W p OF THE HENDERSON-HASSELBALCH EQUATIONFOR HYDRION CONCENTRATION OF SERUM.*

By GLENN E. CULLEN, H. R. KEELER, AND HOWARD W. ROBINSON.

(From the John Herr Musser Department of Research Medicine, Universityof Pennsylvania, Philadelphia.)

(Received for publication, August 1, 1925.)

This paper presents the pK' values for human sera from a seriesof abnormal conditions. pK' values were determined at both38° and 20°. In addition are given values for several normal dogsera.

The Henderson-Hasselbalch equation for expressing the relationshipbetween C02 tension, [BHC03], and pH, has been of first importance instudying the acid-base equilibrium of the blood. Its greatest value hasbeen in calculating the pH value when both pCO2 and [BHCOs] are known,but with the present colorimetric methods of determining pH in bloodplasma or serum, it is of equal importance in calculating the C02 tensionactually existing in the blood.

The value of pK, first determined by Hasselbalch (1916-17), has been re-determined by a number of workers, especially by Parsons (1917), Donneganand Parsons (1919), Warburg (1922), and by Cullen (1917). All writers areagreed that when Hasselbalch put Henderson's equation in logarithmicform, his use of carbonic acid in terms of normality instead of molality wascontrary to the usual convention. The pK' values used here are calculatedfrom the equation

[BHCO,]pH = pK' + log [

where brackets indicate molar concentration or volumes per cent of C02.The symbol pK' is used here as in previous reports to differentiate thisvalue from the pK, of Hasselbalch. There are discrepancies between thevalues reported by different workers.

Parsons Pointed out that the pH determined electrometrically in bloodwasinreality the pH of serum. Warburg emphasized the fact that the pKIof Basselbalch was a composite constant for the heterogenous system(serum and cells) that included factors for cell volume, 02 saturation, etc.

Aided by a grant from the Edward N. Gibbs Memorial Fund of theew ~York Academy of Medicine.

301

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

302 pK' of Serum

Warburg also discussed the influence of the presence of hemoglobinattendant oxygen error on the accuracy of the electrometric pi detertion.

Most of the values for pK' have been made on ox, horse, or on hblood. Although theoretically the changes in protein and salt con,tion between these bloods and abnormal human blood should not bcient to change the constant, any change would be so important inpalogical physiology and in clinical studies that direct determinationsdesirable.

For these reasons, it was considered desirable to redetermine, wiyprecision of technique now available, the pK' in human sera fromraaof pathological conditions. Serum, not whole blood, was used, beeaukpointed out above, it is a simpler system since it can be studied withgrmaccuracy than blood in regard not only to pH but also to saturationwithQand finally because its pH is what is meant by the pH of the blood. F&serum was used rather than plasma because it was desired to avoiddilbance of the electrolyte distribution between cells and serum by theoij

The relations between serum values and whole blood values forpKHbe calculated most accurately by use of the relations established byburg (1922), by Peters, Bulger, and Eisenman, and by Van Slyke, W,McLean, which are based upon the principle that the differences[BHCO3] of serum and of blood is a function of cell volume.

Warburg' worked out a factor log p' CO 2 relating the pK' of serumblood. Peters, Bulger, and Eisenman (1924) determined this faA pK', on a large series of human bloods and plasma by the mostmethod, namely that of determining the total [CO21 of the blood anddplasma after saturation at known CO2 tension. Van Slyke, Wu,andLean (1923) determined the same value (pK' - pKIs') for the bloodolhorse.

Both Peters, Bulger, and Eisenman's, and Van Slyke's valuesamclose agreement and are higher than Warburg's.

Standardization of pH Values.

One of the most puzzling questions in regard to the hydrconcentration of blood or serum is that of the standard of referfor the determination. The arguments for and against the ardization of hydrion concentration to the newer activityhave been summarized by Clark (1920) who decides that beesof the present uncertainty of the values for the activity coeliaand because most of the biological work has been standardto the conductivity values, it is better to continue to use values. He proposes then a series of values for the N/10

l Warburg (1922), p. 219.

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson

ectrode which is to be used as the provisional standard. More[:etly Srensen with Linderstr0m-Lang (1924) has supportedClark in this dictum, so that we may accept as final the decisionrefer all biological hydrion values to the conductivity basis and

to continue to call these values pH values to distinguish them fromlog of activity values of G. N. Lewis and Bjerrum, which Sorensenand Lindertrm-Lang designate as paH.

