resonance 

### (EPR)studiesand to N. 

### P. Marullo of our department for the free-radical formulations.



### LITERATURE CITED

(1) E. de Barry Barnett, J. Chem. Soc., 97, 63 (1910). (2) J. Boeseken, Red. Trav. Chim. Pays-Bas, 55, 1040 (1936). (3) V. A. Golovnya and G. T. Bolotova, Zh. Neorg. Khim., 6, 2254 (1961). (4) V. A. Golovnya and S. K.Sokol, Zh. Neorg. Khim., 4, 596 (1959). (5)W. R. Schoeller, “The Analysis of Minerals and Ores of the Rarer Elements”,

(6) N. K. Pshenitsyn et al., Zh. Anal. Khim., 18, 761 (1963). (7) I. V. Prokof’eva and A. E. Bukanova, Zh. Anal. Khlm., 20, 598 (1965). (8) V. A. Golovnya and G. T. Bolotova, Zh. Neorg. Khim., 6, 566 (1961). (9) C. J. van Nieuwenburg and J. W. L. van Ligten, Cbim.Anal. (Paris),36, 41 Hafnsr Publishing Co., New York, 1955.

(1954). (IO) V. G. Ackerman, J. Prakt. Chem., 5, 298 (1957). (11) P. Krug, J. SOC. Dyers Colour., 69 (13), 606 (1953). (12) E. 0. Fischer and W. 2. Hieber, 2.Anorg. Allg. Chem.,271, 229 (1953). (13) P. H. Gore, Chem. lnd. (London), 1355 (1954). J. Boeseken, Red. Trav. Chim. Pays-Bas, 67, 603 (1946). K. Jellinek, 2.Anorg. Allg. Chem., 70, 93 (1911). W. G. Christiansen and A. J. Norton, Ind. Eng. Chem., 14, 1126 (1922). W. F. Hillebrand et al., “Applied Inorganic Analysis”, 2d ed., John Wiley and Sons, New York, 1953. “ASTM Methods for ChemicalAnalysis of Metals”, 1960, American Society for Testing Materials, Baltimore, Md., 1961. D. Wojtasiewicz-Obrzut, Chem.Anal. (Warsaw), 10, 1133 (1965); Chem. Abstr., 64, 14,968 (1966). E. E. Jelly, Analyst(London),55, 34 (1930). W. J. Lem and M. Wayman, J. SOC. Dyers Colour., 83, 227 (1967). W. G. Hodgson et al., Nature, 178, 489 (1956). R. G. Rinker et al., J. Phys. Chem., 63, 302 (1959). S.Lynn et al., J. Phys. Chem., 68, 2363 (1 964).

RECEIVED for review April 28,1976. Accepted September 17, 1976. References to 

### U.S.S.R. publications are from Consultants Bureauwith their pagenumbers. Thisinvestigation was supported in part by the National Science Foundation through Grant GE-7921.



# Determination

# of Hydrogen Ion Concentrations in Seawater 

# from 5 to 40 

# ‘C: Standard Potentials at Salinities from 20 

# to 45%0

K. 

### H. Khoo,l Richard

### W. Ramette,2 Charles 

### H. Culberson, and Roger 

### G. Bates“

Department of Chemistry, Universityof Florida, Gainesville, Fla. 326 1 1

Evidencehas been presentedto show that seawater behaves

as a “constant ionic medium”, stabilizing the activity coefficients of solutes present in small concentrationsand reducing

or eliminating the residual liquid-junction potentialencountered in measuring the pH of seawater systems. Under these conditions, an experimentalscale of hydrogen ion concentration becomes a practical possibility. The standard emf of the H2/Ag;AgCI cell, neededto establish standard reference buffer solutions inseawater, has beendetermined In synthetic seawater at salinitiesfrom 20 to 45% and temperaturesfrom 5 to 40 OC. Supplementary measurements in seawaterto which HCI has been added lead to values of 

## pHso.,, the formation constant of HS04-, in this range of salinity and temperature.

In earlier contributions (1-3), we have examined the possibility of determining experimentally, by electrometric methods, the hydrogen ion concentration of natural seawater. Itwas concluded that seawater of 

### 35%0 salinity possesses the favorable characteristics of a “constantionic medium”. Thus, the liquid-junction potentialbetween seawater and the customary concentrated potassium chloride solution of the reference electrode is nearly constantwhen small changes in the composition of the seawater solution occur. Furthermore,the activity coefficients of solutes present in relatively small
amountsin the seawater medium are stabilized,changingbut little as the concentrations of these substances are altered. 

### As

a consequenceof these favorable conditions,itappears feasible
to standardize

### a scale of pH,defined as -log CH, for seawater that can be experimentally realized through measurements with the electrometric assembly of the usual glass-calomel type. Thepractical advantage of such a scalederives both from the utility of the quantity CHand from the greater simplicity

On leave 1975-76 from the University of Malaya, Kuala LumOn leave 1975-76 from Carleton College, Northfield, Minn. pur.

I of the concept of hydrogen ion concentration as compared with that of the hydrogen ion activity.

