resonance (EPR) studies and 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). 

(1 1) 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 Chemical Analysis 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 Bureau with their page numbers. This investigation 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, University of Florida, Gainesville, Fla. 326 1 1 

Evidence has been presented to show that seawater behaves 

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

or eliminating the residual liquid-junction potential encountered 

in measuring the pH of seawater systems. Under these conditions, an experimental scale of hydrogen ion concentration 

becomes a practical possibility. The standard emf of the 

H2/Ag;AgCI cell, needed to establish standard reference buffer 

solutions in seawater, has been determined In synthetic seawater at salinities from 20 to 45% and temperatures from 5 

to 40 OC. Supplementary measurements in seawater to 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. 

It was concluded that seawater of 35%0 salinity possesses the 

favorable characteristics of a “constant ionic medium”. Thus, 

the liquid-junction potential between seawater and the customary concentrated potassium chloride solution of the reference electrode is nearly constant when small changes in the 

composition of the seawater solution occur. Furthermore, the 

activity coefficients of solutes present in relatively small 

amounts in the seawater medium are stabilized, changing but 

little as the concentrations of these substances are altered. As 

a consequence of these favorable conditions, it appears 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. The practical advantage of such a scale derives both from 

the utility of the quantity CH and 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) isknown (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 cells without liquid junction, 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,l atm) I HCl(m) in sw 1 AgC1;Ag (B) 

The compositions of the solutions in synthetic seawater were 

adjusted in such a manner as to keep both the ionic strength 

and the molality of chloride ion 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 29 
H+ + S042- = HS04- 

The results of these studies, covering the 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 the mean activity coefficient of HC1 in the 

cell solutions, k is written for (RT In lO)/F, and Eo is the 

standard emf referred to the customary standard state, the 

hypothetical ideal 1 m 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 at zero molality of solutes in the pure seawater solvent 

instead of in pure water (Ti) (7,8). This change in reference 

state is accomplished through the following substitutions in 

Equation 3: 

write 

where my5 is the transfer activity coefficient or medium effect, 

which yields 

E = Eo* - k log mcl - 2k log rk*(HC1) + k pmH (5) 

Inasmuch as mcl is fixed (and known) for seawater of a given 

composition and pmH is equal to -log m (cell B) 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 to m = 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 to only 0.04 

mV at m = 0.01 mol 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 at mHcl = 0.01 instead of at rn = 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 HC1 or buffer substances), can be obtained, the value of Eo* - 2k log y+* is not 

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 to the problem. Nevertheless, 

since 2k log y** is only 0.04 mV in the presence of 0.01 m HCl 

in sulfate-free seawater, it seems unlikely that its value 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 (0.002 pH 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* pmH = ~ + log rnC1 N ___ + log ma (6) k k 

In the use of this equation, one makes the implicit assumption 

that the activity coefficient of HC1 is 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 1 is based on the use of pmH standards prepared in synthetic seawater containing no sulfate to determine pmH(X) in solutions of natural seawater of the same ionic 

strength but which contains sulfate and small amounts of other substances, for example, fluoride and borate. It is possible therefore that 

the liquid-junction potentials at the boundaries Soln S IIConc. KC1 

and Natural swl/Conc KC1 in cell A may not be identical. Earlier 

measurements have nonetheless suggested that the residual liquidjunction potential due to this difference of composition amounts to 

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

We have explored in detail the 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 to offer any real advantage over 

the former at the present time. 

At the Berlin Dahlem Conference on the Nature 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 solutions be prepared from the three salts NaC1, MgC12, and 

NaZS04 (23). In this work, a closer approximation to the composition 

of natural seawater was achieved by the inclusion of both potassium 

and calcium ions. The synthetic seawater 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 

The molality of chloride ion was 0.5691 mol kg-I, and the formal ionic 

strength was 0.7229. 

The synthetic seawater without sulfate was designed to match the 

ionic strength of the synthetic seawater containing sulfate. It contained KC1, CaC12, and MgClz at the same molalities, but the contribution to the ionic strength due to the sodium sulfate was achieved 

by increasing the molality of NaC1. The solution 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%0 are related to the molalities ma5 of the seawater given above by 

27.5109 

1000 - 1.0016s mi = m35 (7) 

The calculation of the ionic strengths (I) of the solutions not containing sulfate is straightforward, as is also the evaluation of the formal ionic strengths of the solutions containing sulfate. The latter are 

readily obtained by Equation 7, where I and 135 replace 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. The equilibrium constants of Kester and Pytkowicz (14,15) 

for the formation of NaS04- and MgS04 formed the basis for this 

calculation. To obtain values of the constants at a salinity of 44.55%0, 

it was necessary to resort to an extrapolation. The minor constituents 

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

0.01001 6 

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 

0.3 6 3 2 1 

0.36210 

0.36203 

0.36129 

0.39069 

0.38801 

0.38324 

0.38 22 2 

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 

0.3 7 7 9 0 

0.37477 

0.37175 

0.36916 

0.36781 

0.36781 

0.36643 

0.36435 

0.3 6043 

0.3 60 33 

..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-containing seawater 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) show that the 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 formal and real valugs given above, the error resulting from neglect 

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, Solutions were 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 emf E" 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 containing aqueous 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 correcting the 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 

15 0.5026 0.08719 0.07 

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 

40 0.5242 0.08441 0.07 

a At all temperatures, p = 1.394 

Table 111. Comparison of the Activity Coefficient of 

HCl (m = 0.01 mol 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 about 0.01 mol kg-l) 

in synthetic seawater without sulfate are summarized in Table 

I. The data cover the temperature range 5 to 40 "C at intervals 

of 5 "C, and the total ionic strength (I) varied from 0.28 to 0.88 

(corresponding to salinities from 15 to 45%0). The ratio I/mcl 

in all 16 solutions was 1.107 f 0.0014. 

