Metrological challenges for measurements of key climatological observables. Part 3: seawater pH

A G Dickson1M F Camões2, P Spitzer3, P Fisicaro4, D Stoica4, R Pawlowicz5 and R Feistel6

Published 15 December 2015 • © 2016 BIPM & IOP Publishing Ltd • 

Abstract

Water dissolves many substances with which it comes into contact, leading to a variety of aqueous solutions ranging from simple and dilute to complex and highly concentrated. Of the multiple chemical species present in these solutions, the hydrogen ion, H+, stands out in importance due to its relevance to a variety of chemical reactions and equilibria that take place in aquatic systems. This importance, and the fact that its presence can be assessed by reliable and inexpensive procedures, are the reasons why pH is perhaps the most measured chemical parameter. In this paper, while examining climatologically relevant ocean pH, we note fundamental problems in the definition of this key observable, and its lack of secure foundation on the International System of Units, the SI. The metrological history of seawater pH is reviewed, difficulties arising from its current definition and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent TEOS-10 seawater standard. It is concluded that the International Bureau of Weights and Measures (BIPM), in cooperation with the International Association for the Properties of Water and Steam (IAPWS), along with other international organisations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems.

List of symbols

SymbolQuantity

Remarks

A

Debye-Hückel constant(30)

a

relative activity

a

reduced practical activity

B

2nd Debye-Hückel constant(30)

c

solute concentration

E

electrode potential, with super- and subscripts

E°

standard electrode potential

E°’

auxiliary electrode-potential variable (11), (12)

EJ

liquid junction potential, LJP

F

Faraday constant F = 96 485.332 89 C mol−1

I

ionic strength

KA

molality quotient (10)

, KA

acid dissociation constant

hybrid acidity constant (9)

k

uncertainty coverage factor

m

solute molality (with subscripts)

m

molal solute-composition vector (24), (25)

m*

total molality (22), (25)

m°

standard molality m° = 1 mol kg−1

mSW

molal composition vector of synthetic seawater (24), (25)

solvent (water) mass

MS

solution mass

n

number of moles (with subscripts)

p

absolute pressure

p(aγCl)

acidity function

pH

pH value

‘pH’

operationally-defined pH-like quantities

R

7molar gas constantR = 8.314 4621 J K−1 mol−1

S

standard solution (14)

SA

Absolute Salinity

SP

Practical Salinity, PSS-78

SR

Reference-Composition Salinity, TEOS-10

T

absolute temperature, ITS-90

u

standard uncertainty

V

volume

X

test solution (14)

trace activity coefficient product (22)

γ

molal activity coefficient (with subscripts)

unspecified apparent activity coefficient (10)

mean-ion activity coefficient

trace mean-ion activity coefficient (20)

pH measurement is often deceptively easy …. pH measurement can also be exasperatingly difficult.

G. Mattock, 1963

1. Introduction

This is part 3 of a series of companion papers (Feistel et al 2015, Lovell-Smith et al 2015, Pawlowicz et al 2015) examining metrological challenges for measurements of key climatological observables; in this paper we examine seawater pH. The concept of pH was introduced in 1909 by Sørensen (Sörensen 1909) in terms of a logarithmic function of the hydrogen ion concentration in an aqueous solution, pH = −lg [c(H+)/(1 mol L−1)]. This was later replaced by the reduced practical activity (as defined in Appendix B of the Digital Supplement to Part 1 of this series, Feistel et al 2015),

Equation (1)

to better account for effects of ionic interactions in the solution (Sørensen and Linderstrøm-Lang1924). The pH value is an important property of aqueous solutions, including natural waters, as it provides an estimate of the free acidity in solution, which plays a role in regulating the nature and rate of many chemical reactions including those important to living organisms. Furthermore, pH is a measurable parameter that (together with other measured parameters) allows us to describe fully the acid-base composition of a seawater sample.

Modern use of the pH concept is widespread, in large part because it can be measured using a relatively straightforward potentiometric technique, although important technical aspects of this technique are often not adequately taken into account. Over the last decades, because of these technical issues, a variety of related but different operationally-defined pH-like quantities have been introduced (IUPAC 1985). However, as Bates and Popovych (1981) noted more than 30 years ago, related problems of incompatibility are inevitable. Only for a few selected calibration procedures in media of low ionic strength can the traceability hierarchy be established successfully between conceptually defined values, equation (1), and experimentally assessed pH values with inherent uncertainties (Baucke 2002, Buck et al 2002).