In practice,the pH of 

### an “unknown” solution (X)is derived from the emf 

### (Ex) of the cell

Glass electrode 

## 1 Soln 

### X 

## (1 KCl, Reference electrode (A)

and from the corresponding emf 

### (Es)for the same cell in which a standard solution 

### (S) of known or assigned pH [pH(S)]replaces Solution 

### X. Use 

### is made of the operational definition

When the ionic strengths and compositions with respect to the preponderant electrolytes are the same in the solutions 

### X and 

### S, Equation 

### 1 yields an experimental measure of prn~(X) if pm~(S) is known (m= molality). In order to establish hydrogen ion concentrations or molalities for buffer solutions in synthetic seawater (sw) in the pH range close to that of natural seawater,we have chosen
to study the emf of cellswithout liquidjunction,in a manner similar to that used to derive pH(S) for the NBS standard reference solutions (4). Hydrogen electrodes and silver-silver chloride electrodes are used in this method. The standard potentials required for studies in seawater have now been derived from emf measurements of cells of the type Pt;Hn(g,latm)

# I HCl(m)in sw 

## 1 AgC1;Ag (B)

The compositions of the solutions in synthetic seawater were adjusted in such a manner as tokeep both the ionic strength and the molality of chlorideion constant in all of the cells. The synthetic seawater was composed of NaC1, KC1, CaCln, and MgC12; the only major component of natural seawater missing from this formulation is sulfate ion.In a supplementary series of measurements, HCl solutions in synthetic seawater containing sulfate ion were studied in cell B. These data, interpreted with the aid of the standard potentials, yield values for
&SO.,, the equilibrium constant for the ion association process

4NALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977 29H+

# + S042-= 

### HS04-

Theresults of these studies,coveringthe salinity range 20 to 

### 45%0 and the temperature range 5 to 40 “C, are reported here.



### METHOD

By application of the Nernst equation to cell B, one can



### E =

### Eo

# - k log mcl 

### - 2k log y*(HCl) 

# + k pmH 

### (3)

where yi(HCl) is themean activity coefficient of HC1in the cell solutions, 

### k is written for 

### (RT In 

### lO)/F,and 

### Eois the standard emf referred to the customary standard state, the hypothetical ideal 

### 1m aqueous solution. Values 

### of

### Eo over a considerable range of temperature have been determined 

### (5, 6).It is permissible, and often useful, to alter the standard reference state, 

### so that the activity coefficient (y-+*) becomes unity atzero molality of solutes in thepure seawater solvent instead of in pure water 

### (Ti) (7,8). Thischange in reference
stateis accomplished through thefollowing substitutions in Equation 3: write

where my5is thetransfer activity coefficient

### ormedium effect, which yields



### E =

### Eo* 

# - k log mcl 

# -2k log rk*(HC1)

# + k pmH 

### (5)

Inasmuch as mcl is fixed (andknown) for seawater of a given composition andpmH is equal to -log m (cellB)when sulfate and other bases are absent, the value of

### Eo* can be obtained easily by plotting the quantity 

### (Eo* 

# - 2k log y**) as a function of m and extrapolating tom = 0. Such plots have been found to be straight lines,both in this and earlier studies (1). The slopes demonstrate that 

### 212 log -y** amounts toonly 0.04 mV atm = 

### 0.01mol kg-l and increases by a like amount for each increment of 0.01 mol kg-l. In view of this very small effect, the standard emf of cell 

### B was, for convenience, determined atmHcl = 0.01 instead of atrn = 0. 

### It is therefore designated 

### E*rather than 

### Eo* in the following discussion. Evidently, 

### E* in seawater of a given salinity can be used interchangeably with 

### Eo*which, by definition, is the true standard emf.

Unfortunately, it is not easy to estimate (a) the effect on yl(HC1) of adding buffer substances to the solution under similar conditions of constant ionic strength and chloride molality, or (b) the effect on ri(HCl) of adding sulfate to a seawater in place of 

### a part of its chloride content. Although 

### Eo* or 

### E*, the standard emf in the seawater solvent containing no added foreign solutes (such as HC1or buffer substances),can be obtained, thevalue of

### Eo* -2k log y+*isnot usually known exactly 

### at a finite molality of foreign solute species. Theories of ionic interactions in mixed electrolytes (9-12) offer some guidance, but they are as yet incapable of offering a quantitative solution totheproblem. Nevertheless, since

### 2k log y**is only0.04 mV in thepresence of 

### 0.01m HCl in sulfate-freeseawater, it seems unlikely that itsvalue in,for example, 0.01 m acetic acid/0.01 m sodium acetate 

### or in 0.01

m tris(hydroxymethy1)aminomethane (“Tris”)/O.Ol m Tris. HCI in the same synthetic seawater would exceed limits of about fO.l mV (0.002pH unit)when the same conditions of
constant ionic strength and constant chloride molality are maintained. Hence, if one can accept an uncertainty of a few thousandths of a unit in pmH, it becomes reasonable 

### to determine pmH in dilute standard reference solutions by means of the relationship



### E -Eo* E-E* 

# + log rnC1 N

___ 

## + log ma pmH =

~ (6) k k 

### In the use of this equation,one makestheimplicit assumption thatthe activity coefficient of HC1is virtually constant in the
seawater medium, even when small amounts

### of a buffer system or sulfate are substituted for an equivalent amount of sodium chloride or HC1.


### EXPERIMENTAL
Composition of Synthetic Seawater. The procedure outlined above and embodied in Equation 1is based on theuse of pmH standardsprepared in synthetic seawater containing no sulfate todetermine pmH(X) in solutions of natural seawater of the same ionic strengthbut which contains sulfate and smallamounts of other substances, for example, fluoride and borate. It is possible therefore that the liquid-junction potentials atthe boundaries Soln SIIConc. KC1 and Natural swl/ConcKC1 in cell A may not be identical. Earlier
measurements have nonetheless suggested that theresidual liquidjunction potential due tothis difference of composition amounts to

no more than a few thousandths of a unit in pmH (I).