In attempting to establish the relationship between the pH atoom temperature and that at body temperature, we had pre-

viously adopted (Cullen 1922, a) the use of N/10 HCl as the mostreproducible system. We preferred a direct standardization witha reproducible solution to the indirect standardization with thetenth normal calomel electrode, for our experience, and that ofmany other workers, has been that the tenth normal calomelelectrode is liable to variation. When prepared from especiallypure material and when continually checked with new electrodesas in Clark's and S0rensen's laboratories it is undoubtedly satis-factory, but in laboratories where the interest and experience instandardizing is not so great, it is apt to give an entirely unwar-ranted sense of reliability. The N/10 calomel electrode may beconstant at its theoretical value for some time and then suddenlybecome variable (for example see Fales and Mudge (1920)). Onthe other hand a standard HCl solution is reproducible anywhere,and is stable, and since it is the ultimate standard used in deter-mining the value of the standard electrode, it seems safer, as wellas more logical, to use it as the working standard.

Moreover, when in the future the relation of temperature changeto pH and to activity change becomes more definitely establishedit will be a simple matter to correct all values which are baseddirectly upon reproducible solutions.

Cullen (1922, a) adopted the activity values for N/10 HCIgiven by Noyes and Ellis (1917) because we found that thesevalues, when used without correction for diffusion potential,gve, within 0.01 pH, Srensen's values at 200 for his standardPhosphate solutions. By mistake the values for N/10 HCl wereePorted as pHs1 38 = 1.090 and pH200 = 1.085. The value of 1.080

which is correct for 38° is now used at all temperatures from15-400. This gives even more exact agreement (within 0.005 pH)With Sorensen's phosphate solution at 20° (see also Hastings and

303

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

pK' of Serum

Sendroy (1924)) and has therefore been used as an arbitrary,,easily reproducible, which gives those values at 20° for the tard phosphate which have been used so widely in biological WWe have preferred to use the same value for 380 and 20 beof the uncertainty of the actual temperature correction.

However, now that both Clark and Sorensen are agreed the use of the tenth normal calomel electrode at all temperateit is desirable to know what relationship our system has to0electrode.

We have no direct determination of our N/10 acid againsttenth normal calomel electrode, but we have indirect measpSince the solution 0.01 N HC1 + 0.09 N KCI has been so istudied, since it eliminates the diffusion potential, and sincethe solution used by Srensen and Linderstr0m-Lang (1924)their recent work, it would seem to be the desirable standard

TABLE I.

N10 HC1 0.01 N HCI Srerense'8Temperature. N0 0.09 N KCI M/15 P0 4, pH1l

Assigned pH. Observed pH. Observed

°C.

20 1.080 2.05 7.40

38 1.080 2.04 7.37

reference for pH work. The pH of such a solution in our sytis shown in Table I.

The phosphate difference of 0.03 for 18 ° of temperature has1irepeated many times and holds for the entire Sorensen phosplseries, (confirmed recently by Hastings and Sendroy (19but the values for the solution, 0.01 N HCl + 0.09 N KCl, rePsent the average of two determinations only, and are therOlprovisional but serve to show that at 200 we are probablyagreement with Srensen's value to 0.01 pH. The, temperdifference between 38° and 20° will probably be more, ratherlbless, than 0.01 pH, but left at its assigned value it happens tPthe rounded value, see below, of 6.10 for the pK' of human seOwhich is also a value that has been used extensively in lstudies.

In view of the lessened diffusion correction, it will probably

304

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson 305

to use the solution (0.01 N HCI in 0.09 N KCI) in the future.the reference standard with the value 2.04 at 38 °.

Technique.

The blood was withdrawn without stasis from an arm vein intotubes under oil. The serum was obtained in either of two ways,depending upon the time required to draw the blood. If possiblethe blood was stirred rapidly but gently with a glass-footed rod

ays in the same direction for about 5 minutes by which timethe fibrin is all wrapped around the rod. This technique whichwas introduced by Dr. H. C. Gram is the only one by which wehave been able to defibrinate dog blood consistently withouthemolysis.

If there was any evidence of clotting, the clotting was allowedto continue until completion and then the fibrin was loosenedfrom the glass with a platinum wire.

In either case the tube containing the blood was stoppered,as described in the technique for colorimetric pH determination,and centrifuged. The serum was then removed to a samplingtube or to a test-tube under oil. No serum which showed hemol-ysis was used.

Equilibration with C02 at Known Tensions.

The equilibration was carried out by the second saturationmethod previously described (Austin et al. (1922)). The buffercurve of serum is so flat that two successive saturations are suffi-cient. The CO2 concentration in the tonometer was attained bymeasuring the CO2 in a burette over mercury. An improvementin the measuring system over that previously described consistsin the simple device of placing a small tube alongside the buretteconnected to it at the bottom and open to air above (see Fig.1, A). One can then sight across the mercury surface in theburette to the mercury surface in the small parallel tube which isat atmospheric pressure and be sure that the gas inside theburette is also at atmospheric pressure. (The final reading ismade with a lower cock (No. 2) closed, and the slight differenceineniscus level due to difference in capillarity of the two tubes

the same at every reading of the burette and introduces anktirely negligible error in the volume measured.)