These technical issues are particularly problematic in seawater studies. First, seawater has a high ionic strength, which causes problems when using conventional pH calibration standards. Second, some current research problems such as the detection of the long-term anthropogenically-driven changes in ocean carbon chemistry over multi-decadal timescales would benefit from an extremely small standard uncertainty in pH measurements (as small as 0.003, see Newton et al 2014, Bockmon and Dickson 2015), albeit over a fairly narrow range of pH, and this is far smaller than the differences between many of the available operationally-defined ‘pH’ quantities. The notation ‘pH’ in quotation marks is used here to emphasise that, although commonly called pH, these various operationally-defined quantities are not identical to the accepted definition, equation (1).

Dickson (1984) stated that ‘the field of pH scales and the study of proton-transfer reactions in sea water is one of the more confused areas of marine chemistry’. Despite theoretical and technological progress since then in understanding oceanic pH and its variations, the overall coherence of measurements has improved only marginally (Marion et al 2011, Spitzer et al 2011, Brewer 2013). Direct measurement of the single-ion activity of hydrogen ions is not possible and several mutually inconsistent conventions are used to estimate pH from measurements.

Similar to the situation for salinity (Pawlowicz et al 2015), quantitative understanding of exactly what we are measuring is significantly worse than the repeatability that can be achieved by particular measurement techniques. However, unlike the situation for salinity, there is as yet no single recommended measurement procedure, nor is there an internationally accepted reference standard for seawater pH measurement that enables different laboratories to achieve comparable measurements reliably. On the other hand, pH has the advantage of having a theoretically sound basis for metrological traceability (Buck et al 2002).

In the meantime, the growing amounts of anthropogenic carbon dioxide that are being added to the atmosphere are lowering seawater pH and changing the composition of the oceans through the process known as ocean acidification, ultimately affecting marine ecosystems (Gattuso and Hansson 2011). The requirement that marine scientists standardise how they define and measure seawater pH, a problem raised a century ago by Sörensen and Palitzsch (1910), has become increasingly urgent.

The current state of knowledge of the carbon dioxide budget and climate-related effects on the pH of the oceans together with its potential consequences are briefly reviewed in the next section. We then discuss the current status of seawater ‘pH’ measurements, and describe the use of Harned cells to characterise buffers based on synthetic seawater that are used for the calibration of both potentiometric and spectrophotometric procedures. Although there is no obvious solution ensuring traceability to the SI, options are presented as promising candidates for future metrological and research activities.

2. Climatological relevance

Many important processes in the ocean require pH for their characterisation, and pH in turn is affected by these processes. In particular, the ocean carbon dioxide (CO2) system is central to a wide variety of biological processes in the ocean, with CO2 being taken up by photosynthetic organisms, and remineralised by a variety of respiration processes. Furthermore, a wide variety of calcifying organisms such as pteropods or coccolithophores rely on their ability to form calcium carbonate (CaCO3) from the surrounding seawater (Bednaršek et al 2012, Smith et al 2012). All of these processes affect and are affected by seawater pH, which can exhibit pronounced diurnal and seasonal cycles as well as strong irregular fluctuations related to local mixing and many other factors (Buch 1945, Hofmann et al 2011, Doney 2013, Omstedt et al 2014).

Over the past two centuries, the release of CO2 from human industrial and agricultural practices has resulted in atmospheric CO2 levels that are now higher than has been experienced on the Earth for at least the last 800 000 years (Lüthi et al 2008). During this period, the oceans have taken up about 30% of the total amount of CO2 produced by human activities (IPCC 2013, Khatiwala et al 2013). This addition of anthropogenic CO2 to the ocean has reduced the surface ocean pH by about 0.13 to date and is expected to reduce pH by a further 0.3 by the end of this century (Feely et al 2004). When CO2 reacts with seawater, it acts to reduce the amount of carbonate ions and can thus affect shell formation for marine organisms such as corals, shellfish and some plankton. This process could influence fundamental biological and chemical processes of the sea in coming decades (Fabry et al 2008, Doney et al 2009). The effect of pH changes on marine sulphur fluxes may even enhance global warming (Six et al 2013).

Paradoxically, although the fraction of CO2 in the global atmosphere has increased from approximately 280 μmol mol−1 in pre-industrial times to more than 400 μmol mol−1 at present (NOAA 2015), a change of over 40%, the relative increase in total oceanic carbon levels is nearly 200 times smaller. This is not because oceanic uptake is small. About 155 Pg8 of the carbon released by human activity between the beginning of the industrial revolution and 2010, has moved into the oceans (Ballantyne et al 2012, Khatiwala et al 2013), and for the decade 2003–2012 the estimated average ocean uptake rate was 2.5 ± 0.5 Pg per year (Le Quéré et al 2014). However, of about 40 000 Pg of carbon present at the Earth’s surface, the oceans store 95.5%, the biosphere and soil 3% and the atmosphere only 1.5% (Bender 2013). Thus, the seemingly large oceanic uptake causes only a small relative change in average total seawater carbon concentration because the background reservoir is so large.