We have explored in detailthe alternative procedure in which the standard is prepared in synthetic seawater containing sulfate. This method requires either the estimation of the activity coefficient of HCl in the sulfate-containing medium or a knowledge of PHSO~, the equilibrium constant for Equation 2. From the practical point of view, the latter procedure does not appear tooffer any real advantage over the former atthe present time.

At theBerlin Dahlem Conference on theNature of Seawater held in March of 1975,a panel on conventions for seawater equilibria found it permissible that artificial seawater solvents used for standard refereqce solutionsbe prepared from thethree salts NaC1, MgC12, and NaZS04 (23). Inthiswork, a closer approximation to the composition of natural seawater was achieved by theinclusion of both potassium and calcium ions. Thesyntheticseawater of salinity 35% containing sulfate had the following composition, based on molality m (moles per kilogram of water):

m,mol kg-l glkg soh

NaCl 0.42664 NaZS04 0.02926 KC1 0.01058 CaClz 0.01077 MgCL 0.05518 24.061 4.011 0.761 1.153 5.069

Themolality of chloride ion was 0.5691mol kg-I, and the formal ionic strength was 0.7229.

The synthetic seawater without sulfate was designed tomatch the ionic strength of the synthetic seawater containing sulfate. It contained KC1, CaC12,and MgClz atthesame molalities, but the contribution to the ionic strength due tothe sodium sulfate was achieved by increasing the molality of NaC1. Thesolution which matched the above seawater of salinity 35%0 had the composition

m,mol kg-’ glkg soln

NaCl 0.46444 KCl 0.01058 CaClz 0.01077 MgCh 0.05518 26.193 0.761 1.153 5.069

The molality of chloride ion was 0.6069 mol kg-I, and the ionic strength was 0.6729.

The compositions expressed in moles per kilogram of seawater 

### (Mi)

are directly proportional to the salinity 

### (S). Thus, the molal compositions (m,)of seawater solvents of salinities other than 35%0are related to themolalities ma5 of the seawater given above by
27.5109
1000 - 1.0016s mi = m35 (7)

Thecalculation of theionic strengths (I) of the solutions not containing sulfate is straightforward, asis alsothe evaluation of theformal ionic strengths of the solutions containing sulfate. Thelatter are readily obtained by Equation 7,where I and 135replace mi and m:(~, respectively. To derive the real or effective ionic strengths of the
seawaters containing sulfate,however, corrections for ion pairing must be made. Theequilibrium constants of Kester andPytkowicz (14,15) for the formation of NaS04- and MgS04 formed the basis for this calculation. Toobtain values of the constants ata salinity of 44.55%0, it was necessary toresort to anextrapolation. Theminor constituents

30 ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977Table 

### I. Electromotive Force of the Cell: Pt;H,(g, 

### 1 atm) 

### 1 HCI in 

### sw 

### 1 AgC1;Ag in Sulfate-free Seawater 

### from 5 

### to 40 "C, 

### in Volts0

Ionic strength, I mH mCI 5 OC 10 

### "c 15 OC 20 

### "c 25OC 30 "C 35 

### "c 40 OC
0.2795 0.3126 *0.3867

0.3993 0.4587 0.5197 0.5805 0.6407 *0.6727 *0.6730

0.6983 0.7593 0.8200 *0.8621 *0.8627

0.8792 0.009991 0.010027 0.010029 0.009996 0.010018 0.009997 0.010001 0.010001 0.010034 0.010016 0.010036 0.009997 0.010076 0.010102 0.010070 0.010001 0.2531 0.2829 0.3491 0.3611 0.4148 0.4698 0.5246 0.5789 0.6068 0.6070 0.6309 0.6859 0.7407 0.7773 0.7779 0.7940 

## ... 0.38878 0.38439 0.38347 0.38012 0.37724 0.37453 0.37217 0.37091 0.37100 0.36983 0.36779 0.36547 0.36426 0.36422 0.36365 0.39148 0.38899 0.38455 0.38361 0.38018 0.37724 0.37451 0.37212 0.37082 0.37094 0.36972 0.36764 0.36526 0.36408 0.36405 0.36344 0.39161 0.38905 0.38455 0.38361 0.38011 0.37718 0.37434 0.37194 0.37063 0.37076 0.36948 0.36740 0.36496 0.36376 0.36377 0.36309 0.39156 0.38899 0.38441 0.38344 0.37991 0.37692 0.37407 0.37161 0.37032 0.37044 0.36913 0.36701 0.36457 0.36335 0.36334 0.36262 0.39142 0.38880 0.38412 0.38315 0.37959 0.37656 0.37368 0.37117 0.36986 0.36997 0.36866 0.36651 0.36403 0.36279 0.36273 0.36204 0.39110 0.38846 0.38373 0.38275 0.37912 0.37608 0.37314 0.37061 0.36930 0.36935 0.36804 0.36590 0.36 3 21 0.36210 0.36203 0.36129 0.39069 0.38801 0.38324 0.38222 0.37856 0.37549 0.37251 0.36994 0.36859 0.36865 0.36727 0.36518

0.36133 0.36121 

### ...

... 

