Measurements of total carbon dioxide and alkalinity by potentiometric titration in the GEOSECS program

Earth and Planetary Science Letters, 55 (1981) 99-115

99

Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands (61

Measurements of total carbon dioxide and alkalinity by potentiometric titration in the GEOSECS program Alvin L. Bradshaw, Peter G. Brewer, Deborah K. Shafer Woods Hole Oceanographic Institution, Woods Hole, MA 02543 (U.S.A.)

and

Robert T. Williams Scripps Institution of Oceanography, La Jolla, CA 92093 (U.S.A.) Received August 28, 1980 Revised version received April 12, 1981 Approximately 6000 determinations of the alkalinity and total carbon dioxide content of seawater have now been made in the AtlantiC, Pacific and Indian Oceans as part of the GEOSECS program by a computer-controlled potentiometric titration technique. The equations used to locate the equivalence points of the carbonic acid system on this titration curve were developed in 1971 but have not previously been published. These functions may be represented by: Fi _ ( V2 -- V) N I n + ]/Ktc + ~

v0

( [ n + ] + [HSO 4- ] + [HF.] - [B(OH)4 ] )

x (1 + [H +]/x,~) F2 = ( Vo + v ) ([H + ] + [HSO~ ] + [HF] - [ H C O f ]) Upon inspection, these functions are analogous to the modified Gran functions of Hansson and Jagner [25] with the omission of the contributions of [OH-] and [CO2-], and with the contribution of B(OH)~ being assessed at a chlorinity of 19%o for all samples. Reprocessing the original titration e.m.f.-volume data with appropriate corrections and modified Gran functions reveals an error of about + 12 ~mol/kg in the GEOSECS total carbon dioxide data. In addition, the protonation of dissolved phosphate species during the titration results in a contribution to measured total carbon dioxide equal to the total phosphate concentration. Differences in the application of the GEOSECS functions between the Atlantic and the Pacific-lndian Oceans expeditions are also to be found so that the error deriving from this source for the Atlantic expedition was only + 5 ~mol/kg. The application of the correct functions increases precision enabling smaller differences, such as those attributable to fossil fuel carbon dioxide, potentially to be observed, and increases accuracy so that the error in titrator total carbon dioxide previously diagnosed by Takahashi [14] can be logically accounted for.

1. Introduction T h e d e t e r m i n a t i o n of t h e a l k a l i n i t y a n d t o t a l carbon dioxide of seawater by means of potentiometric titration has been one of the basic tools of Woods Hole Oceanographic Institution Contribution No. 4664.

t h e G E O S E C S p r o g r a m . A p p r o x i m a t e l y 6000 det e r m i n a t i o n s h a v e n o w b e e n m a d e in t o t a l in the A t l a n t i c , Pacific, A n t a r c t i c a n d I n d i a n O c e a n s , a n d a s y n o p s i s o f t h e e n t i r e d a t a set has r e c e n t l y b e e n p r e s e n t e d b y T a k a h a s h i et al. [1]. T h e results o f this e x p e r i m e n t a r e o f g r e a t i m p o r t a n c e to m a r i n e g e o c h e m i s t s in d e f i n i n g t h e c a r b o n d i o x i d e

0012-821X/81/0000-0000/$02.50 © 1981 Elsevier Scientific Publishing Company

100 status of the world oceans at a specific point in time. The results have been used to examine carbonate dissolution [2,3], to characterize 14C penetration [4-6] and to determine fossil fuel CO 2 increases [7-9] in oceanic waters. Although the titrator results have been widely disseminated in the form of data reports from the various cruises, and will soon be available in published atlas form, no formal publication of the procedures followed has yet occurred. In this paper we document the theory behind the titration procedure and make note of certain experimental practices. Full documentation of the experimental details of titrator design, construction and calibration is to follow (R.T. Williams et al., in preparation).

2. The GEOSECS titration data set

The titration results from the GEOSECS program have been carefully examined by Takahashi and co-workers. The results from the GEOSECS Atlantic expedition were reviewed by Takahashi et al. [10] who found the data to be internally consistent with the apparent dissociation constants of Lyman [11], Hansson [12] and Mehrbach et al. [13]. The total carbon dioxide determinations were compared with independent gas chromatographic total carbon dioxide determinations, and with measurements of p C O 2. The internal consistency was found to be good after the application of several correction terms for blank effects of +0.85% (titrator), and for temperature effects on sample loop volume changes of +0.85% to 1.85% (gas chromatograph). Takahashi [2] presented GEOSECS titrator results for the Atlantic and Pacific Oceans. He calculated the in situ carbonate ion concentrations and degree of saturation with respect to calcite and aragonite. He noted a problem in that the titrator alkalinity and total carbon dioxide data from the Pacific yielded calculated p C O 2 values which were consistently 15% greater than his direct p C O 2 measurements, and that this discrepancy led to a considerable uncertainty in the calculated calcite saturation depth. Takahashi [14] further reviewed the consistency of the entire GEOSECS Atlantic and Pacific

carbonate chemistry data sets, and concluded that significant differences in total carbon dioxide (approximately 14/xmol ECOE/kg ) existed between the two data sets, but that it could not be proven whether the Atlantic total carbon dioxide titrator data were low, or the Pacific data were high. Broecker and Takahashi [3] later examined the relationship between lysocline depth and in situ carbonate ion concentration and concluded that the GEOSECS Pacific titrator total carbon dioxide data were too high by 14 /~mol/kg. They subtracted this quantity from the shipboard results but were compelled to report that no physical basis for this apparent over-estimate could be found. This correction, although apparently small, has a large effect on the calculated calcite saturation depth, changing this quantity by 1.5-2.0 km, and thus resolution of the source of this error is critically important. Recent results from the Indian Ocean again show pCO 2 values computed from titrator data to be 15-20% high compared to directly measured values (T. Takahashi, personal communication), and comparison with directly measured total carbon dioxide using a manometric technique again shows the titrator values to be high (C.D. Keeling, personal communication). In order to resolve these differences a meeting was held in La Jolla in December, 1979, convened by H.G. Ostlund. The work presented here stems from this meeting and copies of the computer programs described are to be found in the meeting report [15].

