A METHOD OF ALLOWING FOR THE INFLUENCE OF DIFFUSION IN MANOMETRIC MEASUREMENTS OF

CERTAIN RAPID BIOCHEMICAL REACTIONS

BY F. J. W. ROUGHTON

(From the Physiological Laboratory, University oj Cambridge, Cambridge, England)

(Received for publication, February 1, 1941)

Manometric methods are widely used for measuring the rate of oxygen uptake and carbon dioxide output by enzyme solutions and tissue suspensions, and do indeed give the true chemical rates of such processes if these are slow compared with the rate of diffusion between the gas and liquid phases. With faster pro- cesses diffusion also becomes a limiting factor and the manometric readings then vary with the speed of shaking of the vessel and the relative volumes of the gas and liquid phases (Dixon and Elliott, 1930). If these conditions are kept constant, the observed rate should, in the case of a given process, be a definite function of the diffusion and chemical reaction velocities, and it might be possible to deduce from the observed over-all rate that due to the chemical reaction alone. If HO, the manometric method could then be extended to faster biochemical processes than could previously be followed by its aid. The matter has lately been brought to a head by the need of studying the kinetics of CO2 uptake and output by buffer solutions, in the presence of carbonic anhydrase, at far higher rates than those for which the usual manometry was hitherto available. A procedure for calculating the true rates of chemical reactions in the body of the liquid ha.s been worked out, and has been shown to be valid not only for carbonic anhydrase but a.lso for 02 evolution from catalase solutions. The treatment, is based on the stationary liquid film theory of physical chemists, which, though widely used for inorgaaic processes such as CO2 uptake by NazC03 solutions, does not seem to have been used before in biochemical reactions, to which it may well have other applications besides the cases considered in this paper.

129

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130 Influence of Diffusion in Manometry

STATIONARY FILM THEORY OF GAS-LIQUID INTERCHANGE

When a gas and a liquid are stirred or shaken together, it is assumed that the main bulks of the gas and liquid phases are infinitely well stirred but that on either side of the interface there are stationary films of gas and liquid, diffusion through which governs the rate of the interchange process (see reviews by Taylor (1930), Sherwood (1937)). In the case of gases of poor and moder- ate solubility, such as O2 and COz, the gas films can be neglected and the diffusion rate is then determined solely by the area and thickness of the liquid stationary film. The thickness of the liquid films varies from 0.001 to 0.04 cm., according to the speed of stirring or shaking. It is difficult to picture the physical forces responsible for maintaining such films many thousands of molecules thick, but their tangible existence seems to be shown beyond doubt by the direct optical observations of Davis and Crandall (1930).

Simple Physical Solution of Gas-When solution of the gas occurs without any chemical reaction, the stationary film theory states that

Rate of gas uptake = $ A (ci - CL) (11

where Di = diffusion coefficient of the dissolved gas 6 = thickness of the stationary film

A = area of the stationary film c, = concentration of the dissolved gas at the outer surface of the

stationary film = a-pi (Y = solubility coefficient of the gas in the liquid

pi = pressure of the gas in atmospheres CL = average concentration of the dissolved gas in the bulk of the

liquid phase

Equation 1 also holds good for liberation of dissolved gas from liquid. It has already been verified by numerous observers but, since its validity and application are crucial for the present paper, we have made further tests by the boat-manometric method (de- scribed by Roughton and Booth (1938)). In one such experiment 4.2 cc. of water were shaken smoothly at 290 times per minute with a 59 cc. gas phase containing COz at about 5 per cent atmosphere and the COz uptake followed manometrically. The results are plotted in Fig. 1, A.

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F. J. W. Roughton 131

I f p0 = initial CO2 pressure in the gas phase (in atmospheres) p, = CO2 pressure in the gas phase when equilibrium with the liquid

is reached Cal = CO2 concentration in the liquid at equilibrium (measured in cc.

of CO2 per cc. of liquid) VO = volume of gas phase in cc. V, = volume of liquid in cc.

G = total amount of CO2 in the gas and liquid phases

then from Equation 1 it follows that the rate of COz uptake in cc. per second =

-v a!23 Va dci

a dt =---=vLdt a dt s=;A(ci -CL)

Now

Therefore

ci - CL = (Ci - Cm)

( ) 1+ Va

OrVL

From Equations 2 and 4 it follows that

-v,$ = ;A(pi - p-1

Integrating, we have

logPo-Pw D -=aA(;G+&)t Pi - PC0

(2)

(3)

(4)

(5)

(6)

Log (pi - p,) plotted against time should therefore give a straight line of slope equal to DA (oL/V~ -I- l/VL)/G. Fig 1, B shows that this is so and the value of DA/6 in the above units comes out at 0.44.