Equation 3 was used to derive values of ylt(HC1) for the 0.01 

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 31 
Table 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 

0.01001 6 

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-' 

0.38915 0.38976 0.39027 0.39072 0.39110 0.39148 0.39180 

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 0.34 864 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 

0.3 607 8 

0.35235 

0.35236 

0.34577 

0.34572 

0.37997 

0.37998 

0.36030 

0.34844 

0.34765 

0.3401 1 

0.34005 

0.33341 

0.33306 

... 

... 

0.37 398 

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. The values of the parameters of Equation 

9 were adjusted until the sum of the squares of the deviations 

of all 122 experimental values of log yk(HC1) was at a minimum. This procedure yielded p = 1.394 and 

Bo + Blt B = 0.08885 - 1.11 X t (10) 

The values of A and B are listed in Table 11. The last 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 1.394 for p corresponds to an ion size (distance of closest approach) of 4.24 8, 

at 25 "C. When pure water is the solvent, a value of 4.3 A has 

been found at this temperature (6). 

In terms of 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 9 and 10, one 

can write 

E* = E" - 2k log rA(HC1) 

= E" + 2kA11'2 - 2k(0.08885 - 1.11 X 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 (5 to 40 "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 9 with the aid of the values of A and 

B given in Table 11. Some values 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, the relative partial molal entropy of HC1 (rn = 0.01 mol 

kg-l, t = 25 "C) is found to be -13.7, -12.9, and -12.3 cal K-' 

mol-' at ionic strengths of 0.3,0.5, and 0.7, respectively. 

Calculation of PHSO~ in Synthetic Seawater. Three series 

of measurements of the emf of cell B containing solutions of 

HCl in synthetic seawater containing sulfate were also made 

over the temperature range 5 to 40 "C. The seawater solvent 

had a salinity of 20.31,34.99, and 44.55% and the molality of 

HCl (~HC,) varied from 0.01 to 0.05 mol kg-'. The data are 

collected in Table IV. 

If the stoichiometric molalities of total hydrogen and total 

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 1977 
mso4 = (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~ inthe vicinity of 12 (22) was assumed 

and (H+) calculated by Equation 16 from the data at each of 

the five different values 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+) 

These values of E*’, which varied linearly with (H+) and which 

become equal to E* at (H+) = 0, were fitted by least-squares 

methods to the 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 12 was found. The constants 

&+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 

The value of 11.92 at 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 that pH 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 determining pH(SWS) from the 

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 of molality. They are lower when expressed 

in terms of moles per kilogram of seawater. Under these conditions, the values of Table V would have to be 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 the range 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 measurements of cells 

without liquid junction as well as on pmH measurements. 

A detailed analysis of the relationships set forth in earlier 

sections of this paper nonetheless emphasizes that an exact 

determination of the molality of free hydrogen ion in a buffer 

solution prepared from synthetic seawater (with or without 

sulfate) is possible only when the buffer 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 an equivalent amount of 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 likely to change r*(HCl) 

by an appreciable amount. At a 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, it is evident that 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 0.003 to 0.008. It has 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 strength can 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. Dryssen and 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 mlcrocalorimetrlc procedure has baen developed for 

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 (1 h compared wlth 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 to be 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 to demonstrate 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 

as foreshadowed by Rubner in 1906 (9) and later by Prat (10). 

The modern microcalorimetric technique (for a review see 

(11 )) has been used to study the family Enterobacteriacea (12, 

13), and the thermograms 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. It has been shown (10) that addition of 

streptomycin to growing cultures of Escherichia coli reduced 

the heat output by about a half within a period of 2 h. 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, it has been shown that 

the addition of ampicillin to a growing culture of Escherichia 

coli in a complex medium significantly affects the thermogram 

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 current well-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). Both these features are essential for biological activity. These antibiotics are active 

against fungi, particularly yeast forms and eukaryotic organisms, but are not generally active against prokaryotic cells 

(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, the preparation 

conditions of the inoculum and the experimental conditions 

used. The material leaked from the cell ranges from simple 

constituents of small size, such as K+ and NH4+ (21) to larger, 

more complex molecules such as nucleotides and proteins (22). 

The overall effect of the addition of antibiotic to a yeast inoculum was felt likely to be more rapid than that which would 

be observed with other groups of antibiotics such as those 

which, for example, interfere with protein synthesis (23). The 

polyenes were, therefore, regarded as particularly 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