EFFECT OF TEMPERATURE ON THE pH OF SEAWATElR’ Joris M. Gieskes2 Institut fiir Meereskunde, Kiel, Germany ABSTRACT The temperature coefficient of the pII of seawater, calculated from existing data on the carbonate system in seawater, is confirmed experimentally as +0.0114 pH units per degree Celsius at 1 atm pressure. Although pH measurements with a given system are reproducible to -c-O.005 or 20.006 pH units, direct pH measurements on seawater are accurate only to about kO.02 pII units; hence computations of components of the carbonate system are uncertain by 1% in bicarbonate and 5% in carbonate. These uncertainties can be halved if pH values are derived from precise determination of other components of the carbonate system, such as alkalinity and total Con. on the NBS plE-I scale (Skirrow 1965). If measurements are carried out using high ioaic strength standards, then presumably the values of the apparent constants would have to be adjusted also. This adjustment would depend on differences due to’ salt effects on the electrode system. The data of Smith and Hood (1964) indicated that differences as high as apH = 0.012 can occur due to such salt effects. In areas where there are large variations in salinity of the seawater, such as the Baltic Sea, the use of high ionic strength buffers would become impractical. In such areas the NBS standards should bc used. Dyrssen and Sillen (1967) asked for a new series of equilibrium. constants, determined in such a way that all species of the carbonate system can be calculated without having to rely on pH measurements. Li (1967) used measurements of total carbon dioxide and of the partial pressure of CO2 to calculate in situ pH, using Lyman’s (1956) apparent dissociation constants, But until new constants are available, the data of Buch or Lyman will have to be used for calculation of the carbonate spcties using the pQI as determined directly o,r indirectly, In practice, the “pH of seawater is mcasured at a constant temperature on board ship. The in situ value of the pH must ’ This research was supported by the Dcutsche Forschungsgcmeinschaft. then be computed. Recently Culbcrson 2 Present address: Scripps Institution of Occanand Pytkowicz ( 1968) using the technique ography, La Jolla, California 92037. I wish to of Disteche and Disteche ( 1967) deterthank Mr. Jiirgen IIeinemann for carrying out the pH measurements. mined coefficients for the pressure correc679 INTRODUCTION The determination of the pH of seawater has always been a rather difficult problem. Bates ( 1963) mentioned that the measured pH “value” in saline solutio,ns is probably not a reliable indication of the actual value of the hydrogen ion activity. Only for dilute solutions of simple solutes, whose pH values match closely that of a standard, can the “pH be regarded as an approximate measure of the hydrogen ion activity of the solution. Spencer (1965) realized this difficulty and proposed the establishment of a suitable operational scale for the pII of seawater using high ionic strength standards. Smith and Hood (1964) described such buffer solutions, and they used seawater as a secondary buffer system. Usually the value of the pH of seawater is o’btained to gather information on the carbonate equilibria in this medium, For this, use is made of the apparent dissociation constants as reported by Buch (1951) or Lyman (1956). The latter constants are based on pH measurements using National Bureau of Standards (NBS) standard buffer solutions, Buch’s data are also based on 101~ ionic strength buffers using the Sorensen pH scale. These apparent constants can be converted into a set based 680 JORIS M. tion of pH to the in situ pressure. In this paper, the temperature dependence of the pH of seawater will be discussed. CORRECTION OF THX pH TEMPERATURE TO IN an (HCW) ( CO2 + H&OS) ’ (1) and K’ aI(ca2-) 2 = (HCOs-) ’ in which K’ 1 = first ap!