3. Experimental details

Full experimental details will be published elsewhere. A brief reporting is given here for the sake of completeness. The titration cell was constructed of lucite, in the form of a jacketed cylinder of approximately 110 ml internal volume. Water circulated around the external lucite shell maintained temperature at 25°C. The acid used was 0.25 N HC1, fortified with NaC1 or KC1 (0.45 N) as a supporting background electrolyte to maintain approximately constant ionic strength during the course of a titra-

101

tion. The burette, a 2.5-ml glass syringe, micrometer mounted (Cole-Parmer 7874), was held in the vertical position. The burette was fitted with an optical shaft encoder and driven by a stepping motor, the whole ensemble being under computer control. We are indebted to the late A.E. Bainbridge for his skill and leadership in developing this elegant system [16]. The glass electrodes used were Beckman Model 41263 general purpose electrodes of lithium glass, which may be shown to have negligible sodium error at the maximum and minimum pH attained during the titration of a seawater sample. The procedure was standardized by titration against sodium borate decahydrate (Na2B40710 H20 ) prepared by recrystallizing the reagent from distilled water at a temperature of < 50°C and placing the washed recrystallized product in a dessicator over a solution containing 150 g sucrose and 150g sodium chloride in 100 ml distilled water [ 17].

4. Development of titration theory The first application of the potentiometric titration technique to the determination of the alkalinity and total carbon dioxide content of seawater was by Dyrssen [18]. He carried out the titration in a beaker covered by "parafilm" to conserve carbon dioxide and prevent evaporation. He used Gran [19] plots to locate the equivalence points of the titration curve and noted that these were subject to small error due to the presence of other protolytes such as CO32- , B(OH)4 HPO4:- and F - in the system. Dyrssen and Sillen [20] expanded upon this procedure and presented a full development of the titration equations and theory. They developed a relationship for the hydrogen ion excess over the second equivalence point incorporating terms for HCO3-, CO 2- , B(OH)~- and OH (their equation 12), but reduced this to consideration of H C O f only for their final result. Edmond [21] repeated the caution of Dyrssen [18] regarding the contribution of minor protolytic species and presented a Bjerrum plot showing their distribution as a function of pH. However, he did not incorporate these in a formal manner into his calculations and

in practice used equations identical to those of Dyrssen and Sillen [20]. He improved experimental practice, employing a dosed titration cell, and carried out measurements of alkalinity and total carbon dioxide at several oceanic stations [22]. In the following discussion we investigate the equations used in the GEOSECS program for locating the equivalence points of the potentiometric titrations; we compare these equations with theoretical models and with the best equations available to date, and finally we recalculate several titrations from the raw e.m.f, data in order to evaluate any error deriving from this source. The basic equations necessary for locating the equivalence points in the potentiometric titration are as follows: The electrode slope equation from classical Nernst theory is:

E-- E o +-~- ln[H~-]

(1)

The value of E 0 depends on the type of pH cell and on the activity scale for H + , and can also vary with liquid junction effects on the reference electrode. In their simplest forms, the Gran functions for locating the bicarbonate-carbonic acid and the carbonate-bicarbonate equivalence points, Vz and Vl, are, respectively:

and: F, = ( V 2 - V ) l O e x p [ ( E - - E o ) / ( - ~ - - ) ] where RT/F= 59.16 at 25°C. Linear regressions on V of first F2 and then F~ are calculated and the equivalence points are taken as the intercepts of the lines on the V-axis. The accuracy of Gran plots for locating the equivalence points in potentiometric titration techniques has been questioned by many workers [23,24]. The most detailed critique, with particular application to seawater, is that of Hansson and Jagner [25]; the recent paper by Maclntyre [26] appears to be a specific example of the more general contribution by Hansson and Jagner. These authors point out that the simple Gran plots only

102

hold true if the background electrolyte behaves in an inert manner with respect to protonation, i.e., there are no side reactions. This is not the case for seawater. Using an ionic medium activity scale, in which concentrations may be substituted for activities, Hansson and Jagner [25] evaluated the contribution to proton balance, at each step along the titration curve, via an equilibrium model. This permitted an accurate assessment of the contributions due to formation of H F and HSO4-, etc., and led to the use of modified Gran plots. An iterative scheme was described for the accurate calculation of E 0, alkalinity and total carbon dioxide. Their modified Gran functions, F~ and F~, are then given by: F; = (V0 + V ) ( [ H + ] + [H2CO 3 ] + [HSO4-] + [HF] - [ O H -

] --[B(OH):]

-Icon-]) (v, < v < v2)

(4)

and:

= (Vo + v)([H + ] + [HSO.-] + [HFI - [ H C O ; ] ) cc ( V - V2)

(v>

(5)

where [H2CO3], [HCO3-] and [CO 2- ] refer to total molar concentrations of these species. By manipulation of mass balance and proton conditions:

F( = (V2 -- V ) N ( [ H + ]2 _ K , c K E c ) / ( K i c [ H

+

]

+ 2K,cK2c) + (Vo + V ) ( [ H + ] + [HSO4- ] + [HF]- [B(OH,)-] -Ion-])([n

+ ]2

+ K l c [ H + ] 4 KIcK:c)~ (KIc[H +] + 2KicK2c ) cc ( V - V,)

(6)

where N is the acid normality, and V1 and V2 are the carbonate-bicarbonate and bicarbonatecarbonic acid equivalence points. To compute Ff and F~ (at 25°C) the following relations are used: [H + ] = 10 exp((E - Eo)/59.16 )

(7)

[ H C O f ] = [CO2]t/([H + ]/K,c + 1)

(8)

[HSO4--] = [SO4]t/(1 + KHsoJ [H + ])

(9)

[HF] = [F]t/(1 + K n v / [ H + ])

(10)

[B(OH):] = [Sl,/([H + ] / r . + 1)

(11)

[OH-] = Kw/[H + ]

(12)

where the subscript "t" refers to the total concentration of this constituent. The error resulting from the failure to use modified Gran functions varies markedly with the volume interval of the titration taken for extrapolation. Hansson and Jagner [25, table III] suggest that typically errors in alkalinity are - 0 . 8 % (--~ - 1 8 #¢q/kg) and in total carbon dioxide approximately 40.8% (--" + 19 #mol/kg).

Fig. 1..GEOSECS program for calculation of alkalinity and total carbon dioxide from titration data (E, V) at 25°C. V0 is cellvolume (105- l l0 ml) and N is acid normality (0.25). [H +]* is defined by [H +]*--exp[( E - Eo)/25.6886] and is approximatelyequal to [H +].

F~(i) =(1 +y)[H +]* -Ct(i)/{ 1+[H +]*/Krc(i) }/a(i) and:

F~(i)=(At(i)--yN}[H+]*+K~c(i)a(i)(I+y)(I+[H+]*/K~c(i))[H+] * - - ( 2 . 2 × 10-5 × 1 9 × r ~ / ( K h + a ( i ) [ H + l . ) ) ( l + [ H + l . / K r c ( i ) ) K r c ( i ) , where K ~ = 2 . 0 4 5 × 1 0 -9. a(i), K~'c(i ), Ct(i ) and At(i ) approach a = A [ H + ] J A [ H + ] *, K~c=[H+]*[HCO3-]/[H2C03], total carbon dioxide and alkalinity in the iterative calculation. Note: This diagram represents the Pacific (1974) and Indian Ocean 0978) version of the GEOSECS program. The Atlantic Ocean (1972) version contained an additional constraint such that the fourth box of this flow scheme would then read "Select remaining (b~' 2 ,V) such that: F2* > 1 × l0 - 6 find VF~(rain)(i)'" This modification accounts for the differences in the sets of GEOSECS results in Table 4.