## ... 0.38744 0.38262 0.38159 0.37 7 90 0.37477 0.37175 0.36916 0.36781 0.36781 0.36643 0.36435

0.36043 0.3 6033 ..I



### ...

a An asterisk indicates that the standard emf E was higher than that given in Ref. 6 by 0.17 mV at each temperature For the remainder of the measurements, 

### Eo was the same as given in Ref. 6, Table I, column 5.

K+and Ca2+ were included with the Na+and Mg2+, respectively, in making corrections for ion pairing. By this procedure,the real ionic strengths of the sulfate-containingseawater solvents at 25 "C were found to be as follows:



## s,%o I (formal) I (real)

20.31 0.4131 0.3869 34.99 0.7227 0.6729 44.55 0.9294 0.8629

The real ionic strength is related to the salinity by

I = 0.0029 

## + 0.0185758 

## + 1.639 X S2 (8)

with a maximum brror of less than 0.0001 mol kg-*.

The data of Kester and Pytkowicz (14,15)showthatthe real ionic strength of seawater (salinity 35%0) decreases from 0.673 to 0.667 as the temperature is lowered from 25 to 5 "C. It can be shown that complete disregard of ion association alters the subsequent calculations by an amount equivalent to an error of less than 0.1 mV at a salinity of 20%0 and less than 0.3 mV at a salinity of 45%0. As the variatibn in ionic strength due to alterations in the degree of ion pairing with temperature is only about 10%of the difference between the formaland real valugs given above,theerror resulting fromneglect of this variation is less than 0.03 mV in E*.Thus,the value of Z (real)
at 25 "C was used at each temperature in the range 5 to 40 "C when needed for the evaluation of &so4 and the selection of values of E*.

Solution Preparation and Cell Measurements. Sodium chloride, the major component of the synthetic seawater, was recrystallized from one to three times. Tests for bromide (16)showed that the recrystallized salt was essentially free of this impurity. Sodium sulfate, KC1, CaClz, and MgC12 were of reagent quality; they were dried before

use but not further purified. The hydrochloric acid had been twice distilled. Chloride analyses were made by the gravimetric AgCl procedure, Solutionswere prepared by weight methods from the salts,

a standard solution of HC1, and deionized water that had been distilled in an all-glass still.

Silver-silver chloride electrodes were prepared by the thermalelectrolytic method (17).Although the standard emfE" of cell B has been determined (5, 6), values of Eo were established, as recommended for the most accurate work (18), by each investigator individually through measurements of cell B containingaqueous HCl of molality 0.01 mol kg-I. The platinum-hydrogen electrodes were coated lightly with platinum black. The design of the cells has been described elsewhere (19).

The cell emf was measured with the aid of two digital voltmeters which were checked occasionally for accuracy by measurement of the emf of the laboratory standards. In correctingthe hydrogen electrode data to a hydrogen partial pressure of 1 atm, the vapor pressures of the seawater solvents were used. These were calculated from the acTable 11. Activity Coefficient of 

### HCI and Standard Emf 

### (E*)of Cell 

### B in Sulfate-free Seawater. Constants of Equations 

### 9,10,and 

### 12

t, "Ca A B AE, mV
5 0.4952 0.08830 0.06 10 0.4988 0.08774 0.06 0.07 15 0.5026 0.08719 20 0.5066 0.08663 0.07 25 0.5108 0.08608 0.07 30 0.5150 0.08552 0.09 35 0.5196 0.08497 0.07 0.07 40 0.5242 0.08441

a At all temperatures, p = 1.394

Table 111. 

### Comparison of the Activity Coefficient 

### of 

### HCl 

### (m = 

### 0.01mol kg-') in Sulfate-free 

### Seawater with That in Solutions of Sodium Chloride at 5, 25, and 40 "Ca

f, OC I=0.381 I=0.673 I= 0.872

5 NaCl 0.743 0.745 0.758

sw 0.740 0.741 0.752 25 NaCl 0.733 0.734 0.745

sw 0.730 0.729 0.738 40 NaCl 0.726 0.724 0.734

sw 0.722 0.718 0.726

a Data in NaCl solutions from Ref. 21.

tivity of water (ZO),which is nearly invariant with temperature. In general, the correction for the departure of the water activity from unity amounted to no more than 0.03 mV.


### RESULTS
Standard Potentials.The measurements of the emf of cell 

### B containing 

### solutions of 

### HCl (molality 

### about0.01mol kg-l) 

### in syntheticseawater without sulfate are summarized in Table 

### I. Thedata cover thetemperature range 

### 5to

### 40 

### "C atintervals of 5 

### "C, and thetotal ionic strength 

### (I) varied from 0.28 to 0.88 (corresponding to salinities from 15 to 45%0). Theratio

### I/mcl in 

### all 16solutions 

### was 1.107 

### f0.0014.

Equation 3 was used toderive valuesof ylt(HC1) for the0.01



### m solution of HC1 in synthetic seawater without sulfate. Least-squares analysis of the results showed that all of the 

### data for 

### a given temperature could be expressed by the equation (of the Debye-Huckel form):

ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977 31Table IV. Electromotive Force 