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

pK' of Serum

In manipulating this arrangement, one learns to workcocks 1 and 2 at the same time, the leveling bulb B beieplace above the burette and serving as a reservoir. The eawith No. 1 closed is repeated several times to insure aceut

The transfer between first and second saturation was carriedas described before, rapidly and with the tonometer jacketwarm wet towels. After the second saturation, we intr0Aan improvement in the technique of transferring the serum tmercury sampling tube. We used a large water bath, eleetri

AFIG. 1. Showing apparatus employed in saturating serum. . Moi

gas burette; B, technique for transferring saturated serum from tonSto container without loss of C02 or change in temperature.

heated and controlled, in which a rotating shaft carried the toeters. The tonometer after the second saturation was relesfrom its support and brought to the position shown in B, FiThe rubber cap which protected the outlet tube from waterremoved and the sampling tube connected. A trace of i0oil on the edge of the rubber tube facilitates this since the tmust fit so snugly that there is no danger of its being pulled We find the transparent, acid-cured, rubber tubing (A. H. ThOCo., No. 8840) best for this purpose as well as for drawingbla

Next, always under water, the tonometer and sampling

306

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson

, inverted to position C. When cock 3 is open, mercury isse through cock 2 to the outlet to remove all air. Nos. 2 and 3

; now closed and the levelling bulb lowered to below the samp-ling tube. Then Nos. 1 and 2 are opened and the sample drawnito the sampling tube by manipulation of No. 3. When the

face of the sample in the tonometer reaches No. 2, No. 3 isclosed, the pinch clamp, which had been resting over the glasstube, snapped in place, the leveling bulb raised from the bath,and No. 3 opened. The whole is now removed from the bath,the tonometer disconnected, and the sampling bulb placed in itssupport with the serum under pressure. Thus contraction duringcooling can cause no extraction of gas.

It is most convenient for two persons to assist each other withthis technique. One holds the tonometer and leveling bulb, theother holds the sampling tube in one hand while he makes con-nections and manipulates the cocks with the other.

For removal of samples, cock 3 is closed, the pinch clampremoved, a drop or two wasted from the rubber tube, then thepipette inserted into the rubber tube. The pipette is filled bypressure controlled by cock 3. For pH determination a small5 cc. burette is used, containing about a centimeter layer ofmineraloil. The tip of the buretteis filled with oil before insertioninto the rubber tip of the sampling tube.

Total C02 Determinations.-The total CO2 determinations weremade with Van Slyke and Neill's (1924) constant volume tech-nique, using 1 cc. samples. Duplicate determinations almostalways were in agreement within less than 0.1 mM.

Conductivity of the Serum.-The conductivity was determinedby the ionometer method of Christiansen and the results expressedin NaCl equivalents, corrected for protein (Gram and Cullen(1923)) which was determined refractometrically.lemolobin.-The hemoglobin was determined colorimetrically

m an Autenrieth colorimeter, standardized by 02 determinationsby Van Slyke and Stadie's (1921) technique. We are indebtedto Dr. I. C. Gram for these and the conductivity determinations.

Calculations.

CO2 Tension.-Bohr and Bock's values for CO 2 solubility inseaum were used throughout (i.e. 97.5 per cent of water solubility).

307

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

308 pK' of Serum

pH Determinations.

Electrometric pH Determinations.-These were made asscribed before by Cullen (1922, a) by a combination of Jtigas mixture method and Hasselbalch's refill technique. A 42 cc. Clark electrode, modified for temperature control ('(1922, b)) was used. When the pH determinations were madedifferent temperatures on the same solution the CO2 +t- H2I miawas calculated to give the same [H2C0 3] content in the so1ute

Our procedure was to use freshly prepared platinum electrA

for each serum and to determine the "e" (pH = EM F- Lt

of the entire system (including calomel cell and platinum electAagainst standardized phosphate solution, before and after eAdetermination.

Colorimetric pH.-These determinations were made on lo0.5 cc. samples with the technique described before (Cullen 191a) except that the phenol red was measured with a pipette gradated to 0.01 cc. The phenol red was adjusted to such strenog(about 0.04 per cent) that 0.01 cc. was used per 1 cc. of standalsolution. 100 cc. of 0.9 per cent NaCl solution containingllcc. phenol red solution was adjusted to pH about 7.5. Colometric determinations are indicated by brackets, thus, [pl],4distinguish from electrometric determinations.

Calculations.

The formula used for calculating gas mixtures for saturationas[H2C0 3] concentration are the same as those given in an earpaper (Austin et al. (1922)). For the CO2 saturation mixtFormula V,2 and for mM [H2C03 ] Formula I,3 were used.

