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1/9

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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5/9

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).

Published

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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.

1 Pinsent and Roughton,

Trans. Faraday SOC., 951, 47, 263.

2 Faurholt,J. Chim. Ph ys., 1925,

21,

400.

3 Saal,

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4 Brinkman, Margaria and Roughton,

Phil. Trans. A , 1933, 232, 65.

5 Roughton, Pruc. Ro y. SOC .A , 1930,

126,

439, 470.

6

Bateman and Roughton,

Biochem. J. 1935,24,2622, 2630.

7 Roughton, J.

Am er. Chem . Suc., 1941, 63, 2930.

8 Pearson, Pinsent and Roughton, Faraday SOC.Discussions, 1954, 17, 141.

9Downing,

J. Sc i. Znstr., 1948, 25, 230.

10

Hill,

J .

Sci.

Znstr., 1948,

25,

225.

11

Davies, J.

Chem. SO C.,1938, 448, 2093.

12

Sirs, Ph.D. Thesis

(Cambridge University,

1956).

1 3 Moelwyn-Hughes,Pruc. Roy . Sue. A , 1949,

196,

540.

14 Moelwyn-Hughes,

Proc, Roy. SOC.A , 1938, 164,295.

15

Moelwyn-Hughes,

Proc. Roy. SOC .A , 1953, 220, 386.

16 Manov, Schuelte and Kirk,

J.

Res. Nut. Bur. Stand., 1952, 48, 84.

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