OCEANOLOGICA ACTA 1985 -VOL. 8- W 4
~
-----·~-
The determination of pH
in estuarine waters
1. Definition of pH scales
and the selection of buffers
Estuaries
pH scales
Liquid junction
Saline buffers
NBS buffers
Estuaires
Échelles du pH
Potentiel résiduel de jonction
Tampons NBS
Tampons salins
M. WHITF1ELDa, R. A. BUTLERh, A. K. COVINGTONb
a Marine Biological Association of the United Kingdom, the Laboratory, Citadel Hill,
Plymouth PLl 2 PB, UK.
bElectrochemistry Research Laboratories, Department of Physical Chemistry, University of Newcastle upon Tyne, NE 7 7 RA, UK
*Present address: Department of Chemistry, University of Puerto Rico, Mayagüez,
Puerto Rico, USA.
Received 21/11/84, in revised form 30/4/85, accepted 30/4/85.
ABSTRACT
A consideration of the definition of pH scales for estuarine waters indicates the
importance of terms involving the hydrogen ion activity coefficient (yu) and the
residualliquid junction potential (AE1) in controlling the accuracy of the measurements
and in influencing their thermodynamic interpretation. YH is a property of the medium
only and can be estimated (at least on a conventional basis) from theoretical considerations. AE1, is, in contrast, a property of the reference electrode used and shows
considerable variability with salinity, time and electrode type. To assess the practical
significance of this variability, the performance of a variety of commercially available
reference electrodes is compared in NBS buffers and in a range of saline buffers at
25°C. A statistical analysis of the data indicates that systematic errors of the arder of
0.06 in pH can be incurred if a single buffer is used to standardise an electrode
pair over the whole salinity range. Similar differences can be observed between pH
measurements made by different electrodes on the same sample. The choice of buffers
for standardisation is determined more by practical than by theoretical considerations
and satisfactory pH measurements should be possible over the whole estuarine salinity
range using a single buffer standard provided that adequate attention is paid to the
characterisation of the electrode pair employed.
Oceanol. Acta, 1985, 8, 4, 423-432.
RÉSUMÉ
La mesure du pH en milieu estuarien. 1. La définition des échelles de
pH et le choix des tampons
La définition des échelles de pH en milieu estuarien montre l'effet important du
coefficient d'activité de l'ion d'hydrogène (yu) et du potentiel résiduel de jonction
(AE1) sur la précision des mesures de pH et sur leur interprétation thermodynamique.
YH est seulement une propriété du milieu, et peut être estimé conventionnellement par
des considérations théoriques. Au contraire, AE1 est une propriété de l'électrode de
référence et varie avec la salinité, le temps et le type de l'électrode. Pour apprécier
l'importance pratique de ces variations, nous avons comparé les performances de
quelques électrodes de référence commerciales dans les tampons NBS et dans les
tampons salins à 25°C. Une analyse statistique des résultats montre que l'erreur
systématique est de l'ordre de 0,06 en pH si l'on utilise un seul tampon pour
l'étalonnage d'une paire d'électrodes dans toute la gamme de salinité. On obtient les
mêmes écarts entre les mesures de pH effectuées sur le même échantillon avec les
différentes électrodes. Le choix des étalons est déterminé par des considérations
pratiques plutôt que théoriques. Des mesures satisfaisantes du pH peuvent être obtenues dans toute la gamme des salinités estuariennes en utilisant un seul étalon, pourvu
que la paire d'électrodes soit appropriée.
Oceanol. Acta, 1985, 8, 4, 423-432.
0399-1784/85/04 423 1 0/S 3.00/ ~ Gauthier-Villars
423
M. WHITFIELDera/.
INTRODUCTION
Procedures for pH measurement, based on standardisation in a series of dilute buffer solutions (see e. g.
Bates, 1975; Covington et al., 1983 a), have found wide
acceptance for laboratory studies and for work in fresh
water. ln· recent years particular attention bas been
paid to the problems of defining appropriate pH scales
for use in media with a constant background ionie
strength such as blood and sea water (see Culberson,
1981; Dickson, 1984). The work on sea water bas
resulted in the formulation of three distinct pH scales
based respectively on: a) National Bureau of Standards
dilute buffers [pH(NBS), Johnson et al., 1977]; b) the
total hydrogen ion concentration in sea water
[pH (SWS) Hansson, 1972]; and c) the concentration of
free hydrogen ions in sea water (pmH; Bates, 1975).
Although it is more than a decade since the first hydrogen ion concentration scales were introduced (Hansson,
1972) there remains sorne uncertainty about their practical application for field work (Culberson, 1981) and
most workers still persist with the pH (NBS) scale.
careful intercomparison of the behaviour of a range of
glass electrode/reference electrode couples in buffers
standardised on the pH (NBS) and pH (SWS) scales.
THEORETICAL BACKGROUND
National Bureau of Standards (NBS) scale, pH (NBS)
The fundamental definition of pH in terms of the
hydrogen ion activity (Covington et al., 1983):
(1)
is purely notional since single ion activities cannot be
measured and a practical or operational approach is
required. The most widely used operational definition
is based on sequential measurements in the test solution .
and in a series of NBS standard buffers (Bates, 1973)
using celis of the form:
reference electrode 1KCl (aq, concentrated)
While sorne confusion is apparent in the application of
pH scales in marine chemistry, the situation is even
Jess clear in estuarine chemistry where we are dealing
not with one ionie medium but with a continuous
gradation of ionie strength. Although the importance
of pH as a master variable in estuarine processes is
readily acknowledged and the variability of pH within
an estuary bas been weil illustrated (Morris, 1978), the
authors are only aware of one concerted attempt to
provide a consistent protocol for measuring pH in
estuarine waters (Pelletier, Lebel, 1980). In this study
the electrodes were standardised on the pH (NBS) scale
using a 1: 1 phosphate buffer (pH 6.865 at 25°C,
quoted as pH 6.825) and a potassium hydrogen phthalate buffer (pH 4.008 at 25°C). However to avoid the
long equilibration times associated with the transfer of
conventional pH electrode pairs between dilute buffers
and saline samples, a secondary saline buffer, based on
TRIS (2-amino-2-hydroxymethyl propane-1,3 diol) was
prepared with a salinity of 18 using the procedures
described by Almgren et al. (1975). This buffer was
assigned a pH (NBS) value and was used to provide a
ship-board standardisation of the pH electrode pair. A
good working precision of ± 0.005 pH was obtained
between subsamples taken from the same sample bottle.
