Comments on potentiometric pH titrations and the relationship between pH-meter reading and hydrogen ion concentration

63

Analyt~ca Chtmrca Act,

25.5 (1991) 63-72 Elsevler Science Pubhshers B V , Amsterdam

Comments on potentiometric pH titrations and the relationship between pH-meter reading and hydrogen ion concentration Helmut Slgel and Andreas D Zuberbuhler Immure of Inorgamc Chetnrsiry, Unaversrtyof Basle, Sptialswasse 51, CH-4056 Basle (Swtzerland)

Osamu Yamauchl Department of Chemwy,

Nagoya UruverMy, Furo-cho, Chrkusa-ku, Nagoya 464 (Japan)

(Recewed 17th May 1991)

Abstract

It 1s emphasized and shown that the concept of pH 1s more complicated than nught be thought (and to some extent also unsatisfactory), there are (at least) three pH scales m general use and it IS the am to make this fact recogmzed These scales arc (1) an actlvlty scale, where the hydrogen ion actMty IS measured based on NBS or smular standards by carefully ehmmatmg the hquid-junction potentials of the electrode system via experImenta determmatlons, (2) a practical scale, wluch has unmtentlonally developed by convemence over the past ca 30 years, 1s based on now generally available combined glass electrodes together with NBS (or related) buffers used for cahbratlon, and (3) a concentration scale which uses strong acids and/or bases for calibration and defines the pa-meter readmg m terms of -log[H+] Scale (2) 1s clearly the one least well defined, yet d 1s also the one most widely used If a ‘pH’ 1s measured for a given constant Hf concentration m the three scales, its value decreases m the order (1) > (2) > (3) Scales (1) and (3) may be converted mto each other by usmg the smgle ion actiwty coefficients of H’, e g , at 25 o C and at lomc strengths of 0 1 and 0 5 M the differences correspond to 0 11 and 0 15 log unit, respectively The conversion term from scale (2) to (3) corresponds at 25 o C and an lomc strength between 0 1 and 0 5 h4 to about 0 03 log unit It IS evident that any acldlty constant, 1e pK, value, determmed for a given system (HA + A-+ H’) IS affected to the same extent, hence, the mentloned conversion factors have to be apphed d pK, values determmed m different scales are to be compared or used It may be added that many workers beheve that combmed glass electrodes measure the hydrogen Ion actlvlty and that they are workmg m scale (11, yet tius 1s llot the case, they are actually workmg m scale (2) Moreover it 1s also barely (or not at all) recogmzed that the values m scale (2) are m fact closer to those of scale (3) and not to those of scale (11, as is often assumed Some general comments regardmg potentiometnc pH titrations and the determmatlon of eqmhbrmm constants (1e , pK, values and stab&y constants of metal ion complexes) are also made, and the advantages of different tltratlon procedures are discussed and pItfalls are pomted out Keywords Potentiometry, Tltnmetry, AC&y constants, Glass electrodes, Hydrogen Ion concentration, pH, Stab&y

constants

There IS significant confusion about what combmed glass electrodes, If applred to aqueous solutlons, are measurmg IS it simply the hydrogen ion 0003-2670/91/$03

actlvlty which may then be converted, If so desired, mto the hydrogen ion concentration by applymg actlvlty coefficients? Long and mtense

50 0 1991 - Elsevler Science Pubhshers B V All rights reserved

64

drsputes wrth colleagues drd not lead to an unequrvocal clarrficatron of this point, mstead they led us to conclude that the problem IS more complicated Indeed, “ a pH measurement IS definitely not Just a matter of swrtchmg on a pH meter, plunging the electrodes mto the test solution and takmg the meter readmg” [l]. Thrs fact stmnrlated us to write this paper knowmg that a question so controversral and long debated as this one mrght be dtffrcult to settle for good by a smgle effort Still, rt 1s our hope that some clarrfrcation wrll have been achreved and that other colleagues may become more aware of the problems one has to face with apparently “rumple” pH measurements For detailed mformatron regarding the development of the pH concept, the defrmtrons of pH, the development of the glass electrode, procedures of measurements, etc , references D-31 should be consulted