‘arent dissociation constant, K’ 2 = second apparent dissocia. tion constant, aI1 = hydrogen ion “activity” (based on NBS scale), and the concentrations of the various ionic species are expressed as molality. For total carbon dioxide X0, and also CA -1 X02 (an + 2K'2) K$ =A. aTr2+ aII Kfl + Kfl Kf2 (8) SITU Correction of the pH as measured in the laboratory to the in situ temperature is usually carried out using the coefficients reported by Buch and Nynas ( 1939 ). These values, however, are based on the older set of data of Buch ( 1938). In the following, I have calculated new correction factors based on the recent data of Lyman (1956) and also on the revised data of Buch ( 1951). I have used the equations for the dissociation coastants for the carbonic acid system as defined by Lyman ( 1956) : K’l = GIESKES = (H2603 + CO,) + (HC03-) + (co32-), (3) and for carbonate alkalinity CA = ( HC03-) + 2( COs2-) . (4) ‘The amounts of the various species can then be calculated from the following equations: e2 .(I-I&03 + CO2) = aE12+ aII K’I + K’I K’2 x so2 ; I(HCOs-) = aa K’l X02; aI.? + aII El + Kf11C2 (6) (CO32-) = Kfl K12 x02; aI? + aEJG + IQ1 Kf2 (7) This formula is similar to the one used by Buch and Nynas (1939) to calculate their temperature coefficients. In the pH mcasurements, care is taken that ZC02 remains unchanged and that a value of A can be caIcuIated for any vaIuc of the activity arI at a temperature tl. This value of A can then be used to, calculate the corresponding arI at a temperature t2, provided that the apparent equihbrium constants KI1 and K'2 at that temperature are known. The results of Buch and Nynas (1939) were obtained in this manner. This caIculation, of course, assumes that no change occurs in the value of A. However, although X02 remains constant, and also the total alkalinity is nonvariant, the carbonate alkalinity will change with temperature. The change in pH will primarily be due to a change in the carbonate equilibria. Hence the ratio A does not remain constant, and the USC of equation ( 8) for calculation of the temperature coefficients is not entirely justified. Changes will also occur in the borate equilibria, but these will not have to be considered in the subsequent treatment because the apparent constants of the carbonic acid system. have been obtained with seawater after correction for the borate effect. Therefore, only the changes in the carbonate equilibria will be considered, using the reported constants as functions of temperature and chlorinity. With an increase in pH value, there will be a change in free CO2 concentration ( co2 + I-I2CO3 >, and also small changes in the amounts of HC03- and of COs2-. These will, of course, cause a change in the carbonate alkalinity, even though the total alkalinity remains unchanged. From equation (4) it is seen that if I-I&O3 forms only bicarbonate, then a(CA) = -8 ( H2C03) on the above basis. Therefore, tion (5) (9) from equa- TEMPERATURE TAI)I,E 1. PH 7.4 7.6 7.8 8.0 8.2 8.4 Temperature coefficients EFFECT for pH in seawater B&N* Buch 1 Buch 2 Buch 3 0.0088 0.0095 0.0103 0.0110 0.0115 0.0118 0.01009 0.01093 O.Oll.67 0.012.14 0.01238 0.01249 0.00994 0.01076 0.01155 0.01207 0.01234 0.01247 0.01257 0.01257 0.01258 0.01258 0.01258 0.01258 ON 681 pII of Cl = 16%; tl = 2OC and b = OC Lyman 1 0.00781 0.00884 0.00996 0.01077 0.01120 0.01141 Lyman 2 Lyman 3 0.01138 0.01145 0.01150 0.01153 0.01154 0.01156 0.01127 0.01127 0.01128~ 0.0'1128 0.0,1128, 0.01128 * B&N = Buch and Nyniis (1939). Buch 1 = Buch (1951) on Siirensen pH scale, equation (8). Buch 2 = Buch ( 1951) on NBS pH scale, equation (8). Buch 3 = Buch ( 1951) NBS pH scale, equation ( 15). Lyman 1 = Lyman (1956), equation (8). Lyman 2 = Lyman (1956), equation (11). Lyman 3 = Lyman (1956), equation (15). 