Solution of Gas Accompanied by Chemical Reaction with Non- Volatile Solute-In this case the solute also penetrates into the stationary film and reacts there with the dissolved gas as well as in the body of the liquid, so that conditions become very complex. If the chemical rate is very fast compared with diffusion and is

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132 Influence of Diffusion in Manometry

irreversible, then if various simplifying assumptions are made (see Davis and Crandall (1930)) the initial rate of gas uptake =

Dici + D.sca ii (7)

where D, = diffusion coefficient of the reacting solute cs = concentration of the reacting solute in the body of the liquid

Equation 7 has been roughly verified in a few cases in which the reaction products do not alter conditions by their effect on

FIG. 1. Rate of uptake of CO? by wal.cr. A = pressure of COZ in gas phase versus time; B = test of Equation 6.

(a) the solubility of the gas, the diffusivity of the solutes, and the apparent thickness of the films, (b) the convection due to the heat produced in the films by the reactions.

il good qualitative example of the theory underlying Equation 7 is furnished by Dixon and Elliott’s observation that at the usual rate of shaking (about 120 round trips per minute) the rate of oxygen uptake from air by concentrated yeast suspensions in the Barcroft apparatus is far less than by alkaline pyrogallol solu- tions. In the yeast suspensions D, and c, are both negligible com- pared with Di and ci, whereas in the pyrogallol solutions, in the

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F. J. W. Roughton 133

concentrations used, cS is 20 or more times greater than ci and D, is probably not less than half of Di. The DA term in Equa- tion 7 should therefore be much greater than Dici and the rate of OS uptake should be correspondingly exalted. A quantitative test of Equation 7 is not, however, possible in this case, since the rate of reaction of O2 with pyrogallol is not “instantaneous” compared with the diffusion rates.

CALCULATION OF EFFECT OF DIFFUSION IN GAS-ENZYME REACTIONS

Enzymes, being proteins, have diffusion coefficients which are only about 1 to 5 per cent of those of dissolved 02 or COS; the concentration of the enzyme is, as a rule, even lower relative to that of the dissolved gas. The Dscs term in Eauation 7 is thus negligible in comparison with Dici, and it therefore seems justifiable to disregard the chemical reactions within the stationary film, and, from the diffusion view-point, to treat the latter as equivalent to pure solvent. This simplifying assumption not only seems a priori sound, but also leads to good agreement of theory and experiment.

Uptake Processes

Hydration of CO:! in Presence of Carbonic Anhydrase-Ac- cording to the Michaelis theory the true rate of this reaction equals

Ic,uEc~

CL + Km (8)

where E = concentration of enzyme K,,,, = Michaelis’ constant of enzyme

k., = velocity constant for dissociation of the enzyme-substrate complex

The validity of Equation 8 for carbonic anhydrase has been confirmed by Roughton and Booth (unpublished). If cr. is small compared with K,,, R tends to the value k,,EcL/K, and at fixed enzyme concentration the reaction is thus practically unimolecular with respect to dissolved COZ. This is the simplest case to work out and test. The solution is as follows: when the steady state is reached, the rate of diffusion of COz through the stationary film equals its rate of combination in the body of the liquid.

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134 Influence of Diffusion in Manometry

Therefore

Di keu ECL VL TA(ci-CL)= K = eucLvL = RL

mu

where e, = k,,E/K,,. Whence

DiA D<A CI, = - ci

6 6 + euvL

>

and

DiA T+euvL

(9)

If there were no restriction due to diffusion, the concentration of COz in the bulk of the liquid would be equal to c;, and the true rate R would be given by

R = B,ciVL (12)

From Equations 10, 11, and 12 it follows that

R = D+ciRL DiA - Ci -

6 RI,

As the enzyme concentration is raised, the observed rate RL tends to a maximum value R,, the reaction in the bulk of the liquid be- coming so fast that cL tends to zero. From Equation 9 it therefore follows that

R sDLAc. m- 6 t

and from Equations 13 and 14 that

R = R&kI. m L

(14)

05)

R, can be measured by a direct experiment at high enzyme con- centration and Equation 15 then gives a simple way of calculating the t.rue rate R from the observed rate RL when the latter is limited by diffusion. From Equation 14 DiA/G = R,/c;; so that if the treatment is correct the value of DcA/G obtained in this way should agree with the value obtained from the rate of uptake of COZ in plain physical solution, as described above.