Although they estimated their accuracy as ± 0.01 pH,
no indication was given of the extent to which systematic errors might distort the assigned pH values as the
sample salinity diverged from that of the secondary
buffer. Furthermore, the measurements were confined
to one electrode pair despite the fact that measurements
in sea water indicate considerable variability in the
performance of commercial reference electrodes
(Dickson, 1977; Culberson, 1981).
Il test solution 1glass electrode( )
2
where the double vertical !ines indicate the presence of
a Iiquid junction. lgnoring this junction for the time
being, the conventional pH in the test solution,
pH (NBS, X)*, can be related to that in the standard
buffer, pH (NBS, S) via the corresponding cell potential
differences so that:
pH(NBS),X)*=pH(NBS,S)+ E(S);:(X)'
(3)
where g=Rln 10/F=0.19841 and E(S) and E(X) are
the cell potential differences (mV) measured in the
standard and test solutions respectively. The pH values
of the standard buffers (Bates, 1973) are assigned according to the convention:
pH (NBS, S) = p (aH yz) 0 -
Altt2
•
1+Bal 112
,
(4)
where Z represents a halide ion and â is an adjustable
ion size parameter. A and B are the Debye-Hückel
constants and 1 is the ionie strength. The activity term
p (aH Yz) 0 is obtained by extrapolation of measurements
made in the dilute buffers over a range of halide ion
concentrations to mz=O. By arbitrarily fixing the same
value of â for each buffer a conventional pH (NBS)
scale is defined which is internally consistent to within
±0.005 pH. As a consequence of the conventional
nature of this pH scale, the relationship between
pH (NBS) and the properties of hydrogen ions in
concentrated salt solutions or dilute solutions of other
compositions is by no means clear eut.
When NBS buffers are used to standardise cell (2)
for estuarine measurements the difference between the
liquid junction potentials generated in the test solution,
E(J, X), and in the standard buffer solution, E(J, S),
will not be negligible so that equation (3) must be
In the present paper we will review the theoretical
background to the pH (NBS) and pH (SWS) scale with
special emphasis on the measurement of pH in
estuarine waters. Having clarified the theoretical basis
·of the measurements we will present the results of a
424
ESTUARINE pH- THEORY AND BUFFER SELECTION
modified to give the true pH on the NBS scale,
pH (NBS, X), so that:
pH(NBS,X)=pH(NBS,X)*+ .1E1 ,
gT
sely matched that of the test solution, Hansson intended to minimise the residual liquid junction potential
and to ensure rapid equilibration of the electrodes on
transfer between the sample and test solution. This
would reduce the dependency of the measured pH value
on the actual electrode couple employed.
The relationship between pH (SWS) and pH (NBS) for
a particular estuarine sample can be obtained by rdating both pH scales to the notional hydrogen ion activity scale [equation (1)] so that:
(5)
where .1E1 =E(J, X)-E(J, S). A difference in liquid
junction potential (.1E1) of only ± 1 mY is equivalent
to an error of ±0.017 pH at 25°C so that for most
purposes in estuarine waters this term cannot be ignored. Since .1E1 will depend on the physical structure of
the junction, the composition of the sample and salt
bridge solution and the temperature it is likely to be
an important source of uncertainty in estuarine pH
measurements. Consequent! y liquid junction effects will
only strictly cancel when pH (NBS) values are combined with operational stability constants (known as
"apparent" constants) also determined on the
pH (NBS) scale if the same reference electrode is used
in both sets of measurements.
/
pH (NBS, X)*= pH (SWS, X) -log fH (X),
where:
.1E
log fH (X)= log y~ (X)+ - 1.
gT
Implications for estuarine pH measurements
This brief summary of the relationships between two
pH scales for saline waters raises a number of important questions relating to the measurement of pH in
estuaries. If dilute NBS buffers are used to standardise
the electrode pairs, to what extent does the residual
liquid junction potential (.1E1, equation 5) vary from
time to time and from one electrode pair to the next?
The variability of this parameter will be directly reflected in the reproducibility of pH measurements taken
at different times or with different electrode couples.
If a single, saline buffer standardised on the NBS scale
is used as a secondary buffer (Pelletier, Lebel, 1980) to
what extent will variations in the salinity of the samples
influence .1E1 and bence introduce systematic errors
into the pH measurements?
It is not possible to answer such questions by statistical
studies of pH measurements in natural samples since
the pH of such samples cannot be determined independently. Consequently we have considered an experimental design in which the equilibrium potentials of a
number of electrode pairs are measured sequentially in
an NBS buffer and in a series of TRIS buffers made
up in fluoride-free artificial sea water.
A pH scale with a clearer conceptual significance can
be defined in terms of the total hydrogen ion concentration of the test solution so that, for sea water,
(6)
where m~ is defined by:
mHT = mHF + mHSo4 + mHF
~ m~ ( 1 + J3Hso4 m~o4 + J3HF m~)
F -
=mH.cx,
(7 a)
(7 b)
(7 c)
m~ is the concentration of free ( uncomplexed) hydrogen
ions in sea water and J3Hx is the formation constant of
the HX complex. If sea water, rather than pure water,
is considered as the solvent, the activity coefficient of
components contribu ting Jess than 1% of the total ionie
strength of the medium will be approximately equal to
unity (Whitfield, 1979, and references therein). The
pH (SWS) scale is therefore equivalent to a hydrogen
ion activity scale in the sea water ionie medium. In the
estuarine context the adoption of this concept implies,
in principle, a separate pH scale for each salinity. In
practice, the number of buffers required to cover a
given salinity range will depend upon the acceptable
accuracy of the pH measurements - the lower the
accuracy demanded the smaller the number of buffers
required.
