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1512
C O M B I N A T I O N O F C 0 2
W I T H
O H -
THE KINETICS OF COMBINATION OF CARBON DIOXIDE
WITH HYDROXIDE
IONS
BY
B. R.
W . PINSENT,
.
PEARSONND F.
J.
W . ROUGHTON
Dept. of Colloid Science, University of Cambridge
Received 24th April, 1956
The velocity constant
k ,
of the reaction C02
+ OH-
HC03- has been determined
by the rapid thermal method over the range
0
to 40" C, by mixing together CO; solutions
with NaOH solutions
of
concentrations,
0.005
to
0.05
M.
The effect of large variations
of
ionic strength has also been studied. The present thermal results are considerably
more extensive than any hitherto available, but check satisfactorily with the more limited
data obtained by Faurholt's carbamino method and by the manometric method.
The velocity constant
is
related to temperature by the equation log k = 13.635-
(2895/T) . The energy of activation
is
13,250 cal.
Previous manometric figures for the velocity constant
k ,
of the reaction
CO2 +
H20
-+
H2CO3 have been corrected with the aid of the present values of k . The corrections were
very slight at 0" C but quite appreciable at 25-38' C.
In an earlier paper two of
us
(Pinsent and Roughton) reported values of
k,,
the velocity constant of the reaction C02
+
H20
--f
H2CO3, over the temperature
range 0-40 . The values of k, were calculated from manometric determinations
of the rate of C02 uptake when gas mixtures containing suitable percentages
of C02 were shaken rapidly with phosphate or veronal buffers, pH
7-5-8.0.
In this pH range only slight corrections are necessary at low temperatures
for the velocity of the concurrent reaction
C02
+ OH- -+ HC03-
:
above
20" C the corrections assume greater importance (see later). Pinsent and
Roughton 1 also measured manometrically the rate of C02 uptake by bicarbonate+
carbonate mixtures, pH
10-0-10.2,
in which range the velocity of the reaction
C02+ OH--+HC03- predominates over that of the reaction
C02+
H20+H2C03-.
From such data they were able to obtain values of
k ,
as defined by the equation,
over the temperature range 0-10 . Higher temperatures were not feasible
for the manometric study of the C02
t OH-
- HCO3- reaction, since the
overall rate then becomes so much controlled by diffusion, that it is impossible
to apply sufficiently accurate corrections for the effects of the latter.
A few determinations of
k
over the range 0-20" C have also been made by
the carbamino quenching method (Faurholt 2), by electrical conductivity measure-
ments (Saal3) and by photo-colorimetry (Brinkman, Margaria and Roughton 4).
Generally speaking, however, the previous data on
k
are either too restricted
-
d[C02]/dt = k"[CO2][OH-] (1)
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B . R . w. P I N S E N T ,
L . P E A R S O N
A N D F . J . w . R O U G H T O N
1513
in number and temperature range,
or
insufficiently precise and there was clearly
scope for an extended series of accurate determinations of k over the range
0-40"C . Th e rapid thermal method
of
measuring th e velocity of rapid reactions
in solution (Roughton,s Bateman and Roughton,6 Roughton 7) seemed par-
ticularly suitable for this purpose, for in the interpretation of data obtained
thereby there
is
much less uncertainty
as
to the effects of ionic strength than is
the case in data obtained by rapid electrical conductivity
or
photo-colorimetric
methods. Furthermore the rapid thermal measurement of
k
provided a n ex-
cellent opportunity for extended tests of recently developed techniques (Pearson,
Pinsent and Roughton 8). In the present paper we have accordingly carried out
measurements, by t he thermal method, of k over a wide range of pH, salt con-
centration an d temperature. Tn the appendix, concordant values of k over the
range
20-30
C ar e derived fr om new manometric da ta o n th e rate of C02 uptake by
veronal buffers, p H 8.6-8.8 . Th e results of the present pape r are of physico-
chemical, biological a nd indust rial interest : these varied aspects will each be
considered later in th e discussion.