### of the Cell: Pt;H,(g, 

### 1 atm) 

### I HCl 

### (m~) in 

### sw 

## I AgC1;Ag for Sulfate-Containing Seawater 

### of Three Different Salinities from 5 to 40 

### "C,in Voltsa

mH

0.010016 0.01999 0.02028 0.02991 0.02999 0.03998 0.03999 0.05006 0.05015

0.009972 0.009998 0.019996 0.02009 0.02021 0.02997 0.03090 0.03993 0.04001 0.05002 0.05041

0.009948 0.010101 0.02086 0.03000 0.03027 0.04003 0.05011 0.05019 5 

### "c 10°C 15 OC 20 OC 25 'C 30 "C 35 OC Salinity = 20.31°/oo; mC1 = 0.3253 t 0.00009 mol kg-'; mSO, = 0.016712 i 0.000004 mol kg-'
0.39110 0.39148 0.39180 0.38915 0.38976 0.39027 0.39072 0.37231 0.37256 0.37271 0.37270 0.37277 0.37272 0.37261 0.37191 0.37216 0.37233 0.37234 0.37235 0.37231 0.37218 0.36244 0.36251 0.36246 0.36229 0.36204 0.36173 0.36133 0.36241 0.36245 0.36238 0.36222 0.36198 0.36165 0.36125 0.35527 0.35517 0.35494 0.35460 0.35416 0.35365 0.35304 0.35529 0.35515 0.35493 0.35460 0.35417 0.35366 0.35306 0.34978 0.34954 0.34916 0.34868 0.34809 0.34742 0.34664 0.34974 0.34947 0.34909 0.34863 0.34806 0.34737 0.34659 Salinity = 34.99°/00; 

### me1 = 0.5691

## * 0.00019 mol kg-'; mSO, = 0.02924 i 0.000016 mol kg-'

0.37679 0.37733 0.37781 0.37826 0.37871 0.37914 0.37952 0.37684 0.37736 0.37784 0.37828 0.37872 0.37914 0.37956 0.35994 0.36011 0.36022 0.36029 0.36036



## ... ... 0.35997 0.36015 0.36025 0.36030 0.36031 0.36034 0.36031

0.34999 0.34995 0.34984 0.34959 0.34942 0.34913 0.34879 0.34928 0.34922 0.34908 0.34889 0.34864 0.34836 0.34802 0.34293 0.34273 0.34245 0.3421 0 0.34169 0.34122 0.34068 0.34290 0.34270 0.34242 0.34194 0.34162 0.34119 0.34064 0.33739 0.33705 0.33663 0.33613 0.33555 0.33491 0.33419 0.33707 0.33664 0.33632 0.33583 0.33527 0.33459 0.33385 0.35993 0.36001 0.36004



## ...

Salinity = 44.55°/00; mCI = 0.7318 i 0.00003 mol kg-'; 

### "so, = 0.03761 i 0.000009 mol kg-'

0.37076 0.37127 0.37173 0.37219 0.37259 0.37303 0.37348 0.37038 0.37089 0.37134 0.37180 0.37221 0.37263 0.37307 0.35282 0.35296 0.35304 0.35310 0.35311 0.35311 0.35311 0.34389 0.34383 0.34370 0.34354 0.34332 0.34310 0.34284 0.3437 1 0.34365 0.34350 0.34333 0.34313 0.34288 0.34262 0.33676 0.33656 0.33626 0.33593 0.33552 0.33508 0.33458 0.33127 0.33092 0.33049 0.32998 0.32942 0.32881 0.32813 0.33116 0.33080 0.33036 0.32987 0.32929 0.32869 0.32803
aThe standard emf E a was higher than that given in Ref. 6 by 0.17 mV at each temperature. 40 OC

0.39212 0.37245 0.37202 0.3608 6 0.36078 0.35235 0.35236 0.34577 0.34572

0.37997 0.37998

0.36030

0.34844 0.34765 0.34011 0.34005 0.33341 0.33306 

## ...

...

0.37398 0.37354 0.35314 0.34258 0.34236 0.33407 0.32742 0.32732

where 

### t is the temperature in 

### "C and p, 

### Bo, and B1 are adjustable parameters. Thevalues 

### oftheparameters ofEquation 9were adjusted until the sum of the squares ofthe deviations of all 122experimental values of log yk(HC1)was at a minimum. This procedure yielded p = 1.394and



### Bo 

# + Blt 

### B = 0.08885 

### - 1.11 X 

### t (10)

The values of

### A and

### B arelisted in Table 

### 11.Thelast column contains values of the mean difference at each temperature between the measured emf and that calculated by Equations 3 and 9.