Although the relative change is small, the changes in the ocean are more complicated than in the atmosphere because of chemical equilibria in the marine carbonate system. Thus, small changes in pH reflect significant changes in the concentrations of different carbonate species. The pH decrease measured between 1991 and 2006 in the North Pacific is consistent with ocean-atmosphere equilibration, with an average decline of 0.0017 per year (Byrne et al 2010), and similar trends have been seen in other oceans (Dore et al 2009, González-Dávila et al 2010, Olafsson et al 2009, Bates et al 20122014, Lauvset and Gruber 2014). In coastal regions this ocean acidification signal may presently be swamped by changes resulting from a variety of other processes. Thus, in the Baltic Sea, no significant trend has been detected in the surface water by some authors (Omstedt et al 2010, Ulfsbo et al 2011), in contrast to other studies (Brutemark et al2011). For comparison, oceanic pH values have been estimated to be about 0.5 lower than today during a large-scale acidification event occurring 110 million years ago (Ridgwell and Zeebe2005, Hönisch et al 2012). The natural decay of such paleoclimatic CO2 excursions takes some 100 000 years, mainly caused by atmospheric weathering of rocks (Bender 2013), resulting in slow pH relaxation.

Trends in oceanic pH may therefore be small but are highly relevant. Unambiguous definition and comparable, stable measurement and calibration procedures will be essential to enable detection in long-term observations (almost certainly combined from many different sources) and to prevent misleading and possibly spurious results.

3. Brief history of pH and its application to seawater

As early as 1725, Louis Ferdinand Comte de Marsilli reported that eau de fleurs de mauve (a colorimetric indicator) went a yellow-green colour in seawater—indicating seawater’s basic nature (Marsilli 1725, Wallace 1974). At the time that Sørensen defined pH, originally termed the ‘hydrogen ion exponent’ (Sörensen 1909), in terms of hydrogen ion concentration, the concept of ion activity coefficients was not yet widely known. He proposed that the pH of an unknown solution could be obtained from the potential (or ‘electromotive force’, e.m.f., Inzell 2014), E, (measured in potentiometric conditions, i.e. null current) of a cell originally developed by Bjerrum (1906), formed by combining two half-cells. One half-cell contained the platinum-based hydrogen-gas electrode (Pt, H2), placed in a sample solution containing hydrogen ions. The other one, introduced by Ostwald (1894), was based on a calomel electrode (Hg, Hg2Cl2) sensitive to chloride ions (Cl−) in a reference solution (typically of potassium chloride, KCl). A salt bridge containing a concentrated KCl solution established electrolytic contact between the solutions of the two half-cells while minimizing fluid exchange.

Sørensen’s pH is then estimated as the difference between the measured cell potential, E, and the standard potential of this reference calomel electrode, divided by a constant that can be calculated from theory (the so-called Nernst factor). Sørensen calculated the standard potential of his reference calomel electrode at c(KCl) = 0.1 mol L−1 from the cell potential measured in various mixtures of hydrochloric acid (HCl) with sodium chloride (NaCl) at a total concentration of c = 0.1 mol L−1. According to the state of knowledge at that time, he assumed that the molar concentration of hydrogen ions in these solutions is given by the product of the molar concentration of the hydrochloric acid and the degree of dissociation of these solutions as determined from measurements of the electrolytic conductivity. Thus he estimated the standard potential to be 0.3377 V at 18 °C (Bates 1954, Sörensen 1909).

Values of ‘pH’ determined this way measure neither the concentration nor the activity of hydrogen ion. Rather, the ‘pH’ is conventional, defined in terms of operations. The measured cell potential includes liquid-junction potentials (LJP) on either end of the salt bridge. The LJP is an additional potential that arises from differential molecular diffusion between cations and anions at the interface between two liquids and is therefore dependent on the chemical composition of both liquids as well as details of the interface. Sørensen was well aware of the fact that the measured cell potential contained an unknown contribution from this LJP. Unfortunately, his suggestion that corrections need to be applied was discarded in later standard procedures (Bates1954).

The Sørensen procedures were applied very early to seawater (Sörensen and Palitzsch 1910, Palitzsch 1911). After the concept of activity was introduced (Lewis 19011907, see appendix B in the supplement of Feistel et al 2015) and the statistical theory of ionic interaction was published (Debye and Hückel 1923), pH was re-defined in terms of the activity of the hydrogen ions in solution (Sørensen and Linderstrøm-Lang 1924). However, as single-ion activities cannot be measured unambiguously (see appendix A in the supplement of Feistel et al 2015), it was necessary to introduce an approximation for the single-ion activity coefficient as a convention.