As a matter of fact we used the formula in the mM form, esmating mM solution from desired mMA. mM, = a'mMA.

cc. C2 = mMA X (V - Vs ) T burette16.04 X B- WB

Where mMA = concentration of CO2 in the gas phase of the tonometmillimols per liter.

2 Austin et al. (1922), p. 140.3 Austin et al. (1922), p. 144.

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson 309

T- ' volume of tonometer in cc.vs - volume of solution in tonometer in cc.

Tburette = absolute temperature C at which CO2 is measured.B.= barometric pressure in mm.

WiB vapor pressure of water in mm. at temperature T burette.cc. C0 = cc. of C02 run from the burette into the tonometer.

In Table II the pCO 2 values are given for convenience but arecalculated only to 0.1 mm.

For calculation of the CO2 + H2 mixture for the hydrogen elec-trode, where the mixture in the electrode is equilibrated at atmo-spheric pressure

pC0 2 . Vcc. CO 2 (B - W)

when both CO2 and H2 are at the same temperature and wherepC02 = CO2 tension in mm., V = volume of the tonometer in cc.,B = barometric pressure in mm., and W = vapor pressure ofwater at the temperature of the electrode.

Correction to Constant [H2CO3] and Constant pH.-The H2CO3]at the two temperatures was planned to be almost the same.Since the correction to constant [H2CO3] was therefore small, it

d[BHCOa]swas considered sufficient to assume that the slope d[HCO is ad[H 2C01I

straight line. The values from human separated serum of Doisy,Briggs, Eaton, and Chambers (1922) seem best for this purpose.

From the protocols for separated serum at the end of their

article one can calculate the following value for d[BHCO 3 between

40 and 70 mm. pC0 2 .Ratio.

For J. M . .. .......... ............................... .... 0.92E. A. D .............................................. 1.22W. H. C ................... .......................... 1.36

Average ................................................... 1.17

We have taken as an approximate ratio 1.2.The correction to constant pH is greater than to constant

[fIC] because the pH values are further apart. Since we hadno0 data for the buffer slope of human serum at 200, we corrected

the 38 [BtCO2 ] to the pH at 200, using the fact that d[BHC 31]dpH

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Condition.

Nephrits.Pulmonary tuberculosis.Primary pernicious anemia.Same 5 days later.Achylia gastrica.

Cardial decomposition lues.Anemia simplex.

Hyperthyroid.Primary pernicious anemia.Carcinoma, liver.

Diabetes.

Carcinoma, liver.Diabetes.

1" (plasma).Pneumonia infection.

Rheumatic fever.Mixed from two patients.Epidemic encephalitis.Normal.

Determinations on Wrf.onAs drawn.

percent

565695t

9140

952982

99

7095t

90105tloot105

97

0

0

percent

6.87.87.16.57.9

9.08.4

8.36.67.8

9.6

7.47.8

6.18.3¶8.3¶8.59.0

7.06.4

t

o2

0.140.134

0.1380.137

0.1340.1340.126

0.118

0.1200.1330. 1290.1350.134

0.1480.143

38

0

2t38

.C.

383838382020382038383820382020383838383838

2038383820

EqQ_ g _Rht

mm. mM

25.45 7.40.6 35.75 7.34.0 25.32 7.50.4 28.75 7.45.0 29.30 7.28.6 31.0228.6 29.7440.7 25.44 7.25.4 27.1940.0 28.97 7.60.0 26.40 7.59.61 29.00 7,37.6 31.0459.6 29.99 7.37.8 32.0237.7 29.4548.4 28.37 7.48.6 29.16 7.40.4 31.52 7.60.2 31.55 7.40.0 25.98 7.40.0 28.45 7.

7.

24.2 23.10 7.44.4 25.60 7.42.2 21.38 7.39.7 23.70 7.21.3 23.92 7.

Average (human) ..........................................................Average total .............................................................

* Brackets indicate reading on 22 X diluted serum.t Estimated from measuring centrifuged cell volume.I CO2 added in two portions.§ Plasma.¶ Very high fibrin.

310

No.

12334

56

789

10

1112

1314151617

Dog 20" 21

" 22

" 23

" 23J.

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Calculated.