103

Vn(ml)= ~-AVn , En(mV),Vo(ml), Eo(mV) = 4t2,N (E/I) . ~ -6 , V(t)=L25(fortron -Lt (bosic progrom) INITIAL VALUES F(~)= 0,0022/N, o(I)-t,Ktc(t)-IXIO progrom)

p,, I~

CONVERSION OF (E,V)DATA TO: )" =V/Vo,[H+]~e(E-Eo)/25 6886

SELECT (F~,V) SUCHTHAT: F~<0.9 F~' Vor (~)

i=i+t "

[

• (MIN)( i, ) FIND VF2

i CALCULATEREGRESS,ON:F~°o(V~VoI+~]

ICA'CULATE A,(,~.o(,)-N~o I

.~PRINT A,C')D

SELECT (FtV) SUCH THAT (IN SEQUENCE):

v~<~(i),~< 0.9F~*(MAX),,>3, F,%t X 10-". •[

FINDVtlMAX)(i ) LET V( i ) = (VF~(MAX)~ i ) +VF:(MIN)( i ))/2 I CALCULATE REGRESSION: F~=o(V/Vo)+ b I

>2o'; >1.1o"

LCALCULATE~ ( ' )= o'N,~'' '=(A,(' )'N'O.~; C,('' ~

PR'NT C,('' D

No

[ PRINT At(i ), cr(A,(i )); Ct(i ),o'(Ct( i ));Kf~c( i )-°(i),E;=eo-::)S.6886 In°(i) I

104

The equations used in the GEOSECS program were developed by the late Arnold Bainbridge and co-workers prior to the publication of Hansson and Jagner [25]. Our belief is that these equations were developed in 1971, however, there is no published record of this. This belief is substantiated by the personal notes left by Bainbridge. We have obtained the Bainbridge equations by decoding the GEOSECS computer programs (see Fig. 1). Letting an asterisk refer to certain quantities in these programs, the Gran functions used in them are at 25°C as follows:

= E~ + 59.16 log[H + ]t

E~ is updated after each titration. It should be noted that would correspond to Hansson's [12] definition of the first dissociation constant of carbonic acid, if the seawater were of the same composition used in his determinations of these constants. Neglecting minor [H + ] reactions, such as those in the phosphate system, ~2 is proportional to:

aK~c

Vo+V\ + -----~0 )([H ] + [ H S O 4 - ] + [ H F ]

[ Vo+V~. ~+

F ~ ' = ~ - - - - ~ o )[H - (1 +

]*-[COEIt

- [HCOf])

(18)

Under this same assumption:

[H+]*/K'~c)/a

(13)

and:

v2- v

(17)

F~/K~c= [lv- - - T-vo

[ v + vo

.

)NtH+

]/K,c + [Vo+V ~~ ]1

x {[H + ] + [nsoz]

+ [HF]

X (1 + [H + ]*/K~'c)[H + ]*a -

- {2.2 × 10-' K~ X 19(%oC1) - (K L + ec[H+ 1")}(1 + [H +

]*/Krc)K'~c

V ~

×2"2X10-SKB

X 19(%oCl)/(K~+ [H + ]')t J

(14)

X (1 + [H + ] / K , c )

where: [H + 1" = 10 (E-Eo)/59"16

(15)

which, using the approximation:

Krc = [ n + ]* [ H C O f ]/[H2CO 3 ]

(16)

( Vo~V) X2.2X IO-SK~ X19(%oCI)/

K~ = 2.045 × 10 -9 is Buch's [27] value of the apparent dissociation constant of boric acid for 19%o chlorinity seawater at 25°C, and a is the reciprocal of the total activity coefficient for the hydrogen ion on the [H+]t activity scale, a and K]"c are evaluated from the slopes of the regression lines of F2* and F~, respectively, on V, found in the iterative computation for the equivalence points V2 and Vl (see Fig. 1). The value of E o depends upon the cell electrode system and the hydrogen ion activity scale. For each cell a starting value of 412 mV is assumed. This determines the [H +]t activity scale by: E = 412 + 59.16 log[H + ]* [H+], = 412 + 59.16 log - = (412 -- 59.16 log a) + 59.16 log[H + It

(K~ +[H + ],) = [B(OH)~]

(19)

(20)

is equal to:

( V2~voV)N[H+]/K,c + ( ~V°+ V\)([H+] + [HSO;] + [HF] -[B(OH)4-]) X (1 + [H + ] / K , c )

(21)

Upon inspection, the functions F~ and F~l are proportional to the modified Oran functions Fd and F~ of Hansson and Jagner with the following differences: (a) [ O H - ] and K2c are set equal to zero in the GEOSECS equations i and (b) the contribution of B(OH)~- is assessed using Buch's value for K~, at a chlorinity of 19700 for all samples and neglecting the acid dilution factor. In order to test the errors introduced from (a)

105 a n d (b), we have carried out a series of m o d e l c a l c u l a t i o n s a n d r e - r u n s of G E O S E C S raw data.

i={ CALCULATE v 2(t ) USING F 2 CALCULATE vt (t) USING F| Ct(t ) =t (v2(t)-v4(4 ))/v o CALCULATE E°(t ) USINGv2(t )

~l

5. Tests of titration programs T h e G E O S E C S p r o g r a m a n d two m o d i f i e d G r a n m e t h o d p r o g r a m s were tested on a theoreticallyg e n e r a t e d t i t r a t i o n d a t a set, a n d on actual G E O S E C S t i t r a t i o n data. T h e G E O S E C S p r o g r a m (Fig. 1) is o u r o w n r e n d i t i o n of the one used d u r i n g the Pacific a n d I n d i a n O c e a n e x p e d i t i o n s in 1974 a n d 1978, m o d i f i e d for use on the W o o d s H o l e W a n g 2200T c o m p u t e r . A n earlier version o f the G E O S E C S c o m p u t e r p r o g r a m , which we believe was used on the A t l a n t i c e x p e d i t i o n in 1972, was also r e p r o d u c e d . T h e p r i n c i p a l difference between these two versions is the e l i m i n a t i o n o f one o f the selection criteria for p o i n t s c o n s i d e r e d for the c a l c u l a t i o n o f F 2 in the later versions of this

i=i+l

CALCULATE v2(i) USING F~,

CALCULATE v( ( i ) USING F AND v2( i )

1

, ~ v : :E Av n ' ~

Ct(i) =t (v2( i )-vt( i ) ) / v o

CALCULATE [H÷1 +[HSO~,]FROM CT=CT^Vo/(Vo+V) AND A=Aovo/ (Vo÷V)~-Nv/(Vo÷V) USING CONDITIONAL DISSOCIATION CONSTANTS K~C, K~C, K~BAND K~ OF HANSSON (t973)

CALCULATE E°( i ) USINGv2( i )

~ E= E'o+'-~ I

PRINT RESULT

]

Fig. 2. From Hansson and Jagner [25]. The expressions for F2, /71, F~ and F{ are given in Appendix 2.