E X P E R I M E N T A L
The apparatus and general experimental technique have been described previously.
Details can be found elsewhere and only
a
brief resume will be given here.
The method consists essentially of driving the reacting solution through tubes into a
mixing chamber, from which the mixed solution flows along an observation tube of
length
10
cm and internal diameter 2 mm. The temperature of the flowing solution is
measured with a thermocouple at a number of known distances from the mixing chamber.
From the temperature rise the extent of the reaction can be calculated.
The bottles containing the solution, the mixing chamber and observation tube were
placed in a thermostat constant to 0.0015" C at
20
C and to 0.0025" C at 0"
C
and
40'
C.
The solutions were driven through the chamber by nitrogen at a pressure of 25cm Hg.
Taps or clips were fitted so that either of the two solutions could be driven alone through
the mixing chamber or both together.
The thermocouple used in the observation tube was made from 30 gauge
B.S.I .
copper
and constantan wires with a single junction at the tip. This was calibrated with known
temperature differences, measured with a Beckmann thermometer. The thermocouple
was connected to
a
galvanometer with
a
period of 11 msec, constructed by Downing.9
The galvanometer deflection was further amplified by means of an optical lever and a
twin photocell in the way developed by Hill.10 The output of the amplifier was recorded
on a voltmeter.
A temperature
difference of 0.1"
C
gave a deflection of
75
to 80 divisions on the meter which was easily
readable to
3
division (approximately
0.0007"
C).
Each reading took at most 4 sec.
The system was calibrated with known voltages from a control unit.
MATERIALS.-&rbon dioxide.-cO2 from a cylinder was bubbled into distilled water
in the storage bottle until the desired concentration of dissolved C02 was obtained. The
concentration of carbon dioxide was determined in a Van Slyke manometric apparatus.
Socliirrn hydroxide.-A saturated solution of
A.R.
sodium hydroxide was stored in an
air-tight plastic bottle. Small quantities of this stock solution were centrifuged and the
required quantity of the clear solution removed in a pipette and added to recently
boiled-out distilled water in a C02-free atmosphere.
Sodiw?i chloride: etc.-When experiments were carried out using solutions of high
salt content the salts were added in equal strength to both the carbon dioxide and the
hydroxide solutions, to avoid effects due to heat of dilution of the salts.
Salts of
A.R .
grade were used and the solutions made up as described above, using a salt solution in
boiled-out water in place of distilled water.
PROCEDURE.-The bottles n'ere filled with the solutions and the calorimeter placed
in the thermostat.
I t
was allowed to come into temperature equilibrium with occasional
stirring of the solutions. This took
1
h at
20 C
and about 2 h at
0"
C and
40" C.
The
thermocouple was then placed in the observation tube and after
a
few minutes the re-
cording system was calibrated with known currents from the galvanometer control unit.
Samples were withdrawn from the bottles for analysis.
The thermocouple and amplifier system gave an output of 9V/deg.
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1514
COMBINATION
O F
c 2
WITH OH-
The gas pressure was then applied and the thermocouple moved to the required
position. Readings of the meter were taken with (i) solution A running alone, (ii) both
solutions running, and (iii) solution B alone. The thermocouple was moved to the next
required position and the procedure repeated. Readings could be made at about 12
positions in the observation tube. At 20" C the readings for solution A and B running
alone remained nearly constant and were checked at only three or four positions. At
other temperatures more checks were made.
To
determine the rate of flow the two bottles were marked with volume calibrations
and the volume of fluid flowing from the bottles in a certain time measured.
This also
gave the relative delivery of the two bottles. The rate of flow was measured with the
thermocouple in several positions in the observation tube, as the rate varies slightly with
the position of the thermocouple (cp. table 1 , Roughton 5). Knowing the diameter of
the observation tube, the time after mixing can be calculated at any distance from the
mixing chamber.