1 SOME REMARKS REGARDING PRACTICE, HISTORY AND ACIDI’W CONSTANTS

Thus work 1s a Jomt effort by the heads of three drfferent independent laboratories, hence, the experlmental methods, the equipment, and the screntlfic vrews are also partly different Therefore, whenever appropriate for a certam phrase or paragraph rdentrficatron 1s made by using the mrtrals of the partrcular author(s) The pH measurements and the pH titrations m the laboratones of H S and A Z m Basle have been carried out since the mrd-1960s with equrpment from Metrohm (Hensau, Swrtzerland) The buffer solutrons used for cahbratron (pH 4 64, 700and900byHS,pH400,700and900by A Z > at 25 ’ C are based on the scale of the US National Bureau of Standards (NBS) [2-S], and were also purchased from Metrohm According to the mformatron obtamed from this company, the pH 4 00 buffer 1s based on potassium hydrogenphthalate (I close to 0 08 M), the pH 4 64 buffer on acetate (I = 0 1 M), the pH 7 00 buffer on phosphate (I shghtly larger than 0 2 M) and the pH 9 00 buffer on borate (I close to 0 1 M),

H SIOEL ET AL

these Metrohm buffers are calibrated by the company wrth the NBS pnmary standards for pH 4 008, 6 865 and 9 180 [3,5,6] In the laboratory of 0 Y , formerly in Osaka and Kanazawa, and now m Nagoya, different equipment has been used over the years [7-91 For cahbratron Horrba buffers (pH 4 01, 6 86 and 9 18,25 o C) are employed, these are based on the Japanese Industrral Standard (JIS) scale, whrch IS essentially the same as that of the NBS In addrtron, laboratory-prepared buffers (pH 4 008, 7 413 and 9 180, 25 ’ 0, according to the prescrrptrons given by NBS [2,3] (see also [4,51), are used, these are prepared with high-purity chemrcals obtained from Wako (Osaka) and Nacalar Tesque (Kyoto) There was no measurable drfference between the pH 4 008 NBS buffer solutions prepared by usmg potassmm hydrogenphthalate from Wako or Nacalar Tesque In the laboratory of H S always the direct pH-meter readmgs were [lo] and still are used 111 calculatrons for acrdrty constants, I e , the pH scale employed as defined vra the NBS standards, 1s the so-called “practrcal scale of pH” [3] Consequently, the resultmg acrdrty constants are socalled practical constants [ll], also known as rmxed or Bronsted constants [11,12], whrch melude “actrvny” (see below) and concentratron terms These practical acidity constants, valid for aqueous solutrons at a given ronrc strength (I) and temperature, may be converted mto the correspondmg, so-called classical W, (pure) concentration constants with the conversion factor A as defined below m Eqn 1 The acidity constants published from the laboratory of AZ were formerly also of the mentioned practical or mixed type, but since 1988 concentratron constants have been presented [13,14] The aadrty constants from the laboratory of 0 Y were always given m the form of concentration constants Consequently, both latter laboratones have prevrously published [7-9,13,141 conversion factors allowing the transformation of the pH-meter reading mto H+ concentratron (=

[H+l) The use of buffer solutrons for standardrzatron means that the measured pH of a test solution depends on the electrode, the romc strength, the

POTENTIOMETRIC

65

pH TITRATIONS

]unctlon potentml between the two systems and the actlvlty coefficient of H+ [12] All these terms are part of the conversion factor A, which may be determmed by measurmg with a buffer-calibrated electrode system the pH of a strong acid (such as nitric acid) with an exactly known H+ concentratlon, A IS then obtamed as the dtfference between the measured and the calculated (concentratIon pH [121 A = pH,,,

- p[H]ca~c/conc

(1)

This defmltlon of the conversion term A follows the procedure of Irvmg et al [12], which is analogous to the factor R used by Van Ultert and Haas [15] when dlscussmg [12] acid-base equdlbna m mnced solvents In a Jomt effort we have now (re)determmed the conversron term A for the main experimental conditions employed m our laboratories, 1 e , for 25°C at I=01 M(NaNO,,HS, KNO,, OY) and I=05 M(KNO,,AZ)

TABLE 1 bt

of electrodes used m the expernnents

Electmde No a

LaboratoIy

Electrode type

Size

Company b

1 2 3 4 5 6 7 8 9 10a lob 11 12 13 14

HS HS HS HS HS HS HS OY OY OY OY AZ AZ AZ AZ

60204ooO 60203000 EL4125 EA 121 ux 6 0214 100 Ross 8103SC Ross 8102SC 39534 Ross 8172BN 39314 39419 6 0203 100 6 0203 101 6 0203 102 6 0219 100

Micro Macro Micro Macro Micro Micro Macro Macro Macro Macro Macro Macro Macro Macro Macro