In Fig. 2 on the lower curve is shown the rate of enzymic CO2 uptake by 4.2 cc. of ~/40 phosphate buffer, pH 7.3, in the presence

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F. J. W. Roughton 135

of various amounts of carbonic anhydrase at 0”. At low enzyme concentration the points fall on a straight line through the origin, but, as the enzyme is increased, diffusion begins to affect R, which finally tends to a maximum at high concentrations = R The upper curve of Fig. 2 represents the true rates, R, as czculated from RL and R, by Equation 15. They fall, within experimental error, on the straight line passing through the origin

CARBONK ANHYDRASE CONCENTRATION

FIG. 2. Rate of CO, uptake by ~140 phosphate, pH 7.3,0”, in presence of various amounts of carbonic anhydrase. X = observed rate; 0 = rate corrected for diffusion by Equation 15.

and the low values of R,. This is to be expected from Equation 8 and is thus a confirmation of the theory.

The value of DiA/G, given by R,,, comes out a.t 0.65. This is about 50 per cent higher than the values given by Fig. 1, for which a less rapid and violent shaker was used than in the present experiment. Two experiments on the rate of CO2 uptake in solution under the same shaking conditions as were employed for the readings in Fig. 2 gave values for DiA/s of 0.64 and 0.63, which agree excellently with the value of 0.65 obtained from R,.

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136 Influence of Diffusion in Manometry

O&put Processes

The general theory has been test,ed out successfully in foul different instances.

Simple Physical DesoZutio7b-Equation 6 therefore again holds; so that log (p, -pi) plotted against time should accordingly give a straight line. This was checked for the rate of CO2 output from a solution of CO2 in dilute HC1, when the latter is shaken with air at $ atmosphere. The value of DA/6 came out at 0.44, in exact agreement with the value in Fig. 1, which should indeed be so, as the shaking conditions were identical in the two cases.

Dehydration of H2C03 to CO2 in Presence or Absence of Carbonic Anhydrase and at Various pH Values-Let HzC03 concentration in the bulk of the liquid be xL.

K = equilibrium constant of the reaction CO2 + Hz0 e H&OS = [COJJ [H&08], = about 990 at 0”

/co = output velocity constant of the reaction H&Oa + CO* + Hz0 in absence of enzyme

e. = output velocity “constant” for additional rate of dehydration when carbonic anhydrase is added

k, = uptake velocity constant of the reaction CO2 = Hz0 + H&03 in absence of enzyme

eu = uptake velocity “constant” for additional rate of hydration when carbonic anhydrase is added

Other symbols have the same significance as above. By the law of mass action

We then have

Z& = observed rate of CO2 output into gas phase = (h + eohvL - (k, + e,)c, vL= (k. + e,) (xL - dK)vL = at steady state DA(c, - ci)/6

(17)

R = true rate of CO2 output into gas phase if diffusion were not limiting = (k. + eohvL - (k, + e,)civL = ho + e,) h - G/K)VL (18)

R, = maximum rate of CO2 output into gas phase at very high enzyme concentration

= DA(xLK - es)/8 (19) for in this case the CO2 and H&O3 are always in equilibrium in the

body of the liquid and therefore CL = xLK

1 e. and 8, are both proportional to the enzyme concentration (but inde- pendent of the substrate concentrations if the latter are small compared with the Michaelis constants).

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F. J. W. Roughton 137

From Equations 17, 18, and 19 it follows that R = R,RJ (R, -RL); i.e., Equation 15 again holds good. The actual value of R,, as shown below, depends upon the pH of the bicarbonate- buffer mixture, whereas in COz uptake processes R, is independent of the pH (between 6.5 and 9.5) of the buffer mixture absorbing the COz.

Let 0 = total CO2 in solution in all forms at t = 0

= [COzlr. + KMXML + [HCWL Under maximum rate conditions

CL = [Co& = K[H&O& = aH f[HCO&/K: where uH = hydrogen ion activity of solution

f= activity coeflicient of bicarbonate ion K: = apparent first ionization constant of carbonic acid

Therefore

b b CL = , =--

1+K :

fan

since K = about 900.

b At zero time R, = y CL = DA --

6 I+ K:/fu~ (20)

The applicability of Equations 15 and 20 has been tested b? measurements of the rate of CO% output from mixtures of bicarbon- ate with cacodylate and acetate buffers at 0”. The HCOs con- centration was held constant at 0.0025 M but the pH was varied from 6.3 to 4.7. The results and corrections are given in Table 1.