I

II

BIIBS

II

m

nrae

1.2911.0781.6001.4301.4371.4401.2931.2771.2701.9051.8911.8911.8941.9001.8931.5361.5411.2831.9101.2701.270

1.2141.4081.3281.2621.072

1.4261.3561.2301.2901.3141.2931.2711.3091.3391.1091.1571.1881.1721.2001.1631.2431.2531.3721.1911.2891.330

1.2561.2341.1781.2501.329

6.0816.0926.1046.095

6.110

6.1026.1056.123

6.099

6.1006.0906.0816.0726.0756.092

6.0936.0986.121

6.095_i_............ 6.096

311

I toIa

0.25

0.310.340.35

0.34

0.260.250.26

0.32

0.290.24§0.270.35

0.330.340.300.280.28

0.30

°a

6.1776.163

6.190

6.169

6.1906.208

6.180

6.176

6.1836.182

xI

-a

0.060.07

0.030.04

0.040.01

0.010.12

0.10

0.04

� -

�

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

312 pK' of Serum

is approximately linear. We used for the slope the value 6.7 mMwhich we obtained by averaging the value from the three seracited above with those from the two plasmas of Peters, Bulger,and Eisenman (1924). The five values give an averaged[BHCO3] serum 38° = 6.7 mM per 1.0 pH unit.

dpHTABLE III.

Race.

Russian Jew.

American.Austrian.

Colored.

Russian Jew.

Jewish.American.

English.

Russian Jew.American.

Colored.American.

¢4

Diagnosis.

Pulmonary tuberculosis(chronic fibroid).

Pernicious anemia.Intestinal adhesions gas-

tric anacidity.Chronic myocardial disease

with anasarca. Tertiarylues.

(Hemolysis?) perniciousanemia? Secondary ane-mia.

Hyperthyroidism.Pernicious anemia.Carcinoma, liver.Diabetes mellitus.Carcinoma, liver. Diabetes

mellitus.Diabetes mellitus (mild).Lobar pneumonia. Pleurisy

with effusion.Lobar pneumonia.Rheumatic fever.Epidemic encephalitis dys-

pituitarism. Diabetesinspidus.

DISCUSSION OF RESULTS.

Table II presents a summary of the analyses and calculationson both human and dog sera at both 20° and 38 °. The discus-sion of the results follows. The clinical data in regard to thepatients studied are given in Table III.

pK' at 38 0 .- Fifteen determinations on sera from thirteenindividuals are included in this series. The values range from

No.

2

34

5

6

789

1011

1213

141517

Name.

M. L.

C. K.M. B.

E. V.

T. R.

L. W.E. J. C.F. C.A. C.E. C.

A. G.E. G.

M. A.S.M. K.

Age.

63

6038

43

40

1754584267

3227

521916

Sex.

Male.

Female.

Male.

Female .

Male.

Female.

Male.

Female.Male.

l ~~~~~

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson

6.123 to 6.072 with an average of 6.095. The average deviationfrom this value is 0.010. There are three values which, perhaps,because of their large deviation from this mean, should be ex-cluded. These are Nos. 9, 14, and 15. (In 9 there was a slightdifficulty in technique, in 14 and 15 there were unusually highfibrin clots upon defibrination.) If we exclude these three deter-minations and that of the plasma of No. 12, the average becomes6.097 with an average deviation of 0.007. The three determina-tions do not, then, alter the average.

The three values on normal dog sera give an average value of6.104.

If the total eighteen determinations are considered as a wholethe average value is 6.096. It is evident that this value 6.096represents the pK' of serum at 380 and apparent that this value isnot greatly disturbed by various disease conditions. This valuerounded off to 6.10 agrees with the value at present most gen-erally used.

pK' at 20°.-pK values at 20 ° were obtained on six sera.The average for these six human sera is 6.183. If we include thetwo normal dog sera, we have practically no change, i.e. an aver-age of 6.182 for the series with an average deviation of 0.011.

The average deviation 0.007 and 0.011 at the two temperaturesrepresents about the expected accuracy of the method, i.e. about0.01 pH. This is discussed fully in the paper by Austin et al.(1922).

pK20 - pK'3 so.-The value for the average temperature differ-ence becomes 6.184 - 6.096 = 0.088 or 0.09. This gives a tem-perature coefficient of 0.005 pK' per 1°C.

Influence of pH, Protein, and Salt on pK' Variation.

In view of the change in base bound by protein at different pH,it is important to determine if this influences the pK' of serum.In Fig. 2, pK' values are plotted against pH values. It is evi-dent that for our series there is no relation between pK' and pHand we may conclude therefore that for serum over thepossiblephysiological range (pH = 7.0 to 7.9) the value 6.10 holds.

In Fig. 3, the values are charted against protein concentration.Over the rather extreme concentration of 6 per cent to 9.6 percent met with in this series, there is no apparent relationship.

313

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

I-

A

1FIG. 2. Relation of pK' at 38 ° and 20° to pH at 38 °.

PK'

I ,38

6.11

6.0IC

6.0:

6.0'

O

----

D__

PK;d

620

6.19

6.18

6.17

6.167 8 9 10 Itpercent serum protein

------

O

--<---

A vet

------

!

rae

0 = 38 °

A =20

; -_ _

FIG. 3. Relation of pK' at 380 and 20 ° to concentration of serum protein.