Hansson (1973) proposed a series of TRIS buffers in
fluoride-free artificial sea water to cover the salinity
range from 10 to 40 salinity and assigned their
pH (SWS) values by a titrimetric procedure. The assigned values can be summarised ( ± 0.003 5 pH) by the
equation (Almgren et al., 1975):
pH(SWS) =(2 559.7 +4.5. S)/T
-0.552 3-0.013 91. s,
(10)
The arbitrary nature of the pH (NBS) values assigned
to estuarine samples can be reduced by direct measurement of f 8 (X) for the electrode pair in use.
Total hydrogen ion concentration scale, pH (SWS)
pH(SWS)= -log 10 m~,
(9)
EXPERIMENTAL
Solution preparation
Ali chemicals used were either BDH or Koch Light
"Analar" reagents used as obtained without further
purification. The TRIS (2-amino-2-hydroxymethyl propane-l, 3, diol) was obtained as a "Trizma" grade
reagent and the TRIS-HCI as a high purity reagent
from Sigma Chemicals. Solutions were prepared from
distilled water whose conductivity was less than 10- 6 S.
Buffer solutions of pH greater than 5.0 were prepared
with distilled water which was purged of col by
(8)
where T is the temperature (Kelvin). By preparing the
standard buffers in a medium whose composition cio425
M. WHITFIELD etal.
especialiy useful electrode for estuarine use. Although
the reference electrode design employed by Hansson
(1973) effectively eliminated liquid junction effects for
sea water measurements its use in estuarine waters is
impracticable since a series of filling solutions would
be required to cover the salinity range encountered.
A glass electrode and up to four reference electrodes
were mounted in a close-fitting plastic stopper fitted to
a 500 cm 3 beaker. Potential measurements were made
using a Data Precision digital multimeter (mode!
DP35000, 51/2 digit) fitted with an impedance·
matching amplifier. For repetitive measurements an
automated data collection and electrode switching system was used. The system was based on a HewlettPackard programmable calculator (HP 9815 A) connected to a DP3500 digital multimeter via a BCD interface. The multiplexer switching unit connecting the
electrodes to the multimeter was designed and built for
the purpose. A total of 1 minute was required for a
five-channel data cycle in which the mean of ten
readings was recorded for each electrode couple. The
experimental design employed, using only a single glass
electrode with a cluster of reference electrodes, provides
a direct and valid comparison of the performance of
the various reference electrodes in moving from one
buffer to the next. However, as the glass electrodes
were only interchanged at infrequent intervals the experiments do not provide unequivocal indication of the
contributions of the performance of the glass electrode
to the systematic errors observed.in pH measurements.
Since the response slope of the electrode pair was
monitored regularly throughout the experiments the
main contribution to systematic errors would be in the
response time of the glass electrode to the change
in solution composition. The time variability of the
electrode response was foliowed using a paraliel connection to a Linseis LS 14 flat-bed recorder. Connection
was made via a potential back-off circuit which aliowed
a 10 mV full scale on the recorder to be used irrespective of the potential of the electrode pair. Electrode
readings were considered stable when the observed drift
was less than O. 01 m Vmn- 1 ( usuali y after 2030 minutes). The foliowing discussion will therefore
focus on the influence of the performance of the reference electrodes on the reproducibility of pH measurements.
In ali measurements the cell temperature was maintained at 25 ± 0.1 oc. For the purposes of the present
study it was considered more appropriate to obtain a
statisticaliy useful data set illustrating inter-electrode
variability rather than to extend the measurements on
a few electrodes over a wide temperature range.
boiling foliowed by nitrogen bubbling. Chemicals used
to prepare the buffers were dried at the appropriate
temperatures (Bates, 1973) and thereafter stored under
vacuum in desiccators containing anhydrous calcium
sulphate.
NBS buffers were prepared according to the instructions provided by Bates (1973). Artificial sea water
media and TRIS buffers were prepared according to
the procedures outlined by Hansson (1973). However,
sorne difficulty with drifting potentials was experienced
with the O. 005 M TRIS/TRIS HCI buffers recommended by Hansson. The buffers used in this study were
therefore made up to 0.02 M TRIS/TRIS HCI concentrations to increase their buffer capacity. The ionie
strength was adjusted by removing an equivalent quantity of NaCI from Hansson's recipe for artificial sea
water. The work of Bates and his co-workers (Bates,
Macaskill, 1975; Ramette et al., 1977; Khoo et al.,
1977) indicates that the influence of such changes in
buffer composition on the pH (SWS) values will be
negligible so that the smoothed values of Hansson
(1972) can be assigned. Where no data are provided
by Hansson (5 and 15 salinity), equation (8) bas been
used to calculate the appropriate pH (SWS) values.
The individual buffer solutions were prepared from
concentrated stock solutions with a salinity of 75 by
weight dilution in stoppered glass flasks. 1 : 1 phosphate
and 1 : 3. 5 phosphate buffers were used in the pH scale
comparison experiments as these gave pH values not
too far removed from those experienced in the saline
TRIS/TRIS HCI buffers. The response slopes of the
electrode couples were tested during the series of experiments using 0.05 M phthalate and 1: 1 phosphate buffers giving a value of 99.04±0.16% theoretical slope
at 25°C (n = 17). In ali of the ensuing calculati ons a
theoretical Nernstian slope (59.157 mV per decade at
25°C) will be assumed unless otherwise stated.
Potentiometry
A selection of three glass electrodes and seven cornmonty used commercial reference electrodes (Tab. 1)
was used to assess the influence of electrode type on
the precision and accuracy of the pH measurements.
Four different examples of the Orion sleeve junction
reference electrode (catalogue number 909-01) were
tested. This electrode bas a tough epoxy body and a
carefully made sleeve junction which is readily cleaned.
These characteristics were considered to make it an
Table 1
Electrodes used in the present study.
Glass electrodes
Identifier
Reference electrodes
Type
Identifier
2
Russell
1 to 4<•l
3
Beckman
5
4
Pro bion
6
7
RESULTS AND DISCUSSION
Type
Fifty-four experiments were performed with sea water
buffers over a period of seven months for the various
electrode couples. In all, C\U fol·r hundred individual
equilibrium potential d~fferencl"" readings were recorded.