By the law of mass action the true rate of the reaction at t = 0 is

R ko(1 + ZA’)aIrfb - = ko(l + ZA’)[HzCOJr. = - a,f + K1 --- VL

where A’ = concentration of buffer anion, i.e. cacodylate or acetate I = catalytic coefficient of buffer anion (see Roughton and Booth

(1938) ) K1 = true first ionization constant of carbonic acid, assumed 2.3 X

10mm4 at 0” (Roughton, unpublished data) k. = is assumed to be 2.0 (Roughton, unpublished data) at. 0”

The last two columns of Table I show that the value of R/V, as calculated from Equation 21 agrees to within 1 per cent on the

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138 Influence of Diffusion in Manometry

average with the value of R/V, calculated from the observed results with the aid of Equations 15 and 20. The maximum divergence is no more than 10 per cent. The validity of the method for output processes is thus strongly confirmed. In the case of t,he carbonic anhydrase experiments it is more accurate to obtain R, from the rate of CO2 output with a high concentration of enzyme added to the bicarbonate-buffer mixture thall by Equation 20, as was done in Table I.

Lag Period in Evolution of CO2 from Bicarbonate-Bugler Mixtures ----When bicarbonate and buffer are mixed and shaken together in a manometric vessel, there is, as has long been known, a lag in

TABLE I

Comparison of Observed Rates (Corrected for Diffusion) and Theoretical Rates of CO;? Output .from Bicarbonate-Bu.ffer Mixtures of Various pH Values

aH x 108

0.57 0.87 1.0 2.3 0.98 0.90 1.88 2.7 1.95 0.91 3.32 3.05 4.8 0.78 6.36 3.28 9.6 0.80 11.3 3.39

12.0 0.81 13.2 3.42 19.1 0.83 17.5 3.46

-

RL - x lo" VL

- R, E x 104

-

I-

R,RL X 106

VL(R,-RL)

1(1+lA)aHfbX lo6 -

qffK1

1.04 1.13 2.04 2.07 3.74 3.78 7.9 8.15

17.0 16.13 21.5 20.6 35.6 33.3

I for cacodyl&e = 9.0; I for acetate = 0.6.

the rate of CO2 out,put during the first 15 to 20 seconds compared with that found later (see Fig. 3). Controls show that the lag is not due to slowness of mixing, which should take only 1 second, nor to temperature changes, evolution or absorption of gases other than COZ on mixing, or inertia of the manometric gage fluid. On the stationary film theory, however, the lag is explicable, for COZ cannot diffuse across this film at the full rate until enough COZ has been formed in the body of the liquid by the progress of the H&O3 -+ COZ + HZ0 reaction. The actual quantitative effect can indeed be worked out as follows.

If the liquid is well buffered and the pH is >6.3, the half time of the reaction is 200 seconds or more, so that the HCOI’ and H+ concentrations are sensibly constant, during the first 20 seconds,

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F. J. W. Roughton 139

and the rate of the back reaction during this period can be neg- lected.

The total COz formed in time t, if 0 <t <20 seconds, is then equal to

V&&(1 + ZA’)[H&Od = V&t(l + ZA’)a,f[HCO,‘l/K, = +Vd

where 4 is a constant which can easily be calculated in any given experiment.

0 5 IO 15 20 25 SECONDS

FIG. 3. Effect of diffusion on early stages of CO2 output from bicarbonate- cacodylate-enzyme mixture. Curve A, theoretical curve if diffusion is “infinitely” rapid; Curve B, curve obtained by allowing for diffusion in accordance with Equations 25 and 26. 0 and X = observed rate of CO2 output in two experiments.

From Equation 3 the total CO2 formed in time t = VGP~ + VLcL. From Equation 2, Vo(dp/dt) = DA(cL -pia)/6.

From these last three equations it follows that

dPi -iii- - wo

_ EA gt - y pi (iE+k)

(22)

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140 Influence of Diffusion in iManometry

Therefore

pi = $ + ; @B1 - 1) d

where

DA Y=,,-dJ,

G

If the diffusion were “infinitely” fast, the pressure of COZ, p’i, which would be developed in time t would be given by Vcp’i + Vr,ap’i = q~V,t. Whence

+VLt

p’i = vo + CYVI,

From Equations 23, 24, and 25 it follows that

T = 1 + 1 (e-61 - 1) Pi Pi Bt

pi/p’; should therefore be independent of pH, bicarbonate, and enzyme concentration.