314

i

-----

FI

-

I

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson 315

The total effective salt concentration is best represented by theequivalent conductivity. Using this and expressing the con-ductivity corrected for protein in terms of equivalent NaClnormality, i.e. normality of NaCI which would give the observedconductivity, we find the conditions expressed graphically byFig. 4.

There is not enough variation here to establish any systematic

pK38

6.12

6.11

6.10

6.09

6.08

6. n7

pK,

6.ao

6.20

6.19

6.18

6.17

6.16

Averat

______-

__ ___-

.100 .110 .IZO .15U .19q- .5aUConductivity Na Cl equivalent normality

FIG. 4. Relation of pK' at 38 ° and 20° to electrolyte concentration inserum.

grouping. It is apparent that the sera with abnormally low con-ductivity all show comparatively large pK' variation but includeboth high and low values. There is also a suggestion that the sixlowest pK' values are grouped about a lower conductivity value.This is contrary to the experience with pure bicarbonate solutionswhere increase in salt concentration decreases pK'. The seriesis too small moreover to do more than indicate that there is nomarked systematic change with conductivity change.

.-

___---.

-------

a. ------

re

0 = 38 °

-=ZOe

Normal

-- -

O

a

----..

_A

------

-------

--------

-------A

-------

------

V . I

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

316 pK' of Serum

pK' of Plasma.

There is no reason to expect that the slight change in electrolyteconcentration introduced by 0.3 per cent oxalate (=0.02 M) willappreciably affect the results for serum. The value calculated byVan Slyke, Wu, and McLean (1923) from Cullen's (1922, a) datagives the same value 6.11 for both horse plasma and serum.

Also in Table II, No. 12, are found the results of an experimentin which blood was drawn simultaneously, by means of two tubesand a Y tube, for plasma and serum. The original total CO2values for the serum and plasma were 28.37 mM and 29.16 m,respectively. The pK' values reported here may then be consid-ered as accurate for plasma.

TABLE IV.

PK' dpK'dt

38°C. 18°C.

NaHCO3 + NaCI* 6.110 6.210 0.005[Na] = 0.16 N.

Serum: ox and horset. 6.096 6.235 0.007200

" human and dog:. 6.096 6.182 0.005

* Warburg (23), p. 242.t Warburg (23), p. 209.t Author's value.

Comparison of pK' with Previous Values.

The value 6.10 compares well with the value of 6.11 calculatedby Van Slyke, Wu, and McLean (1923) for horse serum and plasmafrom Cullen's (1922, a) data (reported as 6.12, now corrected toour present pH standard).

Warburg's (1922) determinations for 0.16 N bicarbonate in sa-line and for horse and ox serum all reduced by 0.048 from Bjerrumto Sorensen's pH values compare with ours as shown in Table IV.

The agreement at 380 is satisfactory. The change with tem-perature for our serum and Warburg's salts is also in agreementbut there is a discrepancy between Warburg's temperaturevariation for serum and ours.

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson 317

Change in [BHCO3]-Combining Capacity with Change inTemperature.

It is known that the blood and serum bind increasing amountsof CO2 with decrease in temperature (Warburg (1922), Stadie andMartin (1924)). The above series includes five human sera andone dog serum which were studied at two temperatures and which

therefore afford opportunity to evaluate the value d[BHCO]dt

TABLE V.

Changes in [BHCO3] of Separated Serum with Change in Temperature at (a)Constant pH and (b) at Constant [H2CO3].

Serum.

4

6

9

10

Dog 23

Tempera-ture.

°C.

3820

3820

3820

3820

3820

[BHCO,]

mM

27.8729.58

24.1525.91

27.1129.15

28.1030.12

22.4422.85

[H2CO3 ]

mM

1.4371.430

1.2931.277

1.8911.891

1.8941.900

1.2621.072

[BHCO]I- 38

°

correctedto [H2CO:3at 20'.

mM

27.88

24.13

27.11

28.11

22.21

pH

7.3957.490

7.3827.498

7.2817.357

7.2717.390

7.3717.505

[BHCO]-38 °

correctedto pHat 204.

maM

27.23

23.37

26.60

27.30

21.54

A[BHCO3I,oo,at constant

[H2CO31

mM

1.70

1.78

2.04

2.01

0.64

Average for human ..................................... 1.88

pH

mM

2.35

2.54

2.55

2.82

1.31

2.56

under various conditions. This has been done for two conditions,constant [H2CO 3] and constant pH. Constant [H 2CO] may beconsidered as constant effective CO2 tension, i.e. the CO2 tensionwhich gives at the various temperatures the same concentrationof H2C0 3.