Hamer and Acree (1939), working at the National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST), showed that it was practical to use the Harned cell (a hydrogen electrode and silver/silver-chloride electrode in a cell without a liquid junction) together with a conventional value for the chloride-ion activity coefficient, to estimate reproducible values for the hydrogen-ion activity in buffer solutions containing known amounts of sodium or potassium chloride. In a number of papers, the NBS established a series of seven primary reference pH buffer solutions (Bates 1973, Wu et al 1988). These NBS buffers had pH conventionally assigned from Harned-cell measurements in portions of the buffer solution with added soluble chloride, the activity coefficient of the chloride ions (at the limit as the concentration of added chloride salt approaches zero) was calculated using the Debye-Hückel model of electrolyte solutions with the introduction of the Bates-Guggenheim convention (Bates and Guggenheim 1960, see also section 5 below). This approximation for the single-ion activity coefficient is reasonable only for low ionic strengths, and hence restricts pH standard-buffer solutions to solutions of low ionic strength, I ≤ 0.1 mol kg−1, and to buffer systems that do not contain chloride ion (Bates 1973). In contrast, the ionic strength of typical seawater is about 0.7 mol kg−1 (Millero et al 2008), well beyond the validity of the Debye-Hückel limiting law. This results in a problem, since minimizing the LJP requires (at a minimum) the matching of ionic strengths between the buffer and the sample. Nevertheless, these so-called NBS buffers have been used over the years to calibrate some seawater ‘pH’ measurements (Takahashi et al 1970, Culberson 1981, Perez and Fraga 1987, Millero et al 1993).

The practical difficulties in using buffers of low ionic strength to calibrate seawater pH measurements were recognized at least 50 years ago by Smith and Hood (1964), who recommended preparing secondary buffers in a seawater background and calibrating them against primary NBS buffers. Later, in an attempt to calibrate buffers that would enable the use of the convenient electrometric pH approach to measure hydrogen-ion concentrations directly (rather than activities), Hansson (1973)—using titration techniques—and Ramette et al (1977)—using Harned cells—calibrated solutions of Tris (2-amino-2-hydroxymethyl-propane-1,3-diol) in synthetic seawaters for use as calibration buffers for measuring ‘hydrogen ion concentrations’ in seawater, though each chose to define ‘hydrogen ion concentration’ differently. Hansson (1973) used the ionic-medium approach of Sillèn (1967) to define a total hydrogen-ion concentration, while Ramette et al (1977) used the Harned-cell measurements of Khoo et al (1977) to estimatefree hydrogen-ion concentrations for their buffers.

In a series of papers, Dickson (Dickson 19901993, DelValls and Dickson 1998) combined these two approaches to define rigorously a total hydrogen-ion scale in seawater media, and to use Harned-cell measurements to realise this scale using Tris buffers based on synthetic seawater solutions. A recent paper (Pratt 2014) from NIST also reports Harned-cell measurements on Tris buffers in synthetic seawaters together with estimates of their uncertainty that are similar to those seen for Harned-cell measurements in key comparisons between different metrological laboratories of low-ionic-strength IUPAC pH buffers. However, an activity-coefficient convention is implicit in all these various published results for buffers based on Tris in synthetic seawater: it is assumed that the activity coefficient of HCl in the Tris buffer solution in synthetic seawater is identical to the trace activity coefficient of HCl in the synthetic seawater without Tris (see section 4).

Tris buffers have also been used by a number of marine scientists to calibrate electrometric measurements of seawater hydrogen-ion concentrations using cells containing a hydrogen-ion probe such as a glass electrode or ion-selective field-effect transistor (ISFET) sensor. Recently, a significant fraction of the oceanographic community has adopted spectrophotometric techniques for measuring seawater pH (Clayton and Byrne 1993, Dickson et al 2007–SOP 6b), typically using the indicator dye meta-cresol purple. This technique is capable, in careful hands, of a repeatability of ca. 0.0005 in pH (Byrne et al 1999, Carter et al 2013), however, for its calibration, this approach also depends ultimately on the same Tris buffers in synthetic seawaters described above (Clayton and Byrne 1993, Liu et al 2011).

Finally, a large part of the present conceptual confusion involved in pH measurements originates from the operational definition of ‘pH’ first recommended by IUPAC in 1979 (IUPAC 1979, Covington et al 1985). In this recommendation, a distinction was made between the notional definition of pH in terms of hydrogen-ion activity, and its operational definition in terms of the method used to measure it—in principle based on the method introduced by Sørensen. Only in 2002 did the IUPAC issue a new ‘Recommendation for a Primary Measurement Procedure for pH’ (Buck et al 2002) that overcomes the shortcomings of the operational definition. Following this recommendation, a metrological hierarchy including an uncertainty budget for calibration can be established, at least for solutions of low ionic strength. The pH measured in a sample can be linked to the pH of primary buffer solutions and to the notional definition of pH.