The temperature rise corresponding to each meter reading was calculated from the
temperature calibration of the thermocouple. Then at any point in the tube, if
temperature rise with solution A running alone
temperature rise with solution B running alone
=
TAY
= TB,
temperature rise with both solutions running together
=
T M ,
relative delivery of A to B : 1: ,
then the temperature rise due to the reaction
= TM- (TA xT~)/( l+ x).
If
A H
for the reaction is known the total temperature rise for the completed reaction can
be calculated and from this the extent of reaction at any time after mixing. If A H is
not known the total temperature rise for the completed reaction can be measured in the
apparatus with a suitable extension to the observation tube.
SCOPE AND ACCURACY OF METHOD
With the apparatus in its present form temperature readings were reproducible to
0 4 0 1
C. The least total temperature rise practicable in order to obtain a reasonably
accurate figure
for
the velocity constant is thus about 0.025"C. The shortest elapsed
time at which reliable readings could be obtained was about 0.5 msec.
The thermal method has hitherto been tested and used with observation tubes of in-
ternal diameter 5 mm : it was therefore necessary to test the reliability of the present
apparatus, with its 2
mm
observation tube, by means of control experiments similar to
those reported by Roughton.*
(i) Blank experiments with distilled water in both bottles gave no measurable
temperature change, i.e.,
TM
- (TA
+
xTB)/ (~ X ) > 0*0007 .
This shows that heat effects due to fluid friction and thermoelastic effects are
negligible.
(ii) The temperature rise when 0.0239 N HCl was mixed with 0.06 N NaOH was
determined in the apparatus and found to be 0165C. The expected tem-
perature rise calculated from the heat of neutralization is 01635"C, howing that
heat losses from the observation tube are negligible.
iii) Effects due to a stagnant film of liquid on the surface of the thermocouple
would be expected to be greater the slower the rate
of
flow of liquid. Experi-
ments were carried out with the same concentration of reactants but varying
the rate of flow. Even with a two-fold variation in the linear rate of flow the
same temperature ( 0 4 0 1 C)
was
recorded for any particular elapsed time at
any rate of flow.
RESULTS
C02+ OH- -+ HCO3- + OH- +
CO32-
+ H20.
The reaction followed was
1)
At concentrations of OH- greater than 0.1 N all the bicarbonate ion formed can be con-
sidered to be transformed instantaneously to carbonate. At the lowest concentration
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B . R .
w.
PIN SEN T, L . PEARSON
AND F . J . w. ROUGHTON 1515
of
OH-
used
(0.0018
N) the error in assuming that all the bicarbonate is transformed to
carbonate is less than as long as only the first
50
of the reaction is used for purposes
of calculation.
The heat change measured is the sum of the heat of the two reactions, and from this
the value of [CO32-], i.e. y , can be calculated. The velocity constant of the reaction
can then be calculated from the integrated form
of
eqn. (l), i.e.,
where a = [COz] at zero time, b = [NaOH] at zero time and kz is the value of k at
ionic strength I . Log [ ( b
-
2y)/(a - y)] was plotted against t and the best straight line
drawn and the slope measured (fig. 1).
An extensive set of results was
obtained for
kz
at
20
with [OH-]
rangingfrom 0.055 to 0.012 M, [COz]
from 0.013 to 04019 M , and the ionic
strength from
0.055
to 0.012. As
would be expected for a reaction, in
which a univalent anion reacts with
a neutral molecule, kI is relatively
insensitive to ionic strength. Values
of
k
at zero ionic strength were ob-
tained from kz by means of the
data displayed in fig.
2.
The largest
correction was only about 3 . The
variations in k over the whole range
of concentrations investigated were
within the experimental error of the
method thus confirming the validity
of the kinetic eqn. (2).
Table 1 gives values of k over
the range
0 -40
C, the values at
temperatures other than
20 C
being
the mean of 7 to 10 individual ex-
periments in each case. These values
were corrected for ionic strength,
assuming that the shape of the line
log
kz /Z
was the same over the entire
temperature range. The corrections
1-3-
1.2
-
1 1
-
n
x
1.0
._
I
Q 0.9-
W
-
0 . 8
T i m e (msec)
FIG. 1 -Typical plot for determination of bi-
molecular velocity constant
kz .
are only about
2
and
so
the errors involved in making this assumption were
negligible.