In([H+]+[HSO~]) ~>

Fig. 3. Flow scheme for generation of E, V titration points in case where composition with respect to total concentrations of all constituents except those of the reactants is constant. Fluoride is assumed to be absent in order to simplify the computation (Hansson's constants were determined in fluoride-free artificial seawater). K[c, K~c and K~n were calculated from Almgren's [28] equations and then, along with Kw, were converted to a molar basis to be consistentwith units of [ ], Note that E~ = E o - ( R T / F ) In(1 + flnsoz [SO2- ] is assumed to be constant.

106

(Figs. 3 and 4) for several 3570o salinity seawater samples with different values of alkalinity, total carbon dioxide, total phosphate and total silicate. In the case of one set of titrations (Fig. 3), the total concentrations of all ions except the reactants were kept constant and no fluoride was present ("constant composition titration"); in the other case (Fig. 4), fluoride was present and the composition of the solution varied as a sodium chloride (or potassium chloride)- hydrochloric acid

program. Both modified Gran method programs follow the Hansson and Jagner scheme (Fig. 2), but include corrections for side reactions with components of the phosphate and silicate systems. The "special Gran method" program includes a correction for the effect of the reduction in free sulfate ion concentration on the amount of H S O f . Two sets of theoretical titration data in the form of E ( E = E o +(RT/F)ln[H+]) versus volume V of acid added were generated at 25°C

ITERATE

CALCULATE [ HCO~]T;[CO~,]T, [B(OI"I~,]T,[Ht]T AND[OH ]T FROM CONDITIONALDISSOCIATION CONSTANTS K;c,K~c,K;BAND KW; AND CT = CTo X Vo/(Vo + v)AND A = A o X Vo/(Vo+ v)- vXN/(vo+V)

.I

I=

v>O

1

CALCULATE FREE ION CONCENTRATIONS, [Ij], FROM EQUATION [Ij] = ~j] T/(!+ ~KBjK[IK]!IN THE CASE OF No + THE EQUATION IS I

t

I

[No']= ([NO÷IToXvo + G Xv/58.45i/(%+ v)/(~i +'~BNOIK ~K])

CALCULATE K I c , K 2 c , K I B , AND K'W FOR SOLUTION MEDIUM AT EACH STEP OF TITRATION g,=,O

v'O

I L

,

v>O

/

CALCULATE DISSOCIATION CONSTANTS (FREE IONIC) KtC = Kt~/(t + K~HIK[IK])/(t * ~ I K HCO3[IK]) K2C = K~C X (1 +~K~IKHCO3[IK])/(t + ~K/gHIK~K])/( 1"1"~K/gZKCO3[IK]) KtB = K'IB / (I .1.~,~H I ~ [,.I K ] ) / ( t + ~,~I KS(OH)4 [IK]) KW = K ~ / (I + Z~KHIK ~IK])/(t * ~K~IKOH[IK])

J IT K] v=O

[H ÷ ]

~ E--Eo÷~-~In[Hi] J~ Fig. 4. Flow scheme for generation of (E, V) titration points in the case where the composition of the solution changes with the addition of acid (N normal HC1 containing G g/1 NaC1) but the ionic strength stays constant. K and K' are the true and total concentration (molar) dissociation constants on the ionic medium activity scale; subscripts "T" and "0" denote total concentration and the seawater sample; C T and A are total carbon dioxide concentration and alkalinity; c is the error tolerance in the ion concentration computation. E 0 is assumed to be constant.

107

titrant was added ("actual titration"). Hansson's [12] values for K~c, K~c and "K~, (as formulated by Almgren et al. [28]) and for K~, were assumed for the calculations, after converting them to a molar concentration basis. Because Hansson measured these constants in fluoride-free artificial seawater, the calculation of the theoretical points for the "constant composition titration" was made simpler by assuming that no fluoride was present. In the case of the generation of "actual titration" points, the ionic composition of 35%o salinity seawater at 25°C was taken from table II of Dyrssen and Wedborg [29], except for assuming the strontium concentration equal to zero and then adjusting the chloride ion concentration to preserve the ionic balance. In the latter case, values for the ion association constants were taken from several sources; they are listed, along with the values used for the dissociation constants of phosphoric and orthosilicic acids in Appendix 1.

6. Results In the case of the "constant composition titration" the modified Gran algorithm gives good agreement with theoretical concentrations for alkalinity and total carbon dioxide when phosphate is low or absent (Table 1). Where phosphate is' present, the alkalinity agreement is still good, but the calculated total carbon dioxide value is high by almost the concentration of the total phosphate in the sample (Table 1).. The latter results can be explained when the proton conditions at the two equivalence points are examined for the case where the phosphate system is present. In this case, the sample alkalinity with reference to the first equivalence point must be adjusted by adding: [PO43- ] 0 -- 2[H3PO4]0 -- [HE PO4- ]o and the sample alkalinity with reference to the second equivalence point must be adjusted by adding: 2 [PO~-]0 + [ HPO2- ]0 - [n3PO4 ]o, where the subscript "0" refers to the sample. Thus, when phosphate is present:

N(V - Vl) Vo

- C t + [H3PO41o + [H2PO4-]o

+ [HPO:-]o +[PO:-]o = Ct + Pt

(22)