The condition of constant pH when used for changing tempera-ture introduces the questions of pH standardization and of therelation between the [H+], the [OH-], and the neutral point(see Austin and Cullen (1) for further discussion of this point.)

_ . _

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

FIG. 5. Showing change in IBHC3O3 ]3820o at constant [H2CO 3] in sepa-

rated serum. A = observed values at 20° , O = observed values at 38°.

Corrections to constant [H 2CO3] indicated by sloping lines.

FIG. 6. Showing change in [BHCO3]38 20o at constant pH in separated

serum. A = observed values at 20°, O = observed values at 38 °. Correc-tions to constant pH indicated by sloping lines.

318

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson 319

The changes in [BHCO3 ] calculated for both constant [H 2CO 31and constant pH are given in Table V. The factors used in cal-culating this table are given above under Calculations.

The pCO2 tensions were planned to give close agreement in[H2CO 31 at the two temperatures so that the error in correctingto the same [H 2CO3] would be negligible.

The corrections and the resulting d[BHCO 3] values are recordedgraphically in Figs. 5 and 6.

The average value for the five human separated sera ford[BHCO 3] at constant [H 2C0 3] is

d[BH_COa 1- _ = - 1 = -0.10 mM per 1C.dt /IH2CO31 18

The average value for d[BHCO 3] at constant pH for 18 is

d[BHCO] 2.56( dt -)p =- - 18 = - 0.14 mM per 10C.

These data are in close agreement with those given by Austinand Cullen (1925, Table II) where in addition the correspondingchanges for whole blood are calculated.

Such data offer no basis for distinguishing between the relativeimportance in vivo of [CO2], [H 2CO 3], pCO2, or pH under condi-tions of changing temperature in regulating the respiratorycenter and the acid-base balance in the blood. Depending uponwhich factor remains constant in vivo the variation in serum pHper degree change in temperature may vary from 0.00 to -0.02.Furthermore, it must be remembered that these calculatons arebased upon the assumption of constant available total base in theblood for combination with protein and HCO3, a condition whichprobably often does not hold in temperature changes in vivo.

The C of the Colorimetric Determination of pH of Serum.

The determination of the pH of normal plasma, colorimetrically,has proved accurate and satisfactory when carried out as previouslyreported (Cullen (1922, a)) on dilute plasma. The plasma readat room temperature, t, is corrected to 380C. by the equation

pH 38 o = [pHi 20o - C

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

320 pK' of Serum

where [pH]2 0o = [pH]t- + 0.01 (t - 20°) and [pH] indicatescolorimetric pH reading. C, for human plasma, has an average valueof 0.23.

The value of this method has been confirmed by further results inour laboratories and by Marrack and Smith (1924) and by Hast-ings and Sendroy (1924).

RelationRelatfion of C to pH C of C to conducfivity

0.36

-I 0028_.30 * /· / · 0I

7.2 7.3 7.4 o.1o0 0.130 0.40

p H ConductivityaCI equivalent normality

FIG. 7. Relation of C to pH and to conductivity.

33 0 0

32

30

28

S6 · · c

245 6 7 8 9Serum protein percent

FIG. 8. Relation of colorimetric factor C to serum protein concentration.

The experiments reported above afforded an opportunity tostudy the value of C for human serum. The values for C arefound in Table II. All colorimetric readings are corrected to 20°

by the correction factor, 0.01 per 1° used for plasma.It is apparent that the C for these abnormal sera has not the

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

Cullen, Keeler, and Robinson

same degree of constancy that it has for normal human and horseplasma. In an attempt to find some explanation for this dis-crepancy the C serum values have been plotted (Figs. 7 and 8)against pH380, against protein content, and against conductivity.

It is at once evident, that the twelve determinations fall intotwo groups, one with an average of 0.26 and the other with anaverage of 0.33 but our data offer no explanation of this grouping.From the figures it can be seen that the variation is not relatedto serum protein or to the pH of the serum itself. This is inagreement with the work of Marrack and Smith (1924), whofound that change in protein concentration had no influence onthe correction C for plasma.

There is a suggestion in the conductivity plot of Fig. 6 that thelower group has a lower conductivity but this difference is notsharp enough to account for the distinct grouping. To the Cvalues for dog sera given above may be added two more, deter-mined on the same dog before and after tetany, of 0.30 and 0.29.This gives an average for dog sera of 0.30 which is consistent withthat previously used. There is reason to believe, however, thatthe variation of C in the dog is greater than in man. Moreover,the extent to which this correction varies under pathologicalconditions has not yet been adequately determined.