1 (10) 1 au2 1 aH2 WA> _ aIr2 + aEIKfl + Krl K’2 SC02 -[ t, m2 aI12+ aII K’1 + K’JC2 =x- t,’ If tl > t2, that is, a (CA) > 0, then at temperature t2 a&A) SC02 = aI12 =A+X- (aH + 2K’s) K’l + aH Kfl + K’JC2 t, Of course, I have assumed that the ratio as given in equation (12) remains constant with temperature, but this is true to a good When equation ( 14) is inapproximation. troduced into ( 11)) the following equation can be derived after some rearrangcmcnt of the terms: 1 (11) 1 aI13 + alI [ K’l - DK’2 ( 1 - X) ] + an K’l K’2 x[~-D(~-X)]+XDK~(K’,)~=O. t, &I2 aH2 + aH K’l + Kfl Kf2 t,’ However, if IICOg is formed, then solmc COS2- will also be formed. This will lead to yet another change in the carbonate alkalinity. From equation ( 2)) (COs2-) =-=-K$ K’2 (HCOS-) an K’1 I> t, an2 -I- &T Krl i- Kfl K’2 (CA)tl+ aII2 aI12 + aIr Kfl + Kfl Kf2 Kr2 an ’ This means that a good approximation taken from the following. If HC03- = I-1’ + COS2-, (12) is (13) then for every change of -7 in ( HC03-) there would be a corresponding change of +y in the carbonate alkalinity, cf. equatioa ( 4). Therefore, for every change in (H2C03) there will be a change in ( HC03-) and also in ( COS2-). The latter amount will be determined by equation (12). Thus (15) In this equation A, X, and D [D = (A + X - 1)-l] are calculated at temperature tr, and the other constants are all at temperature t2. If the hydro’gen ion activity at temperature tl is known, the hydrogen ion activity at temperature t2 can be calculated from this equation ( 15). This is best achieved using a simple computer program. The results obtained with equations (S), ( 11 ), and ( 15) are compared in Table 1. Fro,m this table it is clear that large differences indeed occur if corrections are not made for the change in carbonate alkalinity. If equation (15) is used, identical results are obtained over the entire range of pH. Table 2 summarizes the results of the calculations from equation ( 15). There is no need to present the various initial pI1 values, because these values are all equal (last column, Table 1). The data are based on Lyman’s constants, From the results of Table 2, it is con- 682 JORIS TABLE 2. Temperature coefficients M. GIESKES (x10’) for the pH of seawater, O-21%0 Cl Temp (“C) 2, 0 1 4 9 16 17 18 19 20 21 Avg 20-O 20-5 20-10 20-15 25-O 25-5 25-10 25-15 25-20 1207 1247 1167 1207 1128 1118 1130 1128 1143 1177 1143 1196 1170 1210 1136 1130 1137 1143 1157 1183 1094 1184 1174 1214 1175 1155 1165 1175 1185 1225 1068 1148 1188 1129 12.09 1228 1229 1229 1249 1309, 1158 1206 1166 1206 1150 1134 1154 1162 1174 1206 1097 1157 1167 1208 1162 1148 1163 1182 1193 1218 1049 1136 1170 1210 1197 1170 1190 1216 1223 1257 1014 1094 1175 1214 1224 1215 1235 1265 1275 1315 0988 1068 1188 1228 1269 1229 1269 1329 1329 1350 1165 1160 1180 1200 1170 1170 1180 1200 1230 eluded that the factor 0.0118 -t- 0.0906 can be considered as the temperature coefficient for all ranges of temperature and for all chlorinities. The data show slightly larger deviations fo,r the small temperature intervals, but of course in these cases the calculations become more sensitive to errors in the apparent dissociation constants. If the data of Buch ( 1951) are used for these calculations after a correction to the NBS pH scale, the following temperature coefficient is obtained: 0.0110 -I 0.0009. If the