It is interesting to note that the value of 1.394forp corresponds to an ion size (distanceof closest approach) of 4.24 

### 8,
at 25 "C. When purewater is the solvent, a value of 4.3 

## A has been found atthis temperature (6).

In termsof Equations 4 and 

### 5, the quantity

### E* can be defined as follows:



### E* =E

# + k log 

### rn~ 

## +k log 

### mcl

= 

### E"* 

### - 2k log y,* N 

### E"* (when

### m = 0.01) (11)

From this relationship, together with Equations 9and 10,one

can write



### E* = 

### E" 

### - 2k log rA(HC1)



### =E" 

# + 2kA11'2 

# - 2k(0.08885 

# - 1.11X t)I 1

# + 1.394I1l2 (12) This permits the calculation of 

### E* over the entire ranges of ionic strength (corresponding approximately to 

### 15 to 45% salinity) and temperature 

### (5to40 "C) covered in this study. The standard deviation calculated from 122 experimental points is 0.085 mV.

The mean molal activity coefficient of HC1 (molality 0.01 mol kg-l) in sulfate-free seawater of total ionic strength

### I can be calculated by Equation 9with the aid of thevalues of

### A and 

### B given in Table 

### 11.Somevalues of the activity coefficient at 

### 25 "C are compared in Table 

### I11 with corresponding values in solutions of sodium chloride (21).From these activity coefficients,therelative partial molal entropy of HC1 

### (rn = 0.01mol kg-l, 

### t = 25 "C) is found tobe -13.7, -12.9, and -12.3 cal

### K-' mol-' ationic strengthsof 0.3,0.5,and 0.7, respectively.

Calculation 

### of

## PHSO~ inSynthetic Seawater.Three series of measurements of the emf of cell 

### B containing solutions of HCl in synthetic seawater containing sulfate were also made

over thetemperaturerange 

### 5 to40 

### "C. The seawater solvent had a salinity of 20.31,34.99, and 44.55% andthemolality of HCl (~HC,) varied from 0.01 to 0.05 mol kg-'. The data are collected in Table IV.

If the stoichiometric molalities of totalhydrogen andtotal sulfate are mHCl and 

### rnsoa, respectively, and those of the ions

are designated by enclosing the symbols for the ions in parentheses, one can write

(13)

and the two equations for mass balance,

and

32 ANALYTICAL CHEMISTRY, VOL. 49, NO. 1. JANUARY 1977mso4= 

### (S042-)

# + (HS04-) (15)
By combining these relationships, the molality of free hydrogen ion can be expressed in terms of 

## PHSO~ and stoichiometric molalities, as follows:

where



### b = 1

## +PHSO~~SO~ - mHci) (17)

Values of 

### &sol consistent with 

### E* derived in the manner already described were obtained by the following procedure. First, a value of 

## PHSO~ in the vicinity of 12 

### (22) was assumed and (H+) calculated by Equation 16 fromthe data 

### at each of the five differentvalues of mHC1, with the aid of mso4 known from the composition of the synthetic seawater used. Next, the quantity

### E*’ was obtained from the relationship



### E*‘ =E 

# +h log mcl+ 

### k log (H+)

Thesevalues of

### E*’, which varied linearly with (H+)and which become equal to

### E* at (H+)= 0, were fitted by least-squares methods tothe empirical equation



### E*‘ = 

### E* 

# + a(“+) (19)

and the intercepts 

### E* obtained. The process was repeated until 

### a value of &so4 which yielded the value of the standard potential

### E* given by Equation 12was found.Theconstants &+so4 obtained in this way for seawater of three salinities are summarized in Table

### V. In addition,log &so4 is given in terms of the formal ionic strength 

### I and the thermodynamic temperature 

### T by
log 

### = 647.59/T 

### - 6.3451

# + 0.019085T



# - 0.520811/2 (20)

The standard deviation from regression is 0.0021 in log

Thevalue of 11.92at

### a salinity of 35%0 and temperature of 25 “C given in Table 

### V can be compared with 12.08 f 0.20 from the measurements of Culberson, Pytkowicz, and Hawley (22) and with 11.33 f 0.38 from the work of Dyrssen and Hansson (23). In all three investigations,pH measurements

were standardized in sulfate-free synthetic seawater.

Hansson (24) has suggested thatpH in seawater be defined in terms of the molality (or moles per kilogram of seawater) of the “total hydrogen ion”. 

### His pH unit, designated pH(SWS), is thus PHSO4-

pH(SWS -log [(H+)

# + (HS04-)] (21)

Standard potentials

### EH* for determiningpH(SWS)fromthe emf of cell 

### B are related to our 

### E

## * by
(22)

The association constants of Table V and Equation 20 are based on the scale ofmolality. They are lower when expressed in termsof moles per kilogram of seawater.Under these conditions,the values of Table Vwould have tobe multiplied by 0.980,0.965,and 0.955 at salinities of 20.31,34.99,and 44.55%0, respectively, to obtain values related to the seawater scale.

DISCUSSION
The standard potentials presented here offer a suitable basis for the establishment of a meaningful scale of hydrogen in concentration for seawater of salinities in therange studied, namely 20 to 45%. With the aid of 

### E* from Equation 12,
measurements of the emf of cell 

### B containing dilute buffer solutions in synthetic seawater without sulfate can yield values of pmH(S) with which pH meters can be standardized.They

can also lead to values of dissociation constants for weak 

### EH* = 

### E* 

## + h 1% (1

## + PHS04mS04) Table V. Values 

### of the Association Constant

## OHSO, in Synthetic Seawater 

### of Three Salinities 

### from 5 to 40 OCa

Salinity (O/W)

t,OC 20.31

5 9.02 10 10.27 15 11.64 20 13.04 25 15.23 30 17.58 35 20.01 40 23.10

a Scale of molality. 34.99 7.12 8.06 9.03 10.27 11.92 13.73 15.63 18.02 44.5 5 6.16 6.97 7.88 9.02 10.40 11.93 13.63 15.73

electrolytes in seawater, based on emf measurementsof cells without liquid junction as well 