Metrohm Metrohm Metrohm Metrohm Metrohm OrIon Onon

B&nXlIl OrlOll

Beckman Beckman Metrohm Metrohm Metrohm Metrohm

=All electrodes were combmed glass electrodes, except for No 10 where (a) refers to the glass electrode used m con&lnatlon wth (b) the reference electrode The combmed glass electrodes Nos l-5, 8, and 11-13 contam a single Junction and Nos 6, 7, 9 and 14 a double Junction ’ See Sectlon 2 2

2 EXPERIMENTAL

2 I Mater&s H S and AZ obtamed tns(hydroxymethy1) ammomethane (Trls), potassmm hydrogenphthalate, NaNO,, KNO,, HNO, and NaOH (Tltnsol) (all pro analyst) from Merck (Darmstadt) and the buffers (pH 4 00, 4 64, 7 00 and 9 00) from Metrohm 0 Y purchased the correspondmg reagents (except Tns) plus KOH and dlsodunn hydrogenphosphate from Nacahu Tesque and Wako All solutions were prepared with dlstdled, carbon dloxlde-free water The tltre of the NaOH or KOH used for the potentiometrlc pH tltratlons was determmed with potassmm hydrogenphthalate The exact concentratlons of HNO, and of Trls (titrated m the presence of an excess of HNO,, see Section 2 3) were measured by titration with NaOH or KOH 2 2 Apparatus The electrodes used m the experments are hsted m Table 1 The combmed single-Junction (Nos 1-5, 11-13) and doublejunctlon (No 14) Metrohm glass electrodes (H S , AZ ) were ob-

tamed from Metrohm and the combined doubleJunction Ross glass electrodes (Nos 6, 7) (H S ) from Onon Research (Kussnacht, Switzerland) The combined single-Junction Beckman glass electrode (No 8) (0 Y ) and the Beckman glass (No 10a) and the calomel reference electrode (No lob) were purchased from Beckman Japan (Tokyo) The combmed double-Junction Ross glass electrode (No 9) (0 Y ) was from Japan Sclentlfic Instrument (Tokyo, Japan) The followmg four sets of equipment were used for the experrments described m Sectlon 2 3 (1) Potentlometrlc pH titrations were carried out (H S and AZ ) with a fully automatic pHtitration unit, conslstmg of a combined Metrohm glass electrode, a Metrohm 605 dtgltal pH meter, a Metrohm E665 drgltal burette, a Dolphin mlcroprocessor and a tape recorder (Microcorder ZE601) 1161,and also by usmg an analogous set-up and program based completely on an AT286 personal computer for data acqulsltlon and data reduction and a Metrohm E665 digital burette The electrodes employed were Nos l-4 (H S )

66

and 11-14 (AZ) m Table 1 The final calculations were made mth a Hewlett-Packard HP310 or an AT286 desk-top computer usmg the TITFIT program [17] (2) Pax-wise potentlometrlc pH tltratlons (see also Sectlons 2 3 and 3 4) were carried out m the laboratory of H S with a Metrohm E536 potentlograph, equipped with an E655 dosnnat, and seven combined glass electrodes (Nos l-7 m Table 1) The calculations (see also Sectlon 2 3) were done with a Hewlett-Packard Vectra 60PC MSDOS desk-top computer connected with a Brother M-1509 printer and a Hewlett-Packard 7475 A plotter (3) Smgle pH measurements were made with a Metrohm 605 dlgltal pH meter and the SIXglass electrodes Nos 2-7 (H S ) and the four glass electrodes Nos 11-14 (A Z > m Table 1 (4) The potentlometnc pH tltratlons carried out m the laboratory of 0 Y were done manually with an Orion Research Ion Analyzer EA 920 eqmpped with a Beckman glass (No 10a m Table 1) and a Beckman calomel electrode (No lob), and also a Beckman PHI 71 pH meter connected wrth a combined Beckman (No 8) or a combined Ross glass electrode (No 9) Metrohm E274 plston burettes (5 ml) were used for the tltratlons 2 3 Determmatwn of the conversion tern A All measurements were carrred out at 25 “C under nitrogen Potentmmetrlc pH titrations (H S 1 were carried out with equipment (1) described m Sectlon 2 2 by tltratmg 25 ml of aqueous 3 2 mM HNO, (I = 0 1 M, NaNO,, 25 o C) m the presence of 16 mM Tns with 1 ml of 0 1 M NaOH, Tns was used as a further mternal standard [l] The conversion term A, the apparent ion product of water, K&, and the acldlty constant of H(T&+, K:Vmj, were calculated from fourteen experiments carned out with four different glass electrodes (entries Nos l-4 m Table 11, it may be noted that a! m the TITFIT program [171 corresponds to 10-‘OgA These results are hsted in the first row of Table 2 (vlde mfra) Nme corresponding tltratlons (AZ ) were made with electrodes Nos 11-14 m Table 1 by tltratmg 25 ml of 5 5 mM HNO, (I= 0 5 M,