The potential difference drift from run to run did
not show a definite trend with time and the standard
deviation within a run was usualiy less than ±0.5 mV
( ±0.008 pH).
Different samples of Orion 9001 sleeve juction
Russell calomel ceramic plug
junction
Beckman silverfsilver chloride
asbestos fibre junction
Beckman silverfsilver chloride
glass sleeve j unction
(") mean value for ali electrodes identified as 4J
426
ESTUARINE pH- THEORY AND BUFFER SELECTION
other band show a much greater spread in values and
also produce larger ApH values at the lower salinities.
This greater spread may be due in part to the fact that
four different examples of this reference electrode were
used in the measurements. However, a comparison of
the behaviour of each individual 90-01 electrode over
the course of the experiments suggests that the differences are mainly a reflection of irreproducibility in the
formation of the liquid junctions in these plastic sleeve
assemblies (Whalley, 1982; Covington et al., 1984).
The ground glass sleeve (pair 37) and asbestos fibre
(pair 36) show the highest ApH values at the lower
salinities. Clearly theo, even under carefully controlled
laboratory conditions with well-buffered, temperatureequilibrated samples, large systematic errors can be
introduced into pH (SWS) measurements over the
estuarine salinity range if the electrode is calibrated in
a single saline buffer. To understand the source of these
errors we must look at the relationship between the
measurements we have described and the theoretical
treatment outlined earlier.
Performance of electrodes in artificial sea water buffers
and the determination of ApH values
Since ail of the solutions used are standard buffers it
is possible, in principle, to use any of the potential
readings to calibrate the electrode couple. The difference, ApH, between the pH values assigned by
Hansson, pH (SWS, X), and the values estimated from
such a calibration, pH (SWS, X)*, will then provide an
estimate of the errors associated with the use of a
single, saline buffer over the whole salinity range. For
simplicity we will only consider standardisation relative
to a 20 salinity buffer (Fig. 1, Tab. 3, cf Pelletier,
Lebel, 1980).
60
,.,0
.....
40
)(
:I:
c..
20
Calculation of ApH values
0
The equations describing the response of the electrode
pair in the buffer selected as standard (S) and in the
test solution may be combined to give:
<1
E(S)-E(X)
gT
-zool._--'-_J1o_ __.___z:l:-o--'-----=3o:----1-__.
-pH(SWS, S)+pH(SWS,X)
AE1
•
gT
Salinity
+log[y~(S)/y~(X)]+ -
·Figure 1
Mean pH e"ors (&pH) associated with determination of pH in buf!ers
over the estuarine salinity range using electrode pairs calibrated in a
20 salinity buffer (Tab. 2). The horizontal dashed lines indicate the
boundaries within which an accuracy of ±0.01 pH units is obtained.
The electrode pairs (glass electrode-reference electrode, Tab. 1) are
indicated as follows:
• 2-1; 0 2-5; ô. 3-5; +3-6; >< 3-7; Â 3-4; 'il 4-5; 'Y 4-4.
The broken /ines indicate theo~etical &pH values estimated from
equation (13) using the data collected in Table 3.
Curve 1: using y~ calculated by methods 1) and 2), Table 3. ·
Curve II: using y~ calculated by method 3), Table 3.
(11)
Here AE1 refers to the difference in liquid junction
potential encountered between the sample and the
saline standard buffer. On the basis of the cell potential
difference in the two solutions the operational calibration procedure would assigna pH value, pH(SWS, X)*
such that equation (3):
pH(SWS,X)*=pH(SWS, S)+ E(S)-E(X).
gT
As indicated by other workers (Culberson, 1981; Pelletier, Lebel, 1980) the precision of the measurements is
good with a standard deviation of less than 0.02 pH
in most instances and frequently less than 0.01 pH
(Tab. 2). However, despite the internai consistency of
the individual electrode pairs, there are large systematic
differences between the pH errors displayed by the
different electrode pairs. The systematic nature of these
errors is clearly seen in the plot of ApH versus salinity · .
(Fig. 1) where ApH values as large as 0.06 are observed
at low salinities. The errors encountered at salinities
greater than 20 are much smaller and are generally
grouped within ±0.01 pH although sorne deviations in
behaviour were noted at 35 salinity towards the end of
this sequence of experiments (pairs 4-5 and 4-4). Fairly
clear differences between the various reference electrode
types are also apparent. The ceramic plug junction
(reference electrode 5, Tab. 1) showed relatively small
ApH values throughout the experiments (compare the
trend for pairs 2-5, 3-5, 4-5). Measurements made with
the Orion 90-01 electrode (pairs 2-1, 3-4, 4-4) on the
427
(12)
From equation (11) we can see that the value assigned
by this procedure is related to pH (SWS, X), the true
Table 2
10 3 x &pH errors (") associated with standardisation in Hansson buffers
at 25°C with a salinity of20.
Electrode
pair
(Tab. 1) n
2-1
2-5
3-4
3-5
3-6
3-7
4-4
4-5
Salinity
5
3 34±6
3 11±5
17 48±26
13 25±10
s 63±14
s 58±9
6 15±4
2 4±4
10
15
25
30
35
7±6
-2±3
25±20
14±8
38±17
35±12
4±3
-3±3
-3±6
-6±3
10±12
4±6
12±4
13±4
2±1
-4±0
6±2
8±1
2±7
6±8
0±8
2±8
5±1
8±1
12+2
15±o
7±16
12±16
-1±14
1±16
7±1
12±0
8±3
13±2
3±9
12±9
-2±9
0±11
16±4
23±2
(") &pH shown as mean value followed by the standard deviation.
For the final entry this simply represents the spread of the measured
values.
M. WHITFIELD etal.
pH of .the sample on the total hydrogen ion concentration scale, by the equation:
L1pH =pH (SWS, X) -pH (SWS, X)*
L1E1
.