The effect of ionic strengths up to 5.0 was investigated by the addition of NaCl in
equal concentration to the C02 and NaOH solutions at
20C.
Fig.
2
gives a plot of
TABLE
VALUES OF
THE VELOCITY
CONSTANT
k (M-1 sec-1) FROM 0 -40
C
temp. no. of
k
standard
C
observations mean) deviation
0 7 1095 53
10
8
2550 87
20
27 5900
315
30 10 12400 835
40 9 24000 3680
log
kI
against ionic strength.
line given by the equation
Although the slope of the line is uncertain the errors in using it
for
extrapolation at ionic
strengths below
0.06
must be negligible.
Table 2 shows the effect of addition
of KCI,
Na~C0 3, aN03 and Na2S04 up to ionic
strengths of about
3.0.
With sodium carbonate it was impossible to add the salt to the
The resulting curve converges very roughly to a straight
log
kz = 3.77 + 0-26I .
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1516
C O M B I N A T I O N O F
c 2 WI TH O H -
C02 solution and separate blank runs were carried out at each strength of Na2C03 to
determine the heat of dilution. A correction was made for the small bicarbonate content
of the sodium carbonate. The effects of KCl and Na2C03 are about the same as those
of NaCl at the same ionic strength : the effects of NaN03 and Na2S04, however, appear
to be somewhat smaller, due possibly to incomplete ionization of these salts in concentrated
solution (cp. Davies
11).
FIG.
2.-Relation between velocity constant kz and ionic strength.
TABLE .-vELOCITY CONSTANTS IN CONCENTRATED SALT SOLUTIONS
AT
20
c
tKCI1
1.0
2.0
3.0
3-0
2.0
[ N ~ ~ C O J I
0.0247
M
0.122
M
0.241 M
0.457 M
[NaNOJ
2-35
3-60
[Na2S041
0.5 M
1.0 M
[KOHI
0.0208
0.0134
0 0196
0.02
15
[NaOH]
0.0244
0.0246
0.0244
0.0233
0.0288
0.0203
0.0207
0.0269
0.0203
[COZI
0.005I2
0.004 12
0.00434
0.00457
0.00568
0.00465
0.0053
3
0.00635
0.00745
0.00438
0.00452
0.00519
0.00374
Z
1
*02
2.0 1
3.02
3.02
2.02
0.099
0.360
0.746
1.394
2.37
3.62
I
-53
3.02
kz (M-1
sec-1)
9800
13700
17900
18200
13700
6280
6800
7800
10500
11100
12400
8700
10800
Tables
3
and
4
give the measured heat
of
reaction of CO2 and
OH-
in the various salt
solutions. AH,b,. at high salt concentration will differ from the classical value of A H
in dilute solution, because the specificgravity and specific heat of the solution are
no
longer
unity. The heat of reaction in a number of these solutions was measured by allowing the
reaction to proceed to completion.
It was found that the experimental results (AH,bs. )
agreed well with the values of
A H
calculated from the equation,
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B .
R .
w . P I N S E N T ,
L . P E A R S O N
A N D F. J .
w . R OU GHTON
1517
where = specific gravity of solution and s
=
specific heat
of
solution. The values
of A H
are probably correct to
5
.
TABLE
.-HEAT OF REACTION IN DILUTE
SOLUTIONS (cal)
t C
AHobs. AHCdC.
20 - 20700 - 0580
30
-
21200
-
20990
40
- 22000 - 21270
TABLE. -HEAT
OF
REACTIONS IN CONCENTRATED
SOLUTIONS AT 20
C
(cal)
[NaCI]
AHobs. AHcalc.