4. Current measurement practice for seawater

4.1. Acid-base processes in seawater

The property of interest in many studies of acid-base processes in seawater is usually dependent on the ratio

Equation (2)

where  is the thermodynamic acid dissociation constant for the acid HB, B stands for its conjugate base, m(X) is the molality of the constituent X and  is the corresponding activity coefficient. Although  is known for a wide variety of acids, it has usually not been possible to define the activity coefficient term with adequate accuracy for use in complex media such as seawater. The approach taken instead has been to express this ratio as a product of a term directly proportional to hydrogen-ion molality together with a second experimentally accessible term,

Equation (3)

Here, α is an arbitrary parameter. The second term in brackets can be considered to be a practical acidity constant whose value is a function of the salinity of the seawater (in addition to temperature, T, and pressure, p).

The assumption underlying the approach inherent in equation (3) is that the activity coefficients of species present at low concentrations in an ionic background such as seawater will predominantly depend on the salinity of the seawater and not on the concentrations of the various reacting species. Ideally, for α = 1, the practical acidity constant would be identical to the classical mass-action product for the acid dissociation of HB. However, the only requirement is that the value of α be the same in the (experimentally accessible) hydrogen-molality term and in the practical acidity constant.

The earliest example of this was the so-called hybrid acidity constant, defined such that

Equation (4)

where the activity  was measured using the pH measurement technique proposed by Sørensen and Linderstrøm-Lang (1924). Such hybrid or apparent constants were soon employed widely in oceanography (Buch 1930). However, it was recognized that potentiometric measurements of pH in solutions such as seawater could not yield a meaningful value of  but rather a quantity , where  is a complicated function that depends not only on the (single-ion) activity coefficient of hydrogen ion, but also on the transport numbers of all the ions present in all the parts of the cell (Guggenheim 1930). Nevertheless, one can then write equation (4) in the form,

Equation (5)

It can be seen that the presence of an arbitrary multiplicative constant in no way vitiates the practical value of this approach. The requirement is to ensure that, although typically ‘pH’ and  are determined separately, they are determined consistently (i.e. with the same ).

4.2. Approaches for seawater ‘pH’ measurement.

4.2.1. Electrometric approaches.

One approach to defining ‘pH’ in seawater is based on the operational definition of pH where, in effect, ‘pH’ is defined in terms of measurement results on the particular cell

where the || indicates a liquid junction. As originally suggested by Sørensen, the reference electrode is usually reversible to chloride ion, and the electromotive force (e.m.f.) of this cell can be formally written as

Equation (6)

where E°’ is an abbreviation for the sum

Equation (7)

Here, E° represents the formal standard potential of the cell, EJ is the (formal) liquid-junction potential between the two half-cells, R is the molar gas constant, T is the absolute temperature and F is the Faraday constant.

The expression (6) is really a conventional definition of E°’ and , the value of each depending on the value assigned to the other. Taking the difference between the values E of the test solution (X), EX, and of a standard (S), ES, we get from (6)

Equation (8)

In a similar operational definition, the ‘pH’ of the test solution (X) is related to the pH of a standard (S),

Equation (9)

Comparing equations (8) and (9) term by term, it can then be seen that ‘pH(X)’ can be identified with the conventional single-ion activity of hydrogen ion, equation (1), if two conditions are met: first, the residual liquid-junction potential, i.e. the difference in liquid-junction potential between measurements in X and in S, is zero, , and second, , where  has been conventionally assigned.

If the buffers used to define pH(S) are the conventional NBS buffers (Bates 1973), the values of ‘pH’ measured in seawater media will not correspond exactly to equation (6) but will include an additive offset whose magnitude depends on the value of ; this contributes to the constant term  mentioned at equation (5) above. The exact magnitude of  (and hence ) will depend largely on the salinity, temperature and pressure of the seawater sample, and partly on the buffer composition and on the exact design of the liquid junction used in the pH cell. Seawater ‘pH’ values obtained in this manner are often referred to as ‘being on the NBS scale’, though this is a misleading nomenclature.

A related approach uses a similar pH cell, but chooses standard buffers that are based on seawater media so as to minimise the residual liquid-junction potential, . The values of ‘pH(S)’ assigned to these buffers are functions of the hydrogen-ion molality such that

Equation (10)

where the constant of proportionality, α, will depend on the approach used in defining ‘pH’ (and on salinity, T and p) and mo = 1 mol kg−1 is the standard molality (Covington et al 1985). This approach was first implemented by Hansson (1973), who used a titration approach in synthetic seawater to calibrate a pH cell and assign values of ‘pH(S)’ to his buffers. Values of  are now, more usually, assigned to such buffers in a fashion that is traceable to Harned-cell measurements (see section 3). However, in environments where the salinity varies, it is not practical to match the buffer to the sample in all cases, and the further the salinity of the sample is from that of the buffer, the larger the error (Butler et al 1985, Easley and Byrne 2012).