=- -
gT
-log[y~(S)/r~(X)].
observed experimentally in artificial media simulating
estuarine waters. Good agreement was observed in
most instances so this model might be considered as
providing a reasonable basis for establishing conventional hydrogen ion activity coefficients. From this
model we can write:
(13)
(15)
It will be instructive to see how L1pH values calculated
from this equation compare with those observed experimentally.
The simplest procedure for the calculation of L1E1 is
that derived by Henderson (1908) for the special case
where a continuous mixture is produced between the
bridge solution and the sample. This kind of junction
has rarely been achieved in practice and the indiscriminate use of the Henderson equation has been rightly
criticised (Covington, Rebelo, 1983). Here we will use
the Henderson equation simply to indicate the range
of values and the salinity trends that might be expected
in liquid junction potentials in the saline buffers used
in the present experiments. To conform to the usual
sign convention we can write the Henderson equation
as (Whitfield, Turner, 1981):
E(J, X)=_ xm-XSlog[ym ]•
gT
ym-YS
YS
For hydrogenions B=1.670 and C=0.525. The effective ionie strength (le) is given by the equation (Khoo
et al., 1977):
le=0.0029+0.018575.S+ 1.639x 10- 5 .S 2 •
log ~Hso4 = 647.59/T- 6.3451
+0.019085T -0.5208
and:
'fu(")
log êi(")
y~(")
1;
mf04 = 8.363 x10- 4 • S,
(18)
(17)
to give estimates of r~ according to the equation:
(14)
r~=r~/r.
(19)
The total ionie strength (1,) is given by (Whitfield,
1979):
11 = 19.927. S/(1 000-1.0051. S).
(20)
Values of ApH calculated using these data follow the
same general trends as those observed experimentally
(dashed curve 1, Fig. 1). Because of the conventional
nature of the estimates of r~ and E(J, X) too much
stress should not be placed on the correspondence of
the calculated values with those observed for particular
electrodes. A further calculation of r~ using the Maclnnes convention by Millero and Schreiber ( 1982) gives
L1pH values which follow curve 1 (Fig. 1) closely.
An independent estimate of r~ may be made from
measured values of the mean-ion activity coefficient of
hydrogen chloride in sulphate-free artificial sea water
which may be summarised by the equation (Khoo et
al., 1977):
Table 3
Estimates of E (J, X) and y~ (X) for estuarine waters at 25"C.
E(J, X)Jm V(")
(16)
Values of r~ calculated in this way (Tab/3, method 1)
can be combined with values of a(= 1 + mf04 • ~usoJ
calculated from the equations (Khoo et al., 1977):
where x= -2.85, X= -0.476, y= 149.85, Y =2.261
and m is the molarity of the potassium chloride bridge
solution.
The activity coefficient contribution is unique to the
solution and is not affected by the vaguaries of reference electrode design. It does however depend on the
adoption of a suitable convention for defining single
ion activity coefficients. Following a careful reappraisal of the available data, Dickson and Whitfield
(1981) prepared such a model based on the Maclnnes
convention and compared the predicted stability
constants for a range of acid-base equilibria with those
Property
/
1
Salinity
Mo - - - - - - - - - - - - - del 5
10
15
20
25
30
35
log y± (HCl)= -0.5108
+1.5 +0.8 +0.4 +0.1 -0.2 -0.5 -0.7
+ 0.086 08 1,.
(1) 0.827 0.821 0.833 0.854 0.881 0.912 0.948
(2) 0.822 o. 782 o. 776 o. 783 o. 795 0.814 0.834
(3) 0.805 0.785 0.785 0.794 0.807 0.828 0.847
If'2/(l + 1.394 If'2 )
(21)
These vaues can be combined with estimates of the
chloride ion activity coefficient in sea water based on
the hydration convention (Robinson, Bates, 1979) to
give:
0.038 0.063 0.081 0.096 0.108 0.117 0.126
(1) 0.759 0.710 0.692 0.684 0.687 0.697 0.710
(2) 0.754 0.676 0.644 0.628 0.619 0.622 0.624
(3) 0.738 0.679 0.652 0.637 0.630 0.632 0.634
y~=(y ± (HCIW/rCl.
(4) For a 3.5 MKO bridge solution, equation (14).
(&) 1) Dickson and Whitfield (1981), Maclnnes convention (Curve 1,
Fig. 1). 2) Using hydration theory to calculate Ya (Robinson, Bates,
1979) and measured values of y± (HO) in sulphate-free water (Khoo
et al., 1977; Curve II, Fig. 1). 3) Using ra calculated from Maclnnes
convention (Dickson, Whitfield, 1981) and y± (HCI) from Khoo et
al. ( 1977).
(") From equations (17) and (18).
4
( ) From corresponding y~ values, see note (").
(22)
When values of y~ calculated in this way [Tab. 3,
method (2)] are combined with the E(J, X) values calculated from equation 14 the ApH values obtained also
follow the same general trends as the experimental
data but with somewhat higher errors occurring at low
salinities (dashed curve Il, Fig. 1). A similar procedure
for estimating r~ using . equation 15 to estimate
428
ESTUARINE pH- THEORY AND BUFFER SELECTION
Table 4
Mean values for 103 x log fu [equation (10)] (") at 25°C.
Salinity
Electrode
pair(~
n
5
10
15
20
25
30
35
2-1
2-5
3-4
3-5
4-4
4-5
3
3
7
4
6
2
133±25
134±10
141± 15
127±6
102±10
98±13
160±26
157±13
163± 10
139±11
114±11
105±12
170±28
150±13
174±11
145±15
119±9
106±10
167±30
145±14
181 ±9
145±17
118±9
102±10
161±29
137±12
181±6
143±17
112±9
94±9
156±29
129±14
182±9
138± 16
110±10
90±10
159±28
132±16
179±8
127±19
102±12
79±12
(") Expressed as mean value
(b) Table 1.
± standard deviation, for the final row this sirnply represents the spread of the experimental values.