The Relation between Colorimetric [pH] and Electrometric pHat 20.-In the last column of Table II are given a few deter-minations of the colorimetric [pH]2 0o of diluted serum comparedwith the electrometric pH20 undiluted, the average correction tothe colorimetric reading is -0.04 pH.

SUMMARY.

1. The standardization of pH determination at 38° and 20°

is discussed.2. pK' 38o determined on fifteen pathological human sera gives

an average of 6.095 (CO2 solubility coefficients of Bohr and Bockbeing used in the calculation).

3. pK2o for the same sera is 6.183.4. The values for pK' for dog sera agree with those for human

sera.5. There is no evidence that the nature of the disease, possible

salt content variation, protein variation, or pH itself significantlyaffect these values.

321

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

322 pK' of Serum

6. The temperature coefficient for pK' is -0.005 per 1°C.7.. The temperature coefficient for the C0 2-combining capacity

of human separated serum at constant [H2CO3] and at constantpH are calculated as

d[BHCOsa] -) - 0.10 m per 1°C.dt° ][HCO31

(d[BHC = -- 0.14 m per 1°C.

BIBLIOGRAPHY.

1. Austin, J. H., Cullen, G. E., Hastings, A. B., McLean, F. C., Peters,J. P., and Van Slyke, D. D., J. Biol. Chem., 1922, liv, 121. Austin,J. H., Stadie, W. C., and Robinson, H. W., J. Biol. Chem., 1925, Ixvi,(in press). Austin, J. H., and Cullen, G. E., Medicine, 1925, iv, 275.

2. Barcroft, J., The respiratory function of the blood, Cambridge, 1914.3. Clark, W. M., The determination of hydrogen ions, Baltimore, 1920.4. Cullen, G. E., J. Biol. Chem., 1917, xxx, 369; 1922, a, lii, 501; 1922, b,

lii, 521.5. Doisy, E. A., Briggs, A. P., Eaton, E. P., and Chambers, W. H., J. Biol.

Chem., 1922, liv, 305.6. Donnegan, J. F., and Parsons, T. R., J. Physiol., 1918-19, lii, 315.7. Drucker, P., and Cullen, G. E., J. Biol. Chem., 1925, xiv, 221.8. Pales, H. A., and Mudge, W. A., J. Am. Chem. Soc., 1920, xlii, 2434.9. Gram, H. C., and Cullen, G. E., J. Biol. Chem., 1923, Ivii, 477.

10. Haldane, J. S., Respiration, New Haven and London, 1922.11. Hasselbalch, K. A., Biochem. Z., 1916-17, lxxviii, 112.12. Hastings, A. B., and Sendroy, J., Jr., J. Biol. Chem., 1924, xi, 695.13. Hawkins, J. A., J. Biol. Chem., 1923, Ivii, 493.14. Henderson, L. J., Am. J. Physiol., 1908, xxi, 427.15. Lewis, G. N., and Randall, M., Thermodynamics, New York and Lon-

don, 1st edition, 1923.16. Marrack, J., and Smith, F. C., Brit. J. Exp. Path., 1924, v, 13.17. Noyes, A. A., and Ellis, J. H., J. Am. Chem. Soc., 1917, xxxix, 2532.18. Parsons, T. R., J. Physiol., 1917, li, 440.19. Peters, J. P., Bulger, H. A., and Eisenman, A. J., J. Biol. Chem., 1923-

24, Iv, 687.20. S0rensen, S. P. L., and Linderstr0m-Lang, K., Compt. rend. trav. lab.

Carlsberg, 1924, xv, no. 6, abstracted in Chem. Abstr., 1925, xix, 21.21. Stadie, W. C., and Martin, K. A., J. Biol. Chem., 1924, Ix, 191.22. Van Slyke, D. D., Wu, H., and McLean, F. C., J. Biol. Chem., 1923,

Ivi, 765. Van Slyke, D. D., and Neill, J. M., J. Biol. Chem., 1924,lxi, 523. Van Slyke, D. D., and Stadie, W. C., J. Biol. Chem., 1921,xlix, 1.

23. Warburg, E. J., Biochem. J., 1922, xvi, 153.

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from

RobinsonGlenn E. Cullen, H. R. Keeler and Howard W.

FOR HYDRION CONCENTRATION OF SERUMHENDERSON-HASSELBALCH EQUATION

THE pK' OF THE

1925, 66:301-322.J. Biol. Chem. 

  http://www.jbc.org/content/66/1/301.citation

Access the most updated version of this article at

 Alerts:

  When a correction for this article is posted• 

When this article is cited• 

to choose from all of JBC's e-mail alertsClick here

  t-1

http://www.jbc.org/content/66/1/301.citation.full.html#ref-lisfree atThis article cites 0 references, 0 of which can be accessed

by guest on January 27, 2020http://w

ww

.jbc.org/D

ownloaded from