In recent measuring systems based on the Honeywell Durafet®, an ion-selective field-effect transistor (ISFET) sensor sensitive to hydrogen-ion, an effort has been made to address this issue by using a cell without a liquid junction, employing a chloride-sensitive ion-selective electrode as the reference electrode (Martz et al 2010, Takeshita et al 2014). Insofar as the chloride ion concentration of the seawater can be directly inferred from its salinity, this approach offers some promise, though again some assumptions as to the variation of activity coefficients with salinity, temperature and pressure are required.

4.2.2. Spectrophotometric approaches.

An alternate approach to measuring ‘pH’ in seawater is based on the use of indicator dyes (compounds for which the acid and base form have distinct optical absorption spectra) and a high-quality optical spectrophotometer. For sulfonephthalein indicators, such as cresol red, m-cresol purple or thymol blue, the reaction of interest at seawater pH is the second dissociation of a diprotic indicator (represented here as H2I),

Equation (11)

and as the ratio  can, in principle, be directly inferred from spectrophotometric measurements, it is possible to use this knowledge to estimate the ‘pH’ of a seawater containing indicator (Byrne and Breland 1989, Clayton and Byrne 1993, Zhang and Byrne 1996, Liu et al2011) provided that one can obtain suitable calibration solutions comprising seawaters whose ‘pH’ is independently known. Tris buffers in synthetic seawater are used for this, with knowledge of their composition traceable to Harned-cell measurements. A further confounding factor when employing the spectrophotometric technique is that impurities in the dye can contribute errors to the measurements (Byrne and Yao 2008, Liu et al 2011), and thus it is desirable to use ‘purified’ dye, which is not yet available commercially. Also, the addition of the dye to the seawater necessarily changes the seawater pH slightly, and a correction needs to be estimated for this (Clayton and Byrne 1993, Dickson et al 2007—SOP6b).

Both potentiometric and spectrophotometric approaches to defining seawater ‘pH’ thus trace their calibration to standard buffers (usually based on Tris) prepared in synthetic seawaters that have been assigned ‘pH(S)’ values using Harned-cell measurements. An assumption underlying this is that it is reasonable to assume that the activity coefficients of acid-base species are the same in natural seawater and in the buffer with the same nominal salinity. Furthermore, the electrometric approach also assumes that the liquid-junction potential attributable to the reference electrode of a pH cell is the same in natural seawater and in the buffer with the same nominal salinity.

4.2.3. Quality of measurements.

Ocean scientists commonly report the quality of their ocean pH measurements in terms of precision rather than overall uncertainty. This recognises that it is the ability to detect changes in seawater pH with time, rather than the absolute pH values themselves, that is often of scientific relevance. Relevant time-scales vary from months (Hofmann et al 2011) to decades (Byrne et al2010), depending on the process being studied. Achieving this, however, requires a detailed consideration of uncertainty, and often the only measure of uncertainty provided by current investigators is measurement precision, estimated from repeatability of replicate measurements of field samples.

A significant problem for measurements in natural waters, which is not usually an issue in laboratory studies of simple systems, is that changes in the carbonic-acid system can significantly affect pH. Natural water samples are susceptible to contamination due to the exchange of CO2gas with the atmosphere, or by its production through microbial processes. Special sampling and measurement procedures are required to minimize or account for such changes (Dickson et al2007), and a recent inter-laboratory study of seawater CO2 measurements (Bockmon and Dickson 2015) reveals that these procedures are not carried out optimally in many laboratories. Indeed the results presented in Bockmon and Dickson (2015), which details measurements made by a number of marine laboratories on two test seawater samples (two bottles of each test sample), suggest that the (pooled) repeatability for spectrophotometric measurements of the ‘pH’ of seawater samples is ca. 0.003, and that for electrometric measurements using a glass-electrode cell the repeatability is ca. 0.012. These values are considerably larger than the best published values, which suggest that a repeatability of ca. 0.0005 is achievable for both spectrophotometric measurements (Byrne et al 1999, Carter et al 2013) and for measurements using an ISFET device (Takeshita et al 2014).

4.2.4. Alternate hydrogen-ion scales.

One of the more confusing aspects of seawater ‘pH’ measurements is the variety of seemingly different hydrogen-ion scales that have been used over the years which may deviate from each other by more than 0.1 (Marion et al 2011). Authors have chosen to define ‘pH’ in terms of either the amount of free hydrogen ion (the usual approach in aqueous chemistry) based on H+ and its various hydrates, or in terms of some more elaborate form of hydrogen-ion amount that, in addition, implicitly accounts for the effects of interactions between hydrogen ions and other seawater medium constituents such as sulphate or fluoride.