0 -
20700
-
20700
0.86
-
1150
-
21250
2.00 - 1700
-
1800
3.00
-
22100
-
2000
5-00
- 2800 - 2100
[KCII
2-00 - 22500 - 2700
3.00 - 24000 - 3500
4.00
-
25000 - 4300
DISCUSSION
C O M P A R I S O N W I T H
PREVIOUS
D A T A
The determination of
k
at
0"
and 18 C was first made accurately by Faurholt 2
More recently Pinsent
ith the aid of his dimethylamine quenching method.
10 2 0
3 0
4 0 C
I I
I
PT
FIG. 3.-Temperature dependence of velocity constant k .
thermal results
x = carbamino results
+ =
manometric results.
and Roughton 1 have estimated k at 0" and 10" C by means of their manometric
method, which-in the appendix-is extended by Meda to the temperature range
20-30 C . Fig. 3 gives a plot of log k against
1/T
for our thermal results from
0"
to
40
C
(open circles), together with the results
of
Faurholt adjusted to zero
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1518
C O M B I N A T I O N O F
c 2
W I T H OH-
ionic strength (oblique crosses) and the manometric results (vertical crosses).
All the data conform satisfactorily to the equation,
(5 )
og
k =
13.635 - 2895/T) ,
or
k = A exp (-
E J R T ) ,
where
A
=
4 2
x
1013 and EA
=
13,250 cal. The maximum divergence of any
point from this line corresponds to an error of only 11 , which-considering
the precision of the various methods, their great variety and the wide range of
OH- concentration studied
(-
10,OOO-fold)-is satisfactory.
Less extensive measurements of
k
have also been reported by the electrical
conductivity method (Saal3) and by the optical method (Brinkman, Margaria
and Roughton4). Sirs,12 however, has recently brought to light a source of
systematic error in results by these two methods: when this is controlled the
estimations agree reasonably with eqn.
3,
as will be shown in a paper to be
published by him later.
RECALCULATION OF THE VELOCITY CONSTANT k,
OF
THE REACTION
C 0 2 + H20
H2CO3
Values of the velocity constant of the above reaction over the temperature
range 0-38" C were reported by Pinsent and Roughton.1 These results were ob-
Temperature OC
YT
FIG. 4.-Temperature
dependence
of velocity
constantk,.
tained
in
phosphate buffer solu-
tions at about pH 8.0,and were
corrected for the contribution of
the C02
+
OH- reaction, using
values of k obtained by extra-
polation of results from earlier
determinations of k". These
values of k were lower than the
present figures and this resulted
in the calculated values of
k,
being too high, particularly at
higher temperatures. Corrections
have now been made using the
present accurate values of k ,
and the corrected values for
k,
are given in table 5 .
Fig. 4 gives a plot of log
k,
against
1/T.
The curvature is
marked and the divergence from
the simple Arrhenius relationship
is greater than can be accounted
for by experimental errors. The apparent energy of activation varies from 19,000
cal at
0
C to
10,750
cal at 38" C ; the average value of dEA/dTover this range
is - 217. This is similar to the effects found in the reaction of methyl halides
TABLE.-vELOCITY CONSTANT OF THE c 2 -k H20 -+
H2co3
REACTION
temp. ( C) 0
15
25 38
ku (=-1)
040205
0.0112
0-0257
0 . 0 6 2 0
with water (Moelwyn-Hughes) 149 15 and other reactions such as the hydrolysis
of cane sugar. The falling-off of the apparent EA with temperature is found to
be most marked in reactions involving solute and solvent.
The temperature dependence can
be
expressed in the form
loglo
k,
=
329.850
-
110.541 log
T
-
17265*4/T)
(8)
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B. R . W . P I N S E N T , L . P E A R S O N AND F . J . R O U G H T O N 1519
giving a true
EA
of 79,000 cal. This relationship
has
been used by Moelwyn-
Hughes14 to express the temperature dependence of the velocity constants of
the reaction
where
X-
is a halide ion. These gave values for true
EA
of
about
47,000
cal.
Values of k, calculated from this relation agreed within 2 with the experimental
values at every temperature.