data of Buch and those of Lyman are considere,d to be of more or less equal quality, I estimate that a temperature coefficient of 0.0114 would be representative. The pH at the in situ temperature could then be calculated from: pH (in situ temp t2) = pHt, + 0.0114(tl - t2). (16) Li (1967) reported a similar equation for the range of oceanographic interest, but my calculations show that this formula is applicable for all salinity and temperature ranges. In view o,f the uncertainty oE *O.OOlO in the temperature coefficient, the accuracy of the correction will not be better than about 20.02 pH units if tl and t2 differ by 20C. Notwithstanding the limitations on the accuracy of the in situ pH value, for a series of measurements using the same standardization, the relative accuracy will be as good as the reproducibility of the electrode system. EXPERIMENTAL RESULTS A series of measurements of the temperature coefficient of the pH of seawater was made here to test the calculated value. The measurements were carried out in a water-jacketed cell using a glass clectrode and a calomel reference electrode in co’njunction with a pH meter. The instrumentation was standardized at several temperatures using the secondary pH ( S ) standards of Bates ( 1963). Because electrode pairs may not be linear over the complete pH scale, the instrument is standardized with his 1: 1 phosphate buffer is estabsolution, and the slope AE/A~H lished with his 0.01 m borax buffer solution, For this, either the ApH knob or the compensation potentiometer temperature can be used, The 1:3.5 phosphate buffer solution of Bates is measured to check linearity. Palitzsch (1922) described two solutions, of borax and of boric acid respectively, that can be used for preparing secondary standards. On a 1: 1 basis (0.025 M borax, 0.1 M boric acid) this buffer solution has a pI1 of about 8.5 at room temperatureclose to the maximum pH value of seawater, The temperature coefficients of this buffer system have been investigated by Brujewicz and Karpova (1932). Several measurements of the pH of this buffer solution were made here, using the standardizing technique as described above. The pH values of the Palitzsch buffer and of the 1: 3.5 phosphate buffer are given in TEMPERATURE acicl TABLE 3. The $.I values of the borax-boric solution of Palitzsch and of the 1:3.5 phosphate solution of Bates at various temperatures EFFECT ON TABLE 4. 683 PH Change in pH with temperature buffer solution of Palitxsch . Ap.1-I FhZ ?;e~p 0 1 : 3.5 phg7w~;k 3 25 20 15 10 7.413 7.429 7.448 7.472 1 : 3.5 phosphate measured 7.413 7.428 7.448 7.472 * Deviations are standard 10 measurements. -t- 0.001" k 0.001 Z!I 0.000 -c 0.000 deviations Palitzsch measured 8.481 8.513 8.555 8.596 + IL + IL 0.004 0.002 0.003 0.002 TAB,LE 5, Temperature TZSP PH reports 0 TeFy research 25 20 15 10 -0.032, 0.000 3-0.042 +0.083 Brugay;o;md < -0.030 0.000 $0.036 +0.074 based on at least Table 3, together with the literature values of the latter. The change in pH value with temperature, taking the value at 26C as the reference value, is recorded in Table 4. The data of Brujewicz and Karpova (1932) are reported for comparison. From this table it is clear that agreement between the two sets of data is good, especially in view of the fact that the data of Brujewicz and Karpova are based on interpolated data ( Koroleff, unpublishcd3). The pH value of the Palitzsch buffer solution can serve as an additional check on the linearity of the electrodes. The temperature coefficient of the pH of seawater was determined by the following procedure. From a large storage bottle, s The Institute in Helsinki as 8.507 at 20C. of the this pH