The reason underlying the adoption of these more complex definitions is to reduce the likely uncertainty in the defined parameter—see, e.g., the discussion in Dickson (1990). The synthetic seawaters in common use for the preparation of Tris buffers do not typically include fluoride ions, and thus the ‘total hydrogen-ion scale’ (which is in widespread use in marine chemistry) accounts for H+ and its various hydrates, together with the effect of interactions with sulphate ion to form bisulphate. As noted above, it is desirable to define this in a way that—in a particular sample—ensures that the amount of total hydrogen ion remains directly proportional to that offree hydrogen ion; the constant of proportionality being a function of salinity, T and p.

The ‘seawater hydrogen-ion scale’ also includes the interaction with fluoride ion (present at minor levels in natural seawater) to form hydrogen fluoride (Dickson and Riley 1979). There is, however, little advantage to be gained by accounting for the effect of fluoride in this implicit fashion, rather than accounting for it explicitly.

As an added complication, alternate approaches have been taken over the years to defining the composition of seawater with respect to hydrogen ion in terms of molality (nB/); amount concentration (nB/V), also known as molarity; or amount content (nB/MS), occasionally also termed molonity (McIntyre 1976, Barthel et al 1986): the currently recommended approach (Dickson et al 2007) being amount content (typically, in moles per kilogram of seawater) together with the related practical activity and its reduced, i.e. unitless, definition (see appendix B in Feistel et al 2015—the supplement of the Part 1 companion paper). Here, nB is the amount (i.e. number of moles) of solute in the given sample,  is the solvent (i.e. water) mass, V is the volume of the solution and MS is the mass of the solution.

4.3. Use of Harned cells to characterise Tris buffers in synthetic seawater

As noted above, standard buffers based on synthetic seawater underpin the calibration of most current seawater pH measurements, and the most common such buffer used in seawater studies is based on Tris and its conjugate acid (Tris–H+). The reasons for this are twofold: the use of a buffer based on a synthetic seawater makes it practical to use a Harned cell to characterise theacidity function,

Equation (12)

for the buffer with a known uncertainty, and hence to use a convention of some form to convert this value to a ‘pH(S)’; also the composition of the synthetic seawater can be chosen to resemble natural seawater sufficiently to enable one to assume that activity coefficients (and transport numbers) for the various acid-base species in the synthetic seawater are essentially the same as they would be in a natural seawater of the same nominal salinity.

The Harned cell used for such studies contains platinum (Pt), and silver/silver chloride (Ag/AgCl) electrodes:

the cell reaction is

Equation (13)

where s, g and aq, respectively, denote solid state, gas and aqueous solution, and the e.m.f. (adjusted to a standard pressure of 101 325 Pa) is given by

Equation (14)

where  is the mean-ion activity coefficient of HCl in the test solution.

A particular synthetic seawater composition is chosen as representative of natural seawater of standard-ocean Practical Salinity of 35. The composition of this synthetic seawater of nominal Practical Salinity 35 is based on knowledge of the composition of the surface North Atlantic Seawater that is used as IAPSO Standard Seawater (Dickson et al 2007, Millero et al 2008, Pawlowicz et al 2015). Certain species are omitted from the recipe: bromide to enable accurate use of the Harned cell, acid-base systems such as carbonate and borate to ensure that it can be considered as an ionic medium, and other species such as Li+ or Sr2+ in the interests of simplicity. These are replaced by increasing the amounts of similar major species to maintain the nominal ionic strength approximately constant (in contrast to other properties such as Absolute Salinity).

The composition of this synthetic seawater, which typically contains only water, NaCl, Na2SO4, MgCl2, KCl and CaCl2, is suitable for measurements with Harned cells. Then,

(1)  

Measurements are made with Harned cells on synthetic seawater of a particular nominal Practical Salinity, where varying amounts of the NaCl have been replaced with HCl while maintaining constant nominal ionic strength (Dickson 1990, Pratt 2014).

(2)  

Measurements are made in Harned cells, on the same synthetic seawater but now containing Tris, and where NaCl has been replaced with HCl, again at constant nominal ionic strength, so as to prepare a buffer (usually equimolar) of Tris and Tris-HCl (DelValls and Dickson 1998, Pratt 2014).

In the case of experiment (1) above, the limiting value

Equation (15)

can, in principle, be determined experimentally (however, see discussion below), where  is the so-called trace activity coefficient of HCl in the pure synthetic seawater medium, and  is the standard potential for the Harned-cell reaction (Bates and Bower 1954).

For experiment (2) above on Tris buffers, the expression (14) for the cell e.m.f. can be rearranged as

Equation (16)

In equation (16), the hydrogen-ion molality is estimated from three terms on the right-hand side. The first is experimentally accessible and peculiar to the buffer chosen; the second is also experimentally accessible from equation (15) and depends on the medium chosen. Accurate evaluation of the third term requires a model for the behaviour of activity coefficients in electrolyte solutions, and it has typically been assumed to be negligibly small compared to the other terms.

