technique 4. It was concluded that the reaction proceeds as
kz3
CH,COCOO - + H,O + + CH,COCOOH+ H,O + CH,C(OH)$ZOOH
(21)
By using eqn. (15) the rate constants could be evaluated from the measured
relaxation times. The reaction was found to be acid-catalyzed
kz3 = k&+k&cn
(22)
k 32
(23)
and
=
k;2+k;2cH
The two k” were much higher than the corresponding values for the hydration of
acetaldehyde, This fact was explained by assuming an inner-molecular acid
catalysis.
In aqueous solutions of pyruvic acid, the methyl groups in the hydrated and
the unhydrated form of the acid show two lines in the proton NMR spectrum. From
the intensity of the lines the equilibrium constant and from the line widths the
kinetics may be evaluated. With small concentrations of H30f ions the reaction
is rather slow and the absorption lines are broadened to only a small extent. Preliminary measurements of the equilibrium and the rate constants for reaction (21)
with NMR led to rate constants about 3 times as large as the corresponding values
obtained by the pressure-jump technique. These NMR investigations22 have been
performed with high concentrations of pyruvic acid (344) and with the addition
of a high concentration of HCl in order to obtain (easily measurable) large and
broad signals. In order to explain this discrepancy, further NMR measurements
were performed with varied concentrations of pyruvic acid (0.14-10 M) and of
HCl (0.1-5 M) at different temperatures3. The results of these investigations may
thus be summarized: from the measurement of the equilibrium constant KH = kz3/
k,, at different concentrations, it became clear that the reaction (21) had to be
rewritten as
CH,COCOO-
+ H30+ + 2H20 + CH,COCOOH+
3H,O +
CH,C(OH),COOH
.2H,O
(21a)
A trihydrate is formed, the structure of which was proposed to be as shown in
Fig. 2.
“1
“P
..”
‘0
\
_-b
F-0
H ‘“....O/~-o\H
"'H 'C-H
H'
Fig. 2. Proposed structure of pyruvic acid trihydrate3.
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249
H. STREHLOW
248
The above-mentioned difference in the rate constants was due to activity coefficients very different from unity in the concentrated solutions. Both NMR and chemical relaxation measurements lead to consistent results when a small correction is
applied for the fact that a trihydrate was formed. The measurements of Kn at low
concentrations with uv absorption photometry, which were used in the evaluation
of the pressure-jump experiments, did not show the existence of a trihydrate. An
interesting effect was observed in the line width measurements. With only small
concentration of HCl, it was found that the concentration ratio, as obtained from
the area under the absorption line and from the ratio of the line widths, did not
agree. The reason is that the line width of the hydrate is not only due to the kinetic
broadening according to eqn. (19) but is also enlarged by hindered rotation of the
methyl group. The two water molecules forming a hydrogen-bonded ring between
the carboxylic proton to one of the geminal OH oxygen atoms make the molecule
rigid with the consequence that hindered rotation of the methyl group occurs.
Thus, from a pure kinetic argument, the proposed structure of the trihydrate has
been strengthened. Besides, the relatively large negative entropy of hydration suggests more than one molecule of water in the hydrate.
In Table 2, the data as obtained by the two techniques are collected. The
table clearly shows the usefulness of applying different techniques to the same
system. Whereas the measurements at low concentrations of H+ ions are very
imprecise with NMR and rather reliable with chemical relaxation, the activation
parameters and the thermodynamic data are better evaluated by NMR techniques.
TABLE
2
THERMODYNAMIC
AND KINETIC DATA
Hydration
Dehydration
FORTHE
HYDRATION
k”
(set- ‘)
kH
(M-‘see-
0.55kO.05
(0.5&0.4)
6.310.7
5.0*1.5
9.0*0.6
10.0&0.5
9.4
0.22&0.02
2.5*0.3
2.010.8
17.3*0.5
16.7
(l*l)
&I
‘) (kcallmole)
REACTIONOF
AH:
kcaljmole
PYRUVICACID
ASf:
callgrdmole
AH
kcal/mole
AS
callgrd mole
Method
-7.1
-23
NMR
+7.1
+23
NMR
-._____
Relaxation
-24
Relaxation
+1
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2 (1972) 235-249
RELAXATION
TECHNIQUES
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KINETICS
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14
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22
Advan.
Mol. Relaxation
Processes,
2 (1972) 235-249