With processes which are not too fast, 4 can be accurately calculated from the manometric readings after 20 seconds, for by then the lag is over: Equation 25 then gives p’i and Equation 26 the corresponding value of pi. Fig. 3 shows the results of two experiments upon the early stages of COZ output from a mixture containing 0.005 M NaHC03, 0.006 M cacodylic acid, and 0.006

* A more elaborate set of equations is necessary if the HC03’ and the H+ concentrations do change appreciably during the first 20 seconds, or if the velocity of the back reaction is significant. These equations lead, however, to a final differential equat,ion for pi which does not seem to be exactly soluble, though an approximate solution can be obtained in the form of a fairly rapidly convergent power series

pi = r(P/2) + X8P $- Ad4 + (27) where X8, X4, etc., are constants. The just,ification for assuming such a form is that Equation 23 when expanded gives the convergent power series pi = y(t2/2) - y@t3/3’) + r(p2t4/4’), and when t + 0 the values of pi given by Equations 23 and 27 should tend to the same limits, but for t > 0 the value of pi given by Equation 27 should, from the physicochemical condi- tions of the problem, always he less than the value of p; given by Equa- tion 23.

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F. J. W. Roughton 141

M Na cacodylate, pH about 6.2, temperature O’, with a small amount of added carbonic anhydrase. Under these conditions @ = 0.17, and the lower smooth curve in Fig. 3 is that calculated from Equation 26 by substituting this value of p. The experi- mental points are seen to fall within experimental error upon the

FIG. 4. Rate of 02 output from 0.0048 M HBOa in &r/40 phosphate, pH 7.3, O”, in presence of various amounts of catalase. X = observed rates; 0 = rates corrected for diffusion by Equation 15.

theoretical curve. Equally good agreement was also found for COz output from bicarbonate-phosphate buffer mixtures (pH 6.8) both at 0” and at 15’.

In the output processes covered by Equations 16 to 26 the CO2 concentration is generally so much larger t,han the HzCOz concentration that penetration of the latter into the stationary film has been neglected.

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142 Influence of Diffusion in Manometry

Decomposition of Hz02 by CataZase-From the kinetics of the HzOs-catalase reaction, it can also be shown that the correction formula (Equation 15) should again be applicable. The points on the lower curve in Fig. 4 give the observed rate of O2 output RL (by the boat-manometric method) from a solution of 0.0048 M HzOz in ~/40 phosphat,e buffer, pH 7.3, at O”, in the presence of various amounts of purified horse liver catalase (kindly supplied by Professor Keilin and Dr. Mann). The value of R, was de- termined by a special experiment with excess catalase concentra- t,ion, a further 4-fold increase in the latter producing no change in the rate of O2 output, thus proving that the maximum rate had been attained. The points on the upper curve in Fig. 4 give the values of R as calculated from R, and R, by Equation 15. They fall to within 8 per cent upon the straight line passing through the low values of R, as the theory requires.

The numerical value of R, was found to agree quite closely with that for CO2 at the same concentration, as should indeed be the case, since the diffusion coefficients of O2 and COz in water agree to within 20 per cent.

It was hoped to include an example of an enzymic 02 uptake process as well as the 02 output process just described. Some pre- liminary experiments were done with catechol oxidase (samples kindly supplied by Professor Keilin and Dr. Mann) but even at the highest available concentrations of the enzyme the speeds of O2 uptake were not fast enough for the diffusion corrections to be necessary or applicable. In the time at our disposal we were unable to try any other cases.

DISCUSSION

In the instances given above, the chemical reactions have been unimolecular with respect to the dissolved gas. With reactions of different order the correction equations need modification. Con- sider, for example, the general case of COZ uptake by buffer solu- tions in the presence of carbonic anhydrase when the substrate concentration is not assumed necessarily to be small in comparison with the Michaelis constant K,,. Equation 9 should then read

Di yAki - CL) ~,,EcLVL

=- = R,, CL + Km,

(28)

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F. J. W. Roughton 143

and from Equations 8, 14, and 28 it then follows that

Rm -RI. R=-R,~- m

-R- ci + Km

Rm - RL ci + Knru

RmRr, =- Rm - RI.