In seawater media, where some hydrogen ion reacts with the sulphate ion in the medium to form bisulphate ion, it is not at all straightforward to calculate  accurately in the solutions containing HCl, see experiment (1) above, without a reliable equilibrium model (see discussion in Dickson 1990), though it has been attempted (Waters and Millero 2013). Defining an apparenttotal hydrogen-ion molality, by

Equation (17)

can largely circumvent this problem, where  is the total molality of sulphate ion in the synthetic seawater. The acid dissociation constant of the hydrogen sulfate ion (at the same temperature and pressure) is

Equation (18)

and

Equation (19)

is the corresponding trace activity-coefficient product of the solution in a synthetic seawater of a specified composition. The limit  is assumed to be path-independent, where m is a vector of molalities representing the composition of the solution, and mSW is the composition of the synthetic seawater used as the ionic medium.

The total molality of hydrogen ion is defined by extending the so-called hydrate convention(Pitzer and Brewer 1961) to include not only the hydrogen ion combined with water molecules, but also the amount of hydrogen ion combined with the sulphate ion (a component of the seawater medium) as suggested by Sillén (1967). This definition of a total hydrogen-ion molalityis identical to the sum of the molalities of these species:

Equation (20)

in the limit of the pure synthetic seawater. Nevertheless, the definition chosen here remains exactly proportional to the free hydrogen-ion molalitym(H+), even at finite concentrations of hydrogen ion.

Substituting  from (17) for  in the expression (14) for the e.m.f. of the Harned cell gives

Equation (21)

In the limit  in the synthetic seawater, we have  and

Equation (22)

This expression (22) can then be used to interpret Harned-cell measurements made on a Tris buffer in the same synthetic seawater background and with the same chloride concentration and nominal ionic strength.

Making use of the definition (17), equation (16) for hydrogen-ion molality can be rewritten as

Equation (23)

As in equation (16), there are again three terms on the right-hand side, two of which are experimentally determined quantities for which it is straightforward to estimate uncertainties, and a third term that requires a model for activity coefficients such as that of Pitzer (19731995), both to estimate its value as well as its uncertainty. To date this term has been assigned the value of zero, without any scrupulous estimate of the uncertainty of this assumption (DelValls and Dickson 1998, Pratt 2014).

The benefit of choosing to define a total molality of hydrogen ion, rather than a free molality, thus lies in the likely reduced uncertainty of the value of the second term in this expression when estimated from Harned-cell measurements. At this time, the only careful uncertainty estimates for this pH proxy, , in Tris buffers in synthetic seawater have been made by Pratt (2014), who reports expanded uncertainties of ≤0.004.

5. Problems and deficiencies

It has been agreed at an international level that the Harned cell in principle fulfills the definition of a primary method of measurement (Milton and Quinn 2001) for measurement of the acidity function, equation (12), and that measurement results of this parameter using this cell can havemetrological traceability to the SI provided that all sources of measurement uncertainty have been identified and their effects quantified (Buck et al 2002, De Bièvre et al 2011). It is the decision to define pH as the single-ion activity, equation (1), which causes additional difficulties. Such a single-ion activity is immeasurable by any thermodynamic method and requires a convention for its evaluation (Buck et al 2002).

In the current approach to defining pH, the pH(S) values of internationally recognized primary standard buffer solutions are assigned using measurements made with a Harned cell on solutions of the buffer together with added NaCl or Cl. These are extrapolated to determine

Equation (24)

The pH(S) for the primary standard buffer (at the limit where the amount of added NaCl or KCl is zero) is then assigned using a conventional value for  based on the expression

Equation (25)

where A has at each temperature the value given by Debye-Hückel theory, and the factor B has a specified value; that recommended is  (Bates and Guggenheim 1960). This is done at various temperatures between 5 °C and 50 °C.

Buck et al (2002) detail the uncertainty budget for the assignment of pH(S) values to the recommended primary standard buffers, and estimate an expanded uncertainty (coverage factork = 2) of 0.003–0.004 for ‘conventional’ pH values. This takes into account all sources of uncertainty, with the exception of the uncertainty associated with the Bates-Guggenheim convention for calculating , estimated as 0.01 (k = 2). Hence, if we wish to have metrological traceability to the SI without specification, rather than limited to a conventional measurement procedure, we must report a measurement uncertainty that turns out to be about  times greater, even though the measurement procedure is exactly the same (De Bièvre et al2011).

Of course, the uncertainty of the assignment of pH(S) to the primary standard buffer is not the whole story nor, typically, even the major source of uncertainty in a pH measurement. Figure 1outlines a metrological traceability chain with the likely expanded uncertainties linking this to the end-result: a measurement of pH using a glass-electrode cell performed in a ‘typical’ test laboratory.