Table 5
A series of individual pH measurements in saline buffers based on
standardisation in NBS and 35 salinity buffers.
l
Electrode pair
Salinity
5
10
15
20
25
10
- - Salinity
30
-
3-2
2-2
3-5
2-5
pH range x 103
8.185(")
7.995 (b)
8.213(")
8.171
8.012
8.207
8.048
8.220
8.067
8.222
8.063
8.222
8.063
8.222
8.063
8.165
8.025
8.185
8.044
8.195
8.057
8.201
8.066
8.205
8.068
8.208
8.069
8.172
8.041
8.194
8.062
8.200
8.069
8.200
8.068
8.198
8.066
8.196
8.065
20
46
28
36
31
25
36
10
8.026(~
8.226(")
8.044(b)
8.236(")
8.058(b)
8.242(")
8.062(b)
8.247(")
8.065(b)
44
6
53
6
(") Electrode pair standardised in NBS 1: 1 phosphate buffer.
(~ Electrode pair standardised in 35 salinity buffer.
Figure 2
Mean fu values calculated from equation (10) using measurements in
NBS and saline buffers. The dashed lines indicate the upper and lower
confidence limits for equation (23). The electrode pairs (glass electrodereference electrode, Tab. 1) are identified as follows:
e 2-1; 0 2-5; .Â. 3-4; f'èl. 3-5; T 4-4; +equation (23).
,
Yc1 (B = 1.265, C=0.014; Dickson, Whitfield, 1981)
gives values of y~ that are closely comparable
[(method 3), Tab. 3].
The experimental observations are therefore compatible
with the theoretical estimates of the pH errors incurred
when a single saline buffer is used for calibrating pH
cells in estuarine waters. Clearly sorne attempt must be
made to reduce the systematic errors introduced by
such a procedure. The use of more than one saline
buffer, white increasing the complexity of the measurement, will not necessarily result in significant reduction
in the systematic errors involved; particularly for those
reference electrodes which show a marked increase in
ApH at low salinities (e. g. pair 3-6, Fig. l). To reduce
the uncertainties associated with the behaviour of reference electrodes in a medium of variable salinity it will
be necessary to estimate experimentally the ApH values
· of the electrode couples used.
Comparison of the associated fu values (Tab. 4) with
the values of ApH considered in the previous section
(Tab. 3) indicates that the use of NBS rather than
saline buffers has little effect on the precision of the
measurements made with the individual electrode pairs.
However, a comparison of the maximum range of pH
errors associated with the measurements on the NBS
and saline buffer scales indicates that the differences in
behaviour between the various electrode pairs is in
general more pronounced if the pH cells are standardised in NBS rather than in saline buffers. Consequently,
if no further precautions are to be taken, the difference
between pH measurements made using different
electrode pairs could be reduced by standardising the
electrodes in a saline buffer rather than in a dilute NBS
buffer. A series of pH measurements made with four
different electrode pairs (Tab. 5) provides a direct example of this effect in practice.
The mean fu values (Fig. 2) in general group around
those of earlier workers summarised by Culberson
(1981) in the equation:
'
Performance of electrodes using NBS buffers and the
determination of fu values
log fu= - Ait 12 /( l + 2.16 It 12)
+(O.'t681+6.26x to- 4 t) 1,
In a number of cases the equilibrium potential was also
monitored in NBS 1: 1 phosphate buffers as weil as in
sea water buffers during the course of the experiments.
(23)
429
M. WHITFIELD et al.
Table 6
Calculation of fu values for cells standardised in NBS 1: 1 phosphate buffer.
t
Salinity
Property
<iE1(")
&EJfgT
Log y~
log fu
fu
Mode)
1 (")
2
. 1 (b)
1
2
10
5
-0.4
-0.007
-0.120
-0.124
-0.127
-0.130
0.749
0.741
-1.1
-0.019
-0.149
-0.170
-0.168
-0.189
0.679
0.647
20
15
-1.5
-0.025
-0.160
-0.191
-0.185
-0.226
0.644
0.594
-1.8
-0.030
-0.165
-0.202
-0.195
-0.232
0.628
0.586
30
25
-2.1
-0.035
-0.163
-0.208
-0.198
-0.243
0.634
0.571
-2.4
-0.041
-0.157
-0.206
-0.198
-0.247
0.634
0.566
35
-2.6
-0.044
-0.149
-0.205
-0.193
-0.249
0.641
0.564
(") Using E (J, X) values given in Table 4 togethet with an E(J, S) value of + 1.9 mY for 1: 1 phosphate buffers (Bates, 1973, p. 38).
4E1=E(J, X)-E(J, S).
(") Taken from the corresponding columns in Table 3 (see footnote (") of that table).
where t is the temperature oc and J3uso4 , m~04 and It
are given by equations 17, 18 and 20 respectively. Culberson suggested that the accuracy of this equation
was no better than ±0.03 pH when used to convert
pH (NBS) to pH (SWS) using equation 9. When this
proviso is superimposed on the present experimental
values (Fig. 2, broken tines) it is clear that aU the data,
with the exception of the values measured for electrode
pair 4-4, faU within its scope. It is also apparent that,
at this levet of accuracy the salinity variation of fu is
barely significant. Consequently the experimental evidence presented here and in earlier studies (see Dickson,
1977; Culberson, 1981, and references therein) indicates
that there is considerable variability in the fu values
characterising the electrode pairs and that such variability is likely to introduce large systematic errors into
attempts to provide a uniform scale for pH measurement across the estuarine salinity range.
Using equation 10 and the data collected in Table 3
we can calculate theoretical values of fu for the salinity
range considered. Here the L\E1 term refers to the
difference in liquid junction potential between the
appropriate saline buffer and the dilute NBS buffer.
The calculated values (Tab. 6) are in generallower than
those observed experimentally and do not provide as
good an agreement with the experimental data as the
corresponding values calculated for transfer between
saline buffers (Fig. 1). The calculation of L\pH is subject
to fewer uncertainties than the calculation of fu since
it entails the estimation of a thermodynamically accessible activity coefficient ratio and of the relatively small
liquid junction potential difference between two saline
buffers.