### as on pmH measurements.



### A detailed analysis of therelationships setforth in earlier sectionsof this paper nonetheless emphasizesthat an exact determination of the molality of free hydrogen ion in 

### abuffer solution prepared from synthetic seawater (with 

### or without sulfate)is possible onlywhen thebuffer constituents exert no abnormal specific effect on T*(HCl) in the medium. Although 

### it has been shown that, 

### at constant ionic strength, addition of 0.01 m HCl in place of anequivalent amountof NaCl alters 

### E* by only 0.04 mV in the seawater of composition corresponding to 35%0 salinity, one can only hope that the effect of

a dilute buffer substance of molality 0.01 mol kg-l is also small;no proof of this point 

### is forthcoming.

It is appropriate to consider here whether the replacement of a part of the NaCl in the synthetic seawater by sulfate without altering the ionic strength 

### is likelytochange r*(HCl) by an appreciable amount.

### Ata salinity of 35%0, the molality of Na2S04 is 0.02926 mol kg-l in natural seawater. Due to extensive ion pairing, however, the molality of free 

### S042- is only about 0.01 mol kg-l and thus contributes about 0.03 to the ionic strength. Hence, the ionic composition of the sulfate-containing seawater is in effect altered from that of the sulfate-free seawater, in which 

### E* was determined, by roughly 

### 5%. From Table 

### 111,itis evidentthat replacement of all of the Mg2+, Ca2+, and 

### K+by Na+ in the synthetic seawater without sulfate (a change of 31% in ionic composition) changes y*(HCl) by only 0.003to0.008. Ithas been suggested 

### (7,25) that activity coefficients in constant ionic media are relatively unaffected when the concentrations of reactants are less than about 10%of the concentrations of the medium ions.

Finally, it must be borne in mind that the composition of the standard reference solutions 

### S can never match exactly that of the unknown solution 

### X. It appears from earlier work 

### (1,25) that the ionic compositions of two media of identical ionic strengthcan differ considerably without an appreciable increase in the residual liquid-junction potential. These considerations make it seem likely that standards prepared in sulfate-free synthetic media offer 

### a successful means of setting up a useful experimental scale for determining pmH in natural seawater.

ACKNOWLEDGMENT K.H.K. expresses his thanks to the University of Malaya for the award of study leave.

LITERATURE CITED

(1) R. G. Bates and J. B. Macaskill, in “Analytical Methods in Oceanography”. T. R.P.Gibb, Ed., Adv. Chern. Ser., 147, 110-123(1975). (2) R.G. Bates, in “The Nature of Seawater’’: E. D. Goldberg,Ed., “Physical and Chemical Sciences Research Rpt. 1

, Dahlem Konferenzen, Berlin, 1975, pp 313-338. (3) R. G. Bates and C. H.Culberson, in “Fossil Fuel Carbonates”, N. R. Andersen. Ed., in press.

ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977 33(4)R. G. Bates, "Determination of pH". 26 ed., John Wlley and Sons, New York, 1973,Chap. 4. (5)H. S. Harned and R. W. Ehlers, J. Am. Chem. Soc.. 54, 1350 (1932); 55, 2179 (1933). (6)R.G. Bates and V. E. Bower, J. Res. Natl. Bur. Stand.,53, 283 (1954). (7) L. G. Sillen, in "Equilibrium Concepts in Natural Water Systems", W. Stumm, Ed., Adv. Chem. Ser., 67,45-56 (1967). (8) D. Dryssenand L. G. SillBn, Tellus, 19, 113 (1967). (9) P. J. Reilly, R. H. Wood, and R. A. Robinson, J. Phys. Chem., 75, 1305 (1971). (IO) R. A. Robinson and R. H. Wood, J. Solution Chem., 1, 481 (1972). (11)K. S. Pltzer, J. Phys. Chem., 77, 268(1973). (12)M. Whitfield, In "Chemical Oceanography", J. P. Riley and G. Skirrow, Ed., 2d ed., Vol. 1, Academic Press, New York, 1975,pp 43-171. (13) I. Hansson, S.Ahrland, R. G. Bates, G. Biedermann, D. Dyrssen, E. Hogfeldt, A. E. Martell,J. J. Morgan, P. W. Schlndler, T. B. Warner, and M. Whitfield, in "The Nature of Seawater", E. D. Goldberg, Ed., "Physical and Chemical Research Rpt. l", Dahlem Konferenzen, Berlin, 1975,pp 263-280. (14)D. R. Kester, Thesis, Oregon State University, 1970. (15)D. R. Kester and R. M. Pytkowlcz, Geochim. Cosmochim.Acta, 34, 1039 (1970). (16)W. C. Somerville and A. D. Campbell, Mikrochim. Acta, 991 (1963). (17)Reference 4,Chap. IO. (18)R. G.Bates, E. A. Guggenheim, H. S. Harned, D. J. G. Ives, G. J. Janz, C. B. Monk, J. E. Prue, R. A. Robinson, R. H. Stokes, and W. F. K. WynneJones, J. Chem.Phys., 25,361 (1956); 26,222 (1957). (19) R. Gary, In "Electrochemical Analysis: Studies of Acids, Bases, and Salts by Emf, Conductance, Optical, and Kinetic Methods", R. G. Bates, Ed., NaN. Bur. Stand. (US.) Tech. Note, 271,28 (1965). (20)R.A. Robinson, J. Mar. Biol. Assoc. U.K., 33, 449 (1954). (21)J. B. Macaskill, unpublished measurements, University of Florida, 1976. (22)C. Culberson, R. M. Pytkowlcz, and J. E. Hawley, J. Mar. Res., 28, 15

(23)D. Dyrssen and I. Hansson, Mar. Chem., 1, 137 (1973). (24) I. Hansson, Deep-sea Res., 20, 479 (1973). (25) G. Bledermann, in "The Nature of Seawater", E. D. Goldberg. Ed., "Physical and Chemical Research Rpt. l", Dahlem Konferenzen, Berlin, 1975,pp 339-362. (1970).