Therefore, to obtain the correct total carbon dioxide value of a sample, the total phosphate concentration must be subtracted from that calculated from the acid volume differences at the two equivalence points. Failure to include corrections for phosphate and silicate reactions in the program in the case of the "constant composition titration" appears to have a negligible effect on the location of the equivalence points (Table 1). Seawater samples are usually titrated with an HCI solution to which a salt, such as NaCI or KC1, has been added to bring this solution to approximately the same ionic strength as seawater. In the Woods Hole laboratory, and in the theoretical simulation given here, the acid solution is 0.05 N in the HC1 and contains 35 g/1 (0.60 N) NaC1. The supporting electrolyte used during the GEOSECS Indian Ocean expedition, and during Leg 6 of the Atlantic Ocean expedition, was KC1. We have also run simulated titration curves for 0.05 N HC1 acid solutions in which KC1 (0.60N) has been substituted for NaC1 and have found that this makes negligible change in the final result (A e.m.f.~< 0.005 mV during the course of the entire titration). For the ordinary modified Gran method the change in composition during titration has a small effect on alkalinity and a lesser effect on the total carbon dioxide (Table 1). The use of a higher-normality acid solution in smaller-volume increments, as in the GEOSECS titrations (0.25 N HC1 in 0.45 N NaCl or KC1) reduces the errors somewhat (Table 2). The results when the "special Gran method" is used are very close to the theoretical values (Tables 1 and 2). The GEOSECS titration program (Indian Ocean, 1978 version) is compared with the modified Gran function programs in Table 2. The results indicate good agreement ( --~ 0.3/~eq/1) of the computed alkalinities with the theoretical value in the case of both the special Gran and GEOSECS programs, but show the GEOSECS program total

108 TABLE 1 Titration results for alkalinity (At) and total carbon (Ct) calculated by the modified Gran method of Hansson and Jagner from theoretically generated e.m.f.-vs.-acid volume values for a sample salinity of 35%o at a temperature of 25°C. Corrections for phosphate and silicate are included in the modified Gran functions used, unless otherwise indicated. Concentrations are in gmol/1 and g e q / l , volumes are in ml. Constant composition titration

A cM (H CI) normafity = 0.05, cell volume= 105 ml Sample composition: At 2300 Ct 2000 Pt 0 Si t 0

2300 2000 0.1 5

2500 2400 3 0

2500 2400 0 150

2500 2400 3 150

Theoretical equivalence points: Vt = 0.63 V2 = 4.83

0.63 4.83

0.21 5.25

0.21 5.25

0.21 5.25

Volume ranges used for extrapolation: V1= 0.8-2.2 V2 = 5.2-6.4

0.8-2.2 5.2-6.4

0.4-2.0 5.4-6.8

0.4- 2.0 5.4-6.8

0.4- 2.0 5.4-6.8

Titration error (program result minus theoretical concentration) AA t AC t AA t AC t 0.0

0.0

0.1

0.0

AA t

AC t

AA t

AC t

AA t

AC t

0.0

2.9

0.0

0.0

0.0

2.9

Titration errors when no phosphate and silicate corrections are included Volume ranges used for extrapolation: Vm= 0.4-2.0 V2 = 5.4-6.8 Titration error

0.4- 2.0 5.4-6.8

AA t

AC t

AA t

AC t

0.0

3.0

0.0

3.0

Actual titration

Acid (HCI) normality=O.05, concentration of NaCl in acid=35 g / l (0.6ON), cell volume= 105 ml Sample composition: At Ct P, Si t

2300 2000 0 0

2300 2000 0.1 5

2500 2400 3 150

2500 2400 0 150

Theoretical equivalence points: Vt = 0.63 V2 = 4.83

0.63 4.83

0.21 5.25

0.21 5.25

Volume ranges used for extrapolation: VI = 1.0-2.4 V2 = 5.2-7.0

1.0-2.4 5.2-7.0

0.6-2.4 5.6-7.4

0.6-2.4 5.6-7.4

Titration error (program result minus theoretical concentration) AA t AC t AA t AC t ordinary Gran: special Gran:

2.4 0.0

1.4 0.2

2.4 0.0

1.5 0.3

2500 2400 3 0 ,:

0.21 5.25 0.6-2.4 5.6-7,4

AA t

AC t

AA t

AC t

AA t

ACt

2.4 0.0

4.0 3.0

2.4 0.0

1.3 0.3

2.4 0.0

4.1 3.0

N o phosphate or silicate corrections are included; volume ranges used for extrapolation:

v~= v2= Titration error (ordinary Gran)

0.6- 2.4 5.6- 7.4

0.6- 2.4 5.6- 7.4

0.6-2,4 5.6-7,4

AA t

AC t

AA t

AC t

AA t

AC t

2.4

5.0

2.4

2.0

2.4

4.3

109 TABLE 2 Comparison of GEOSECS program (our rendition) titration results with those obtained by the modified (/ran method. Titration data was generated for the two programs for a sample of given total carbon dioxide and alkalinity by the "actual titration" algorithm. The sample was assumed to be 357oo salinity seawater containing no phosphate or silicate. Temperature is 25°C. Concentrations are in /~mol/1 or/~eq/1; volumes are in ml; cell v o l u m e = 105 ml GEOSECS program

Modified Gran function program

2460 2370

2460 2370

2460 2370

2460 2370

0.25 33.3 *

0.05 35

0.05 35

- 0.05 35

Theoretical equivalence points: Vj = 0.0378 V2 = 1.0332

0.189 5.166

0.189 5.166

0.189 5.166

0.0378 1.0332

Volume ranges used for extrapolation: VI = 0.3-0.55 ** V2 = 0.85-1.45 **

0.6-2.2 5.8-7.2

0.4-2.8 5.2-7.8

0.4-2.8 5.4-7.2

0.1-0.5 1.1- t.45

Sample composition At Ct

Acid HCI normality Composition ( g / l NaC1)

2460 2370 0.25 33.3 *

Titration error (program result minus theoretical concentration)

ordinary G r a n special Gran

AA t

AC t

AA t

AC t

AA t

AC t

AA t

AC t

AA t

AC t

- 0.3

11.7

2.8 0.0

1.7 0.2

2.6 0.0

1.3 0.3

2.1 0.0

0.9 0.3

1.1 0.0

0.6 0.1

* KC1.

** Intervals are selected for each set of data by program. TABLE 3 Effect of volume ranges used for extrapolation on alkalinity and total carbon dioxide values when K2c -----[OH-]-----0 in modified Gran titration program. Tests are on titration e.m.f.-acid volume data generated theoretically by the "actual titration" program for titration of 3 5 ~ salinity sample at 25°C with 0.05 N HC1 containing 35 g/1 NaCI. Concentrations are in # m o l / l and/~eq/1; volumes are in ml; cell volumes = 105 ml Sample composition: At Ct P, Sit

2460 2370 0 0

2460 2370 0 0

2460 2370 0 0

2460 2370 0 0

Theoretical equivalence points: V1 = 0.189 V2 --5.166

0.189 5.166

0.189 5.166

0.189 5.166

Volume ranges used for extrapolation: V~ = 1.4-3.0 V2 = 5.8-7.2

1.0-2.6 5.8-7.2

0.6-2.2 5.8-7.2

0.2- 1.8 5.4-7.0

Titration error (program result minus theoretical concentration) AA t AC t AA t special Gran:

0:0

11.7

0.1

AC t

AA t

AC t

AA t

AC t

t 4.8

0.1

21.6

0.4

42.8

110 TABLE 4 Comparison of alkalinity (A) and total carbon dioxide (C) results obtained from Indian Ocean titration data using various algorithms. Concentrations are in/~mol/1 or/~eq/1 GEOSECSresults (Pacific and Indian Ocean program)

Special modified Gran program results

GEOSECS results (Atlantic Ocean program)

A

e(A)

C

a(C)

A

o(A)

C

a(C)

A

o(A)

C

a(C)

Indian Ocean station 449, sample 305

2361

0.8

2211

4.7

2359

0.6

2194

4.1

2361

1.6

2200

2.3

Indian Ocean station 417, sample 322

2456

2.9

2412

3.0

2456

0.5

2396

0.8

2458

n.c.