CH3X
+
H20
CH30H
+
H++ X-,
BIOLOGICAL APPLICATION
In many biological fluids and cells the pH lies within the range
7.0 to 8.0
and the velocity of the reaction
C02
+
OH- -+
HCO3-
is therefore only about
3 to 30 of the velocity of the reaction C02
+
H20 --f H2CO3 at body tem-
perature, in absence of the enzyme, carbonic anhydrase. In the alkaline digestive
secretions, e.g. the pancreatic juice, the
pH
lies between
8-5
and
9.0
and in such
solutions the rate of the C02
+
OH-
--f
HCO3- reaction is 100 to 300 of the
uncatalyzed
C02
+
H20 H2CO3
reaction and is thus of definite physiological
significance.
INDUSTRIAL APPLICATION
The rate of this reaction is a limiting factor in various industrial processes,
especially in the final stages of C02 absorption in the ammonia-soda process
for the manufacture of sodium bicarbonate. The conditions obtaining in such
processes are often outside-indeed well outside-the range covered in the
present paper, but the data herein nevertheless permit extrapolations to be made
with much greater accuracy than was hitherto possible in these cases. It should
be mentioned that the estimations at very high salt concentrations, recorded in
table
2,
were specially designed for industrial application.
APPENDIX
MANOMETRIC DETERMINATIONS
OF
k
AT 20" C TO 30" C
BY E. MEDA
The overall rate of reaction of CO2 in buffer solutions is given by the equation
- d[C02]/dt =
V,
= k,(l + Im])[CO2]+ k"[CO2][OH-],
(A.
1)
where v, is the overall velocity of disappearance of C02, [B] is the concentration of the
more electronegative constituent
of
the buffer and is the catalytic coefficient of the latter.
Between pH
8
and pH
10
both terms on the right-hand side of eqn. A. 1) are important.
Pinsent and Roughton 1 have already determined k, manometrically over the range
0
to 40 C and have thence estimated k from manometric experiments with bicarbonate+
carbonate buffers at pH
10
from 0" to 10"
C.
Higher temperatures were not feasible
since in this pH range the term [C02][OH-] then becomes so large that the overall rate
of C02 uptake becomes too much controlled by diffusion for corrections for the latter
to be satisfactorily made. By substituting veronal buffers at pH 8.6 to 8.7, however, it
has been possible to extend the temperature range to 20"-30" C, since at this pH the overall
reaction is about 10 times slower than at pH
10.
The technique adopted was the same as that used by Pinsent and Roughton.1
Sodium
veronate + HCI buffers with a salt/acid ratio of
5
to 1 and total veronate concentration
ranging from 0 009 to
0.075 M
were employed. Values of the overall velocity v , were
calculated for each veronate concentration and plotted against the latter.
The points
fell satisfactorily on straight lines, which when extrapolated to zero buffer concentrationgive
ku
+
k [OH-1. Subtraction of ku (see table 5) then
gives
k
[OH-] and thence k , f
[OH-] is known. The hydroxide ion concentration (at zero buffer concentration) was
calculated from the hydrogen ion concentration, which was in turn calculated from the
salt/acid ratio and the pK
of
veronal, as given by the accurate data of Manov, Schuelte
and Kirk
16
over the range 0" to
60"
C. Table
A1
summarizes the results obtained at
20 , 25 and 30" C.
These agree satisfactorily with those obtained in the main part of
the paper by the thermal method
see
fig.
3).
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1520 H Y D R A Z I N E
F L A M E S
TABLE
M M NOMETRIC VALUES OF
k , 20"-30" C
k, in sec-1,
k
in M-1
sec-1
temp. O C P H k, f k [OH-] k, [OH-] k
20 8.75 0-0390 0 0
1
76 3.9 x 10-6 5,500
25 8.68 0.0668
0.0257 4.81
x
10-6 8,500
30 8.61 0.1050 0.0360 5.96
X
10-6 11,600
Acknowledgement is made to two of the Divisions of Messrs. Imperial Chemical
Industries for grants in support of this work.
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