### RECEIVED for review August 18,1976.Accepted September 20, 1976. This work was supported in part by the National Science Foundation under Grant DES75 03635.



# Bioassay 

# of Nystatin 

# Bulk Material by 

# Flow Microcalorimetry

Anthony E. Beezer," Roger 

### D. Newell,' and 

### H. J. Valentine Tyrrell

Chemistry Department, Chelsea College, Manresa Road, London S W3 6LX, England

A flow mlcrocalorimetrlcprocedure has baen developedfor the bloassay of nystatin. The antlblotic is assayed by monitoring thb effect of the antibiotic on a respiring culture of Saccharomyces

### cerevisiae.The yeast inocula are recovered for use from storage in liquld nitrogen. When compared wlth the classlcal agar plate dlffuslon method, the microcalorimetrlc procedure is more reproducible 

### (f3.5% compared with 

### f5-10%), more sensitive (0.5 unit mi-' compared with 20 units ml-'), more rapld(1h comparedwlth 16 h per sample) and, In addition, is simple and capable of automation.

Microcalorimetric methods of analysis have been extensively reviewed recently (1--4),particularly with respect to biochemical systems. However, the potential of analytical applications of microcalorimetry in the microbiological area has yet tobe fully realized. Reports exist of several successful investigations into the enumeration of viable bacteria by microcalorimetry including diaghosis of bacteriuria 

### (5);investigation of bacterial contamination of stored milk (6); identification of bacterial contamination of vacuum packed food 

### (7); preparation, storage, and assay of frozen inocula (8). In addition, evidence has been produced todemonstrate that microcalorimetric methods can be used in the identification of bacteria and yeasts by virtue of the complex but reproducible thermograms obtained from growth in complex media

asforeshadowed by Rubner in 1906(9)andlaterby Prat (10). The modern microcalorimetric technique (for a review see (11)) hasbeen used 

### to studythefamily

### Enterobacteriacea (12, 13),andthethermograms of 200 clinically significant microorganisms have been reviewed (14).However, no reports exist

on the analytical use of the microcalorimetric response of 

### a microorganism to some applied interacting agent, e.g., antibiotic, detergent, etc. Ithas been shown (10)thataddition of streptomycin to growing cultures of

### Escherichia coli reduced theheat outputby about 

### ahalf within 

### aperiod of 2h. Further qualitative results on this system have been summarized by

Present address,Department of Oral Medicine and Pathology, Guy's Hospital Medical School, London 

### SE19RT, England. Calvet and Prat (15). More recently, ithasbeen shown that the addition of ampicillin to

### a growing culture of

### Escherichia coli in a complex medium significantly affectsthethermogram derived from a flow microcalorimetric experiment within 

### 1 h (16). These reports suggest the possibility of an analytical bioassay procedure, based upon microcalorimetry, for antibiotics. However, any technique based upon flow microcalorimetry would have to demonstrate significant advantages

over the currentwell-established procedures. Factors of importance are reproducibility, precision, simplicity, and the speed of assay. 

### A further possibility is that of automation, inherent in any flow procedure.

The heterogeneous group of antibiotics known 

### as the polyenes is characterized by a macrolide ring containing a number of conjugated double bonds (from 3-7) and a varying number of hydroxyl groups (17).Boththese features are essential for biological activity. These antibiotics are active against fungi, particularly yeast forms and eukaryotic 

### organisms,but arenot generally active against prokaryoticcells (this distinguishes the polyene macrolides from other macrolide antibiotics).Many polyenes have been isolated, but the majority are too toxic for clinical use and only nystatin, amphotericin B, candidin, and hamycin have found useful clinical application.

The polyenes are believed to bind with the sterol present in the membranes of sensitive cells 

### (18)leading to the formation of pores 

### (19, 20). The subsequent death of the microorganism is preceded by the leakage of cellular material.

The extent of membrane disruption is dependent on the specific polyene antibiotic,its concentration, thepreparation conditions of the inoculum and the experimental conditions used. The material leaked from the cell ranges from simple constituentsof small size,such as 

### K+andNH4+ 

### (21)tolarger,

morecomplex molecules such

### as nucleotides andproteins (22). The overall effect of the addition of antibiotic to 

### a yeast inoculum was feltlikelytobe morerapid thanthatwhich would be observed with other groups of antibiotics such as those which, for example,interfere with protein synthesis (23). The polyenes were, therefore,regarded asparticularly suitable for

a detailed investigation of antibiotic assay by 

### flow microcalorimetry. The degenerate heptaene nystatin (a tetraene

34 ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977