value coefficients six water samples were drawn into glassstoppered dark brown bottles. The pH instrumentation was standardized at some fixed temperature as described above, and the pH of three seawater samples was measured. Then the instrumentation was standardized at some other temperature, and the remaining three samples were measured. In this manner, the real situation was approximated as well as possible. Measurements were carried out for seawater ranging in salinity from 7 to 35% ( Table 5). The average value of the temperature coefficient is 0.0112 -t- 0.0015 pH units/“C The deviation fro,m this average value is recorded in the last column of Table 5. The reproducibility o,f the electrometric pH measurement has been discussed by Pytkowicz, Kester, and Burgener ( 19661) and was found to be *O.OO& pH units. Gieskes (1969) discussed the results from some intercalibration exercises of the pH for seawater ranging in salinity =EP PH 10 10 10 10 10 15 15 8.074 7.400 7.316 7.656 8.116 8.008 7.640 20 20 20 20 20 25 7.942 7.374 7.185 7.545 7.981 7.893' 7.542 15 8.052 7.615 25 7.918 7.508 15 15 15 15 20 20 20 20 7.600 7.580 7.562 8.002 7.945 7.297 7.246 7.983 25 25 25 20 25 25 25 25 7.496 7.478 7.472 7.943 7.890 7.252 7.196 7.920 saF 7;2 7:07 7.77 14.94 35.20 7.12 14.94 35.20 10.78 10.78 10.78 10.78 7.12 7.12 7.07 7.77 35.20 from 7.12 to 35.20%, Coee;ci;nt 0 Deviation 0.0132 0.0126 0.0131 0.0111 0.0135 0.0115 0.0098 0.0134 0.0107 0.0104 0.0102 0.0088 0.0118 0.0110 0.0090 0.0100 0.0126 +0.0020 +0.0014 +0.0019 -0.0001 +0.0024, +0.0003 -0.0014 +0.0022 -0.0005 -0.0008 -0.0010 -0.0024 +O.OOOS -0.0002 -0.0022 -0.0012 f0.0014 684 JORIS M. measurement and concluded that the reproducibility is *0.005 pH units, but that the accuracy is not better than -+O.O2 @I units. Even with an accuracy of eO.01, the deviation in the temperature coefficient fo’r a temperature interval of 1OC would be -+0.002. The standard deviation of 0.0015 in my measurements, therefore, is within the accuracy of the pH measurements. The experimental data are in good agreement with the calculated data, and I propose, therefore, that the coefficient 0.0114 be accepted as the temperature coefficient of pH in seawater. Equation ( 16) can then be used for the correction oS pH to in situ temperature. DISCUSSION From comparison of the calculations and the measurements, it appears that equation (16) is adequate to correct the “pH of seawater as measured in the laboratory to the in situ temperature. The calculations also indicate that owing to the uncertainty in the temperature coefficient the accuracy of the in situ “pH value cannot be better than 20.02 pH units. With very careful pH measurements, therefore, the pH value in situ will have an uncertainty of about +0.02 pH units or more. As a consequence of this uncertainty, the concentrations of the carbonate species will be uncertain to 1% in the bicarbonate, and to 5% in the carbonate ion concentrations. Estimates of the degree of saturation of calcium carbonate in the ocean, therefore, cannot be better than to at least 5%. Keeling and Bolin (1968) also discussed the sensitivity of the carbonate system to pH. Li ( 1967) calculated the pH of seawater from measurements of total carbon dioxide and partial pressure thereof. The calculated pH at the equilibration temperature is then corrected to the in situ value using an equation similar to equation ( 16). Also a pressure correction was carried out. Because of the uncertainty of the coefficient of equation ( 16), however, the accuracy in the estimation of pI1 is not greatly enhanced by this procedure. J. Edmond (unpublished) made accurate determinations of total alkalinity and