I- 2. ci + Km,

x!z Rm >

(29)

In the particular case of ci being smadl compared with K,, Equation 25 reduces to R = R,RJ(R, - RI,); i.e., Equation 15. Equation 29 must, however, be used when ci is of the same order as Km,,.2 When c< is large compared with K,,,, the reaction becomes of zero order with respect to Cb, and Equation 29 re- duces to R = Ii,,; i.~., no correction for diffusion is required. It is thus clear that before the diffusion correction can be worked out, t.he chemical kinetics of t,he particular reaction must be known. This knowledge! however, can often be obtained by working in a restricted range, in which the diffusion corrections are inappreci- able; e.g., at very low enzyme concentrations.

Perhaps the most striking result of the present paper is the identity of the initial rate of COZ uptake by plain water with that by phosphate buffer containing a high concentration of carbonic anhydrase. This is a strong confirmation, both of the general theory in this paper and of the whole theory of the stationary film, for such a result would be extremely hard to underst,and on any other theory. The difficulty of picturing the nature of the physical forces responsible for the maintenance of the films makes such additional evidence certainly welcome.

According to Conant and Shearp (quoted by Davis and Cran- da11 (1930)) the rate of absorption of 02 and I-I, by a saturated solution of oleic acid in water is the same as by water itself in spite of the absorption of the oleic acid at the gas-liquid interface and the increased t,endency to foam formation, which would perhaps be expected to alter DA/& In the instances reported in this paper

* Similarly for CO, output from bicarbonate-buffer mixtures it can be shown that if the substrate concentration, Q, is not small compared with the Michaelis constant, Km,, then at t = 0,

(301

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144 Influence of Diffusion in Manometry

the total prot.ein concentration has always been very low, but if the concentration is raised enough to affect not only the surface tension but also the viscosity of the solution considerable de- pressions are observed. Thus the rate of solution of gases when shaken with strong hemoglobin solutions or whole blood is found to be only about one-fifth of the rate in pure water. Further work on these lines would be of interest; e.g., on the effect of adding other proteins to strong carbonic anhydrase solutions in regard to the observed values of R,.

SUMMARY

The chemical kinetics of gas-liquid reactions can only be re- corded manometrically (i.e. by observations of the change of pressure of the gas phase with time) if the rates so observed are independent of the speed of shaking of the manometric vessel and of the relative volumes of the liquid and gas phases. Otherwise the observed rates depend on the speed of diffusion of dissolved gas between the two phases as well as on the true speeds of the chemical processes.

The effect of diffusion can, however, be allowed for by assuming the existence, at the boundary between the two phases, of a stationary film of liquid, diffusion through which determines the rate of exchange of gas between gas and liquid, the main bulks of which are both assumed to be infinitely well stirred. If the solute molecule with which the gas reacts is of low concentration and diffusivity compared with the dissolved gas, the solute will pene- trate into the stationary film so much more slowly than the gas that chemical reaction in the film itself can be neglected. With this simplifying condition it is possible to work out correction equations from which the true rates of chemical reactions can in certain cases be obtained, even when the observed manometric rates are only one-third of the true chemical rates. The range of the manometric method is thus greatly extended.

The equations have been checked by observations on (a) the rate of CO2 uptake by, and CO2 output from, simple physical solution, (b) the rate of CO2 uptake by buffer solutions in the presence of various amounts of added carbonic anhydrase, (c) the rate of output of CO2 from bicarbonate-buffer mixtures of various pH values with and without added carbonic anhydrase,

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F. J. W. Roughton 145

(d) the rat,e of 02 output from HzOz-cat&se mixtures. Good agreement between t,heory and experiments is found in each case, and in addition good cross-checks are obtained.

The success so far reached suggests that similar methods may have further biochemical scope and interest.,

The experiments in this paper were carried out by Dr. V. H. Hoot.h either alone or with myself. I wish to thank him warmly for this and other help.

BIBLIOGRAPHY

Davis, H. S., and Crandall, G. S., J. Am. Chem. Sot., 62,3757, 3769 (1930). Dixon, M., and Elliott, K. A. C., Biochem. J., 24,820 (1930). Roughton, I?. J. W., and Booth, V. H., Biochem. J., 32,2049 (1938). Sherwood, T. K., Absorption and extraction, New York (1937). Taylor, H. S., A treatise on physical chemistry, New York, 2 (1930).

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F. J. W. RoughtonREACTIONS

CERTAIN RAPID BIOCHEMICAL MANOMETRIC MEASUREMENTS OF

INFLUENCE OF DIFFUSION IN A METHOD OF ALLOWING FOR THE

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