2407

n.c.

Indian Ocean, station 449, sample 306

2363

2.5

2235

2.9

2363

0.5

2225

2.4

2366

2.3

2234

2.5

Indian Ocean, station 417, sample 302

2438

4.6

2095

6.9

2439

0.7

2083

4.0

2442

1.0

2086

4.5

Sp____eecialmodified Gran results minus reported GEOSECSresults (Pacific and Indian Ocean program): AA=0, o(AA)= 1.3; AC= - 14, a(AC)=3.3 Special modified Gran res___ultsminus results using Atlantic version of GEOSECSprogram: AA= - 1, o(AA)=2.2; AC= --5, a(AC): 1.7 n.c. = not computed. carbon dioxide value to be high by 12 #mol/1. The choice of volume ranges used for extrapolation of the ordinary modified Gran functions has a small effect on the results. As mentioned above, the F~' function in the GEOSECS algorithm is approximately equivalent to the modified Gran function F[ with K2c and [ O H - ] set equal to zero. The special modified Gran program was run under these conditions on a theoretically generated set of points for the "actual titration" case, varying the volume ranges from which the equivalence points are extrapolated. The error in the total carbon dioxide value depends very strongly on the closeness of the F[ volume range to the equivalence point V1 (Table 3). In this simulation we have not given the acid normality the value used in GEOSECS expedition titrations and this may affect the results sli~.htlv. Results from the GEOSECS and special modified Gran programs are compared for alkalinity and total carbon dioxide for four Indian Ocean samples in Tables 4 and 5. Total carbon dioxide

values from the Gran program have been corrected by subtracting the phosphate concentration (see above). The modified Gran method values for total carbon dioxide are lower than the GEOSECS reported values. These results are consistent with the comparison of program results in Table 2. The GEOSECS F[ function is derived by neglecting CO 2 - and O H - reactions and thus depends for its accuracy on choosing a range for extrapolation, somewhat removed from V1, where the concentrations of these components are small. The effect of errors in the titration data on the value of Vt is thus magnified and probably accounts for the disagreements from sample to sample between differences predicted from the error-free titration simulation and actual data.

7. Conclusions (1) On the basis of reported results for four Indian Ocean samples, the GEOSECS titration

acid counts

electrode (mV)

--65.20 --55.46 --40.45 -- 19.14 1.64 16.31 27.11 35.81 43.42 50.21 56.59 62.63 68.61 74.60 80.91 87.50 94.97 103.60 114.38 129.31 152.50 178.38 194.90 205.51 213.06 218.99 223.80 227.86 231.34 234.41 237.21

acid counts

0 1064 2127 3192 4258 5324 6391 7457 8523 9588 10653 11720 12785 13848 14910 15970 17031 18092 19153 20216 21280 22344 23408 24471 25534 26596 27658 28722 29785 20847 31908

0 1068 2135 3202 4269 5336 6402 7466 8531 9597 10662 11726 12788 13950 14911 15973 17034 18095 19159 20223 21286 22350 23414 24478 25541 26605 27668 28729 29789 30848 31907

cell volume= 110.168 ml calculated E o ---410.8 mV calculated Kic = 1.464)< 10 -6 (M)

cell volume= 110.168 ml calculated E 0 =410.6 mV calculated Kic = 1.471 )< 10 -6 (M)

--30.10 -- 10.44 6.06 18.12 27.41 35.10 41.80 47.80 53.42 58.71 63.92 69.02 74.23 79.62 85.33 91.50 98.41 106.51 116.60 130.51 151.51 176.57 193.65 204.60 212.41 218.50 223.40 227.50 231.09 234.20 237.00

electrode (mY)

Sample 322 station 417 d e p t h = 1541 m salinity = 34.992%0 silicate = 107.4/~ m o l / k g phosphate = 2.85/~ m o l / k g

Sample 302 station 417 depth = 34 m salinity = 36.408%0 silicate = 2.8/~ m o l / k g phosphate = 0.45/~ m o l / k g

0 1084 2169 3254 4338 5420 6503 7584 8661 9738 10815 11895 12978 14062 15145 16228 17311 18391 19472 20551 21629 22704 23778 24852 25930 27010 28090 29170 30250 31331

acid counts --47.90 --29.64 --7.94 8.58 20.35 29.60 37.37 44.29 50.63 56.55 62.32 68.00 73.81 79.81 86.27 93.43 101.77 112.05 126.17 148.07 174.74 192.34 203.31 211.10 217.14 222.05 226.20 229.77 232.90 235.70

electrode (mY)

cell volume L_ 110.733 ml calculated E 0 =409.3 mV calculated Kic = 1.449)< I0 -6 (M)

Sample 305 station 449 d e p t h = 115 m salinity = 35.091%0 silicate = 15.9/~ m o l / k g phosphate = 1.42 ~ mol//kg

0 1065 2130 3194 4259 5324 6390 7454 6518 9581 10642 11702 12763 13824 14887 15953 17017 18080 19143 20207 21269 22333 23398 24462 25528 26593 27656 28718 29779 30841 31901

acid counts

--45.48 --26.25 --5.53 9.54 20.72 29.63 37.11 43.77 49.89 55.60 61.21 66.67 72.25 78.04 84.22 91.01 98.96 108.31 120.76 139.21 165.11 185.71 195.50 207.25 213.84 219.10 223.50 227.21 230.50 233.40 236.00

electrode (mY)

cell v o l u m e = 110.741 ml calculated E 0 = 408.8 mV calculated Kit = 1.474)< 10-6 (M)

Sample 306 station 449 d e p t h = 146 m salinity = 35.0247o0 silicate = 21.3 ~ m o l / k g phosphate = 1.64/~ m o l / k g

Raw titration data for samples reported in Table 4. To convert acid volume counts (column I) to ml multiply by 10 4//2. In the calculation of GEOSECS results the acid normality was made exactly 0.25 by adjusting the titration cell volume. The titration temperature was 25°C

