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.