To attain an accuracy of ±0.01 pH more explicit
account must be taken of the variability in reference
electrode performance expressed in the fu values presented here. At first it would appear that ali that is
required is a clearly defined procedure for determining
the fu value of a particular electrode pair as a function
of salinity and temperature. These values could then
be used to correct any subsequent measurements made
with that electrode pair irrespective of the buffer scale
adopted. It must be remembered however that the fuvalues discussed so far have been mean values based
on a series of experiments. The experimental values for
a particular electrode pair can show significant
variation with time (Fig. 3 A) and significant differences can be observed in the fu-values measured on diffe-
r-----------------------~t=O
0·75
l
l
0·75
0-70
fH
fH
1
1
0·65
T
tG-01 pH
j_
0·65
0·60
10
20
--Salinity
0 ' 60 ._____.__..,-~10:----'--~20::-----'--~30::----'-1
---Salinity
-
30
--
Figure 3
A. The variation of fu values with time for electrode pairs 3-1 (open
symbols, broken lines) and 3-5 (solid symbols, continuous lines). The
time is shown on the curves in days.
B. The variation of fu values with different examples of the Orion 9001 plastic sleeve reference electrode measured in the same experiment:
e reference electrode 2;
electrode 4.
430
0 reference electrode 3;
+reference
ESTUARINE pH- THEORY AND BUFFER SELECTION
B.
rent examples of the same reference electrode type
during the same experiment (Fig. 3 B). To provide a
sounder basis for the establishment of useful estuarine
pH scale it would be useful to adopt a pH electrode
pair that enables the variability of the fH-values to be
reduced to a practically acceptable levet. The design of
such a cell will be considered in Part II of this study.
logfH (equation10)
SUMMARY AND CONCLUSIONS
Although ail measurements based on standardisation
in either NBS or saline buffers give reasonable precision
( ± 0.02 pH) over the estuarine salinity range, considerable systematic errors (as large as 0.06 pH) can be incurred (Fig. 1 and 2). These systematic errors are unique
to the electrode pair employed and appear to be Iargely
associated with the variable performance of the liquid
junction at the reference electrode. The errors vary with
time (Fig. 3 A) and can vary considerably for different
examples of the same reference electrode type
(Fig. 3 B). There appears to be a slight practical benefit
in using a 20 salinity buffer rather than a dilute NBS
pH (SWS,X)
./"'
/"'
IE----6,-'-p_H- - - - 1
[equation 6 1
[equation 13 1
c.
O.
Figure 4
Schematic summary of relationships between experimental pH values
(set in circles) with are subject to systematic errors, and corrected or
true pH values (set in rectangles) which are direct/y intercomparable.
Experimentally accessible conversion parameters are shown by solid
arrows whereas factors that entai/ sorne extra-thermodynamic assumptions are shown by broken arrows. The conversion factors themselves
are summarised in Table 7.
Table 7
Interconversion factors between estuarine pH measurements made on different scales.
To convert
From measured value to "true" value
A. (")pH(NBS,X)*
B. pH(NBS, X)
Notes
add
&E1 (NBS)(")
Equations 3 and 5
gT
A. pH(NBS,X)"
C. pH (SWS, X)
D. pH(SWS, X)*
B. pH (NBS, X)
D. pH(SWS, X)*
C. pH (SWS, X)
C. pH(SWS, X)(')
B. pH (NBS, X)
logy~(X)-
&E1 (NBS)
gT
=logf8 , equation (10) (")
log 'Y~ (S) (4) + &E, (SWS)•
gT
y~(S)
&E1 (SWS) =:&pH, equation (13)(")
log--+
'Y~(X)
gT
Table 3
logy~(X)
• Capital letters indicate the corresponding entries on Figure 4.
b &E1 (NBS)=E(J, X)-E(J, S, NBS).
• Experimentally accessible parameter.
Total hydrogen ion activity coefficient in the saline buffer.
• &E1 (SWS)=E(J, X)-E(J, S, SWS).
r True value.
buffer for pH measurements since this choice constrains
the systematic errors [(A pH, equation [!.3)] to zero near
the middle of the estuarine salinity range. The sp..n of
systematic errors introduced by the variability of the
reference electrode is thereby reduced although for commercial electrodes, it stiJl exceeds the ± 0.01 pH tolerance limits for thermodynamicaily useful pH values.
In practice the overaii spread of systematic errors is
only marginally reduced by the use of two or three
saline buffers to cover the estuarine salinity range
because of the sharp increase in ApH at low salinities
(Fig. 1). The advantages of saline buffers are therefore
by no means as clear eut in estuarine measurements as
they are in marine applications and the choice of a
suitable procedure for estuarine pH measurements
depends more on practical considerations than on fundamental theoretical criteria.
From the practical point of view, what is required in
the first instance is a set of guidelines that will
a) improve the intercomparability of pH measurements
made with commercial electrode pairs at different sites
and at different times, and b) enable thermodynamically useful conclusions to be drawn from the data.
Severa! routes to the establishment of intercomparable
pH values are possible (Fig. 4 and Tab. 7). The measured pH values are subject to the systematic errors
summarised in Figures 1 and 2. The "true" pH values
(B and C, Fig. 4), in contrast have been corrected for
variations in AEJ and y~ and will therefore provide a
basis for the intercomparison of pH values irrespective
of the reference electrode employed. The conversion
factors needed for the calculation of pH (SWS, X)
values (C, Fig. 4) from the measured value on both pH
scales can be determined experimentally. Furthermore,
pH (SWS, X) has a clear practical and thermodynamic
significance, being directly related to the total hydrogen
ion concentration in the sample, whereas pH (NBS, X)
remains conventionaily defined. Consequently, whether
d
431
M. WHITFIELD etal.
the electrode pair is standardised using an NBS dilute
buffer or a saline buffer, the conversion factors needed
to calculate pH (SWS, X) should be determined over
the appropriate salinity and temperature range and be
reported along with the measured pH values.
The following recommendations can therefore be made
for the measurement of pH values in estuarine waters
where an accuracy and precision of ±0.01 pH is
required.
1) Electrode pairs may be standardised on either the
pH (NBS) or the pH (SWS) scales. The commercial
availability of buffers makes the pH (NBS) scale the
most convenient in practice at the present time. If the
pH (SWS) scale is to be used, a single buffer with a
salinity in the range of 15 to 20 should be sufficient.