TABLE 5

112

program gives total carbon dioxide values that are too high, by approximately 12 #mol/kg. (2) Total carbon dioxide values found from the difference between the first and second equivalence points of a titration must be corrected by subtracting the total inorganic phosphate concentration. (3) Use of an acid titrant containing NaC1 dr KC1 with a normality of 0.25 or lower introduces small errors in alkalinity (1-3 /~eq/1) and total carbon dioxide (1-2/xmol/1); in general, the lower the normality, the larger the error. (4) There is a significant difference between results calculated with the Atlantic, and Pacific and Indian Ocean, versions of the GEOSECS program. (5) The error discovered here must be present in all samples titrated during the GEOSECS program. In summary, the GEOSECS equations appear to yield values for total CO 2 that are too high by an amount approximately equal to 12 #mol/kg, plus the dissolved inorganic phosphate concentration. The application of the new equations described here should offer increases in both precision and accuracy. Possibly a recalculation of the data set could be considered. It should be noted that there are strict limits to the amount of information that may be recovered by recalculation of the raw data. Blank values, calibration errors in cell volume or acid normality, or electrical noise cannot be improved by this process. Nonetheless, the errors deriving from these sources appear to be small compared to the errors described in this paper. In conclusion, we wish to recognize the very careful work of Takahashi [2,3,10,14] whose pCO2 measurements diagnosed the error found here. His insistence that something was wrong led to this work. This conclusion was reinforced by the gas chromatographic determinations of total CO 2 made by R.F. Weiss, which also yielded values lower than titrator determinations.

ing the titrators and equations discussed here. We are indebted to A.M. Michael for typing this manuscript. We wish to thank D. Dyrssen and D. Jagner for much helpful advice and comment, and H.G. Ostlund for providing a forum to initiate this work. W.S. Broecker, T. Takahashi and D. Bos provided stimulation and documentation for this work. The GEOSECS Executive Committee (W.S. Broecker, H. Craig, H.G. Ostlund and D. Spencer) are thanked for their tireless contributions to the program. This work was supported by National Science Foundation grant No. OCE 79-13205 and OCE 79-81620.

Appendix 1 (1) Values of association constants (fl) used in titration data generation program (units of fl = M-I). Complex

fl

HSO4NaSO4MgSO 4 CaSO 4 KSO4MgCO 3 CaCO 3 HF MgF + CaF + MgHCO3+ CaliCO3+ MgOH + CaOH + MgB(OH)~

31.7 1.8 6.3 25.4 1.84 32 32 800 18.8 4.22 1.04 1.0 37 1.8 5.3

(2) Values of conditional dissociation constants of phosphoric acid (K~p, K~p, Kip) and orthosilicic acid (Ksi) used in "actual titration" and modified Gran programs (units of K = M): pK~a = 1.75, pK~p = 5 . 9 5 , pK~e =8.95 pK~i = 9.2.

Appendix 2 Modified Gran calculation

Acknowledgements We wish to pay tribute to the late Arnold Bainbridge for his skill and leadership in develop-

The calculation follows the flow scheme in Hansson and Jagner [25]. Their fig. 2 is repro-

113

duced in our Fig. 2. The modified Gran functions of Hansson and Jagner have been corrected for side reactions with phosphate and silicate; these are:

[H2PO4-]T- [PO~-]T = {Px ×

>( (1 + K ; p / [ H + ]T,H + K'EpK;p/[ H+ ]2T , H

Fz = (Vo + V)IOE/(RT/F)

,

F, = (V2 -- V)IO e/(RT/F)

[HPO42-]T. - 2[PO43- IT)

where [H + ]T,H = [H + ] + [HSO4- ]. In the F~ pH range, 2[PO43- Ix is negligible. 2 , F 1 = ( V2 - - V ) ( [ H + ]T,H -- K I C ,

•

t

_ (K,c[H

+

,

K2c)

]T.H+ 2K~cK2c)

+ (Vo + V)([H+ ]T.I-I+ [HF]T +

,

,

+ KIpK2pK3p/[H

F~ = (Vo + V)([H+]x,n+ [HF]T+ [H3PO4]T - [HCOf]T-

}

+

2[H,PO, ]T + [H2PO 4-IT

-- [B(OH)4-]T

-[OH- ]T --[PO~-]T --[SiO(OH)3-]T) X ([H + ]2T,H+K~c[H+]T.H+K;cK~c)

- N/(K[c[ H+ ]T.H+ 2K~cK~c), where K~c and K~c are the conditional carbonic acid dissociation constants of Hansson [12], converted to a molar basis, N is the acid normality, and [] indicates molar concentration. Subscript "H" denotes the Hansson definition of this quantity. In the F~ pH range 2[H3PO4] T is negligible. To compute F~ and F~, the following equations are needed:

+ ] 3 ~--I T,H]

[(OH)4-]T= [B]x/([H + IX.H/K;. + 1) [OH-]T = K ~ / [ H + ]T.H

[SiO(OH)3-]T = [Si]T/(1 + [H + ]T,H/K~i} In the above equations, Eg is related to the E o of the Nernst equation:

E = E o +-~- ln[H + ] by:

E ° = E ° - RT F ln(l + flaSO; [S04Z-]) E~ is calculated at each iteration (see Fig. 2) as follows (i indicates iteration number and j indicates point in selected volume range of F~ (or F2):

i=l: r,+ .,

RT

E g ( j ) = L (j)-----f- In

[ N ( V ( j ) - V2) ] ( V ( j ) + Vo}

E~ =E'(j) i>l: I N ( V ( j ) -- V2) _ [HF]T

[H + ]T,H ---- IO(E-E'°)/(RT/r)

[HCOf]T = C T / ( [ H + ]T,H/K~c + 1)

- ([H3PO4 IT --[ HPO2- Ix) + [HCOf-IT/J

[HF]T = FT/(1 + 1/flhF/[H + ]X.U)

Eg =Eg(j)

[H3PO,]T - [HPO2-]T

K~B and K~ are the conditional constants of Hansson [12] for boric acid and water, converted to a molar basis; K~p, K~v, K~p and K~i are conditional constants of phosphoric acid and orthosihcic acid on a molar basis; fl~F is the conditional association constant of hydrofluoric acid, CT, BT, F x , PT and Si T are the total concentrations (M) of

-'- PT X (1 - K~pK~p/[H + ]'~,H) X (1 +K;p/[H+]T.H+K~pK;p/[H + T2, H

+ K[v K~pK;p / [H + ]~,n)-'

114

carbonate, borate, fluoride, phosphate and silicate, corrected for dilution with the added acid by multiplying the corresponding sample concentrations by Vo/(V + Vo).