total carbon GIJZSKES dioxide of seawater using an improved version of the method of Dyrssen ( 1965). These quantities are invariant with pressure and temperature, and they can be used to calculate in &u pH value, For this, the apparent dissociation constants of either Buch ( 1951) or Lyman ( 1956)) after due correction for pressure ( Culberson and Pytkowicz 196S), can be used. This method may yield pH values that are accurate to -to.01 pH units. The data for total alkalinity and X02 can also serve to calculate the pH value at 25C. The latter can be checked by means of a pH measurement using either NBS standards or the high ionic strength buffers of Smith and Hood (1964). In areas with large variations in salinity, the measurement of total CO2 becomes rather involved; also, estimates of pH are required for purposes o,thcr than the calculation of carbonate concentration. In such areas, the use of high ionic strength buffers becomes impractical, and the use of NBS buffers or their equivalents should be advocated. No greater accuracy, however, than about kO.02 pH units should be expec.ted. REFERENCES BATES, R. G. 1963. Determination of pH. Theory and practice. Wiley, New York. 435 p. 1932. BRUJEWICZ, S. W., AND N. P. KARPOVA. Abhangigkeit des pH von der Temperatur in Biochem. Z., 251: 60-69. Puffcrlosungen. Bum, K. 1938. New determination of the second dissociation constant of carbonic acid in Acta Acad. Aboensis, Math. Phys., sea water. ll(5): 18 p. 1951. Das Kohlensaure Glcichgewichts-. Havsforskingsinstitusystem im Meerwasser. tets Skrift Helsingfors, No. 151. 18 p. -, AND 0. NYNXS. 1939. Studien iibcr neuere pH-Methodik mit besonderer Bcriickdes Meerwassers. Acta Acad. sichtigung Abocnsis, Math. Phys., 12(3): 41 p. CULBERSON, C. H., AND R. M. PYTKOWICZ. 1968. Effect of pressure on carbonic acid, boric Limnol. acid, and the pH in seawater. Oceanog., 13: 403-417. DISTI~HE, A,, AND S. DIST~IIE. 1967. The effect of pressure on the dissociation of carbonic acid from measurements with buffered J, Electrochem. Sot., glass electrode cells. 114: 330-340. DYRSSEN, D. 1965. A Gran titration of seawa- TEMPERATURE ter on board Sagitta. Acta Chem. Stand., 19: 1265. -, AND L. G. SILLEN. 1967. Alkalinity and total carbonate in seawater. A plea for pressure temperature indcpendcnt data. Tellus, 19: 113-121. GIESKES, J. M. 1969. The intercalibration of the pH measurement in Copenhagen 1966. UNESCO Tech. Paper Mar. Sci. 9. 90 p. KEELING, C. D., AND B. BOLIN. 1968. The simultaneous use of chemical tracers in oceanic studies. II. A three reservoir model of the North and South Pacific Oceans. Tellus, 20 18-54. LI, Y.-H. 1967. The degree of saturation of CaC03 in the oceans. Ph.D. Thesis, Columbia Univ., New York. 176 p, LYMAN, J. 1956. Buffer mechanism of seawater, Ph.D. Thesis, Univ. Calif., Los Angeles. 196 p. PALITZSCH, S. 1922. Manuel pratique de l’ana- EFFECT ON pH 685 des lyse de l’eau de mcr. III. Dctcrmination ions hydrogene par la methode colorimctrique. Bull. Inst. Occanog. No. 409. 31 p. PYTKOWIUZ, R. M., D. R. KESTER, AND B. C. BURGENER. 1966. Reproducibility of pH measurcmcnts in seawater. Limnol. Oceanog., 11: 417419. SKIILROW,G. 1965. The dissolved gases-carbon dioxide, p. 227-3’22. In J. P. Riley and G. Skirrow [eds.], Chemical oceanography, v, 1. Academic. SMITH, W. H., AND D. W. HOOD. 1964. pH measurements in the ocean: a seawater secondary buffer system, p. 275-293. In Y. Miyake and T. Koyama [eds.], Recent researches in the fields of hydrosphere, atmosphere, and nuclear geochemistry. Maruzen Co., Tokyo. SPENCER,C. P. 1965. The carbon dioxide system in seawater: a critical appraisal. Oceanogr. Mar. Biol. Ann. Rev., 3: 31-57.