2) The electrode pair should be characterised over the
appropriate salinity and temperature range to assess the
systematic errors associated with variations in residual
liquid junction potentials and hydrogen ion activity
coefficients. This entails the measurement of fu
[equation (10)] for electrode pairs standardised on the
pH(NBS) scale and ApH [equation (13)] for measurements on the pH (SWS) scale. The appropria te
conversion factors should be published along with the
measured pH values.
To provide further improvements in the precision and
accuracy of estuarine pH measurements the following
investigations should be undertaken:
3) Consideration should be given to the practical use
of reference electrode designs which will reduce the
variability of liquid junction potentials.
4) The assessment of systematic errors in the measurement of estuarine pH values should be extended to
consider temperature effects.
5) Studies of conventional pH electrode pairs should
be undertaken to assess the extent to which the use of
saline buffers rather than dilute buffers improves the
equilibration times for measurements in saline samples
following calibration.
Acknowledgements
This work was carried out as a part of the Natural
Environment Research Council Special Topic Programme on "Geochemical Cycling". The authors would
like to acknowledge the help of Dr. A. G. Dickson
during the initial stages of this project and of Dr. A.
Sibbald in the construction of the multiplexer switching
unit.
REFERENCES
Almgren T. D., Dyrssen D., Strandberg M., 1975. Determination of
pH on the moles per kg seawater scale, Deep-Sea Res, 22, 635-646.
Rates R. G., 1973. Determinations of pH, theory and practice, Wiley,
New York, 479 p.
Rates R. G., 1975. pH scales for sea water, in: The nature ofseawater,
by E. D. Golberg, edited Dahlem konferenzen, Pergamon Press,
Berlin, 313-338.
Rates R. G., Macaskill J. B., 1975. Acid-base measurements in
seawater, in: Analytical methods in oceanography, edited by T. R. P.
Gibbs Jr., Am. Chem. Soc., Adv. Chem. Ser., 147, Washigton D.
c. 110-123.
Covington A. K., Rebelo M. J. F., 1983. Reference electrodes and
liquid junction effects in ion-selective electrode potentiometry, Ionselective Electrode Reviews, 5, 93-128.
Covington A. K., Rates R. G., Durst R. A., 1983. Definition of pH
scales, standard reference values, measurement of pH and related
terminology, Pure Appl. Chem., SS, 1467-1476.
Covington A. K., Wballey P. D., Davison W., 1984. Improvements
in the precision of pH measurements. A laboratory reference
electrode with renewable free-diffusion liquid junction, Anal. Chim.
Acta (in press).
Culberson C. H., 1981. Direct potentiometry, in: Marine electrochemistry, edited by M. Whitfield and D. Jagner, John Wiley and Sons,
Chichester, 187-201.
"
Dickson A. G., 1977. Sorne studies on acid-base behaviour in artificial
sea waters, Ph. D. Thesis, Univ. Liverpool.
Dickson A. G., 1984. pH scales and proton transfer reactions in
saline media such as sea water, Geochim. Cosmochim. Acta, 48, 22992308.
Dickson A. G., Whitfield M., 1981. An ion-association model for
estimating acidity constants (at 25°C and 1 atm. total pressure) dn
electrolyte mixtures related to seawater (ionie strength
<1 mol kg- 1 H 2 0), Mar. Chem., 10, 315-333.
Hansson 1., 1973. A new set of pH scales and standard buffers for
sea water. Deep-Sea Res., 20, 479-491.
Henderson P. 1908. Zur Thermodynamik der Flüssigkeitsketten Z.,
Phys. Chem., 63, 325-345.
Johnson K. S., Voll R., Curtis C. A., Pytkowicz R. M., 1977. A
critical examination of the NBS pH scale and the determination of
titration alkalinity, Deep-Sea Res., 24, 915-926.
Kboo K. H., Ramette R. W., Culberson C. H., Rates R. G., 1977.
Determination of hydrogen ion concentrations in seawater from 5
to 40°C standard potentials at salinities from 20 to 45°/00, Anal.
Chem., 4?, 29-34.
_ Millero F. J., Schreiber D. R., 1982. Use of the ion-pairing modeL
to estimate activity coefficients of the ionie components of natural
waters, Am. J. Sei., 282, 1508-1540.
Morris A. W., 1978. Chemical processes in estuaries: the importance
of pH and its variability, in: Environmental biogeochemistry and
geomicrobiology, Vol. l, edited by W. E. Krumbein, Ann Arbor Sei.
Pub!. Inc., Ann Arbor, Michigan, 179-187.
Pelletier E., Lebel J., 1980. La mesure du pH en milieu estuarien
·
sur l'échelle NBS, J. Fish. Aquat. Sei., 37, 703-706.
Ramette R. W., Culberson C. H., Rates R. G., 1971. Acid-base
properties of tris(hydroxy methyl) aminomethane buffers in sea
water from 5 to 40°C, Anal. Chem., 49, 867-870.
Robinson R. A., Rates R. G., 1979. Single-ion activities in aqueous
solutions analogons to sea water, Mar. Chem., 7, 281-288.
Smith W. H., Hood D. W., 1964. pH measurement in the ocean; a
sea water secondary buffer system, in: Ken Sugawara Festival Volume,
recent researches in the fields of hydrosphere, atmosphere and nuclear
geochemistry, edited by Y. Miyake and T. Koyama, Maruzen,.185202.
/
Whalley P. D., 1982. Factors affecting the precision of pH measurements in fresh water, Ph. D. Thesis, Newcastle Upon Tyne Univ.
Whitfield M., 1979. Activity coefficients in natural waters, in: Activity
electrolyte
solutions,
Vol. 2,
edited
by
coefficients , in
R. M. Pytkowicz, CRC Press, Boca Raton, Florida, 153-299.
Whitfield M., Turner D. R., 1981. Sea water as an electrochemical
medium, in: Marine electrochemistry, edited by M. Whitfield and
D. Jagner, John Wiley and Sons, Chichester, 3-66.
432