Special modified Gran calculation Hansson's "total" hydrogen ion concentration, which is used above, is given by: [H + ]T,H= [H + ] + [HSO4-]

S/35 [ K + ] = 0.010 S/35 [Mg 2+] =0.050 S/35 [Ca 2+ ] = 0.008 s/35 [S024-]=0.012S/35 [Na + ] = 0.469

References

= [H + ](1 + flHSo;[SO~-]) where [SO~- ] is the free sulfate ion concentration in the sample. During titration with 0.6 N NaC1 or 0.45 N KC1 solutions of dilute acid [SO42- ] decreases. This is the net result of reaction with H + and changes in concentration of SO~- and its complexes that are due to volume dilution and reaction of SO42- with complexing cations in the acid. Thus the [H+]T,H which appears in the F~ and F~ must be corrected for this decrease by adding [H + ] flnso,([SO42- ]l _ [SO~-]0), where the superscripts "0" and "1" refer to the sample and a point of the titration, to [H + ]T,n. [SO~- ]t is estimated by repeating the following calculation until an error tolerance of, say, 0.5% is reached: [Na + ]' = ([Na + ]°Vo +

Gg/INacIV/58.45)/

(Vo + V ) / ( 1 + flNaSo;[SO2-]) ' [K + ] ' = ([K + ]o Vo + Gg/aKcaV/74.6) /

(V0 + V)/(1 + flKSo;[SO2-] ') [Mg2+]' = [Mg2+]TVof(Vo + V)/ (1 + [Ca 2+ 1'= [Ca :+ IT Vo/(Vo +

V)/

+ + v)/ { 1 + tiN,SO; [Na+ ]' + flI
2-- 0 Initial values for the first titration step could be:

1 T. Takahashi, W.S. Broecker and A.E. Bainbridge, The alkalinity and total carbon dioxide concentration in the world oceans, in: Carbon Dioxide Workshop Volume, B. Bolin, ed. 2 T. Takahashi, Carbonate chemistry of sea water and the calcite compensation depth in the oceans, in: Dissolution of Deep-Sea Carbonates, W.V. Sfiter, A.W. Be and W.H. Berger, eds., Cushman Foundation Foram. Res., Spec. Publ. 13 (1975) I I. 3 W.S. Broecker and T. Takahashi, The relationship between lysocline depth and in situ carbonate ion concentration, Deep-Sea Res. 25 (1978) 65. 4 M. Stuiver, Atmospheric carbon dioxide and carbon reservoir changes, Science 199 (1978) 253. 5 W.S. Broecker, T.H. Peng and M. Stulver, An estimate of the upwelling rate in the equatorial Atlantic based on the distribution of bomb radiocarbon, J. Geophys. Res. 83 (1978) 6179. 6 M. Stuiver, The 14C distribution in West Atlantic abyssal waters, Earth Planet. Sci. Lett. 32 (1976) 322. 7 P.G. Brewer, Direct observation of the oceanic CO 2 increase, Geophys. Res. Lett. 5 0978) 997. 8 C.T. Chen and F.J. Millero, Gradual increase of oceanic CO2, Nature 277 (1979) 205. 9 C.T. Chen and R.M. Pytokowicz, On the total CO 2 -titration alkalnity-oxygen system in the Pacific Ocean, Nature 281 (1979) 362. l0 T. Takahashi, PI Kaiteris, W.S. Broecker and A.E. Bainbridge, An evaluation of the apparent dissociation constants of carbonic acid in sea water, Earth Planet. Sei. Lett. 32 (1976) 458. I l J. Lyman, Buffer mechanism of seawater, Ph.D. Thesis, University of California, Los Angeles, Calif. 0956) 196 pp. 12 I. Hansson, A new set of acidity constants for carbonic acid and boric acid in seawater, Deep-Sea Res. 20 (1973) 461478. 13 C. Mehrbach, C.H. Culberson, J.E. Hawley and R.M. Pytkowicz, Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure, Limnol. Oceanogr. 18n 0973) 897-907. 14 T. Takahashi, Consistency of the alkalinity, total CO 2, pCO 2 and pH data obtained in the Pacific and Atlantic GEOSECS expeditions, GEOSECS Internal Rep. (1977) 42 PP.

115 15 A.L. Bradshaw and P.G. Brewer, The titration of sea water with strong acid: an evaluation of the GEOSECS total carbon dioxide-alkalinity potentiometric titration, in: The GEOSECS Carbon Dioxide Results, G. Ostlund and D. Dyrssen, eds., D.O.E. Rep. (1980). 16 D.L. Bos, History and development of the GEOSECS alkalinity titration system, in: The GEOSECS Carbon Dioxide Results, G. Ostlund and D. Dyrssen, eds., D.O.E. Rep. (1980). 17 A.E. Vogel, A Textbook of Quantitative Inorganic Analysis, Theory and Practice (Longman and Green, 1957) 918 pp. 18 D. Dyrssen, A Gran titration of sea water on board Sagitta, Acta Chem. Scand. 19 (1965) 1265. 19 G. Gran, Determination of the equivalence point in potentiometric titrations, II, Analyst 77 (1952) 661-671. 20 D. Dyrssen and L.G. Sillen, Alkalinity and total carbonate in sea water: a plea for p-T-independent data, Tellus 19b (1967) 113-121. 21 J.M. Edmond, High precision determination of titration alkalinity and total carbon dioxide content of sea water by potentiometric titration, Deep-Sea Res. 17 (1970) 737- 750. 22 J.M. Edmond, The carbonic acid system in sea water, Ph.D. Thesis, University of California, San Diego, Calif. (1970) 174 pp.

23 F. Ingman and E. Still, Graphic method for the determination of titration end points, Talanta 13 (1966) 1431-1442. 24 S. Burden and D.E. Euler, Titration errors inherent in using Gran plots, Anal. Chem. 47 (1975) 793-797. 25 I. Hansson and D. Jagner, Evaluation of the accuracy of Gran plots by means of computer calculations: application to the potentiometric titration of the total alkalinity and carbonate content in sea water, Anal. Chim. Acta 75 (1973) 363-373. 26 F. Maclntyre, End point and equivalence point: a tribute to John Lyman, Mar. Chem. 6 (1978) 187-192. 27 K. Buch, On boric acid in the sea and its influence on the carbonic acid equilibrium, J. Cons. Int. Explor. Mer. 8 (1933) 309-325. 28 T. Almgren, D. Dyrssen and M. Strandberg, Determination of pH on the moles per kg sea water scale (Mw), Deep-Sea Res. 22 (1975) 635-646. 29 D. Dyrssen and M. Wedborg, Equilibrium calculations of the speciation of elements in sea water, in: The Sea, Vol. 5, E.D. Goldberg, ed. (John Wiley and Sons, 1974) 181-195.