H SIGEL

El-AL

KNO,, 25 ’ C) m the presence of 3 2 mM Trls with 1 ml of 0 4 M NaOH, these results are listed m the twelfth row of Table 2 Equipment (1) m Section 2 2 was also employed for five and mne tltratlons (m the absence of Tns) at Z = 0 1 and 0 5 M @NO,, 25” C), respectively, usmg lo-80 ml of 20-l mM HNO,, these results are given m the ninth and thirteenth rows of Table 2 Further pH tltratlons (H S ) were made with equipment (2) m Sectlon 2 2 and seven different glass electrodes (Nos l-7 m Table 11, but this time by titrating 25 ml of aqueous 3 2 mM HNO, (I = 0 1 M, NaNO,, 25 ’ C) m the presence and absence of 16 mM Trls with 12 ml of 0 1 M NaOH The value for pKgnsj was calculated from eighteen independent palrs of such trtratlons by using the dtierences m NaOH consumptlon between a correspondmg tltratron pair for the calculations and by takmg mto account the species H+, Tns, and H(Tris)+, and by usmg a curve-flttmg procedure with a Newton-Gauss non-lmear least-squares program wlthm the pH range determmed by about 3% and 97% neutrallzatlon for the H(Trls)+-Tris eqmhbrmm The values of A and Kb were determined from the eighteen HNO, titrations. These results are listed m the second row of Table 2 Next, A (Eqn 1) was also determined via sunple pH measurements [equipment (3) m Section 2 21 At Z = 0 1 M (NaNO,, H S 1, 54 measurements were made with SIXelectrodes (Nos 2-7 m Table 1) and 2 4, 3 9 and 7 1 mM HNO, (see row 3 m Table 2) A further 70 measurements (A Z ) with four electrodes (Nos 11-14 m Table 1) each at Z = 0 1 and 0 5 M @NO,) and 1, 2, 5, 10 and 20 mM HNO, gave the results hsted m the tenth and fourteenth rows of Table 2, respectively The results obtained m the laboratory of 0 Y are gwen m the fifth to seventh rows of Table 2 They were obtained by tltratmg with equrpment (4) m Section 2 2 50 ml of 0 1 M KNO, with 5 ml O1MHNO,or50mlofO01MHNO,(Z=O1 M, KNO,) with 5 ml of 0 1 M KOH With electrodes Nos 8, 9 and 10 m Table 1 SIX,seven and twelve tltratlons were made, respectively For determmmg the apparent Ion product of water, K&, 50 ml of 0 1 M KNO, were titrated vvlth 0 1

POTENTIOMETRIC

67

pH TITRATIONS

M KOH Two titrations were made for each electrode The calculations were performed mth a FACOM M380 computer at the Nagoya Umversity Computation Centre

3 RESULTS AND DISCUSSION

3 1 Results of expenments and constancy of the converswn term A The results obtamed under the expenmental condltlons described m Section 2 3 by the dlfferent methods gwen m Sectlon 2 2 and by the different research groups are summarized m Table 2 It 1s immediately evldent that the general agreement between the results IS excellent

This IS not only true for the combined glass electrodes, lrrespectlve of whether they are constructed with a smgle or a double Junction, but it applies also to the use of a glass electrode m combmatlon with an independent reference electrode Regardmg the results at I = 0 1 M (NaNO,) and 25 OC from the laboratory of H S , It IS satafymg to see that the value A = 0 021 k 0 006 (row 2 111Table 21, which resulted from the expenmental condltlons closest to those usually employed in this laboratory, agrees well wth the weighted mean, A = 0 019 f 0 020 (row 4), obtamed from all the measurements, this latter value corresponds to (Y= l/10 logA= 0 957 f 0 044 (next to A, a IS also often listed in the literature

TABLE 2 Summary of measurements m aqueous soluhons for the determmation of the conversion term A (Eqn 0, together wth some related data (25 o C) a Row

Laboratory

Electrode No b l-4 l-7 2-7

Method c

n d

I

A

PKGv =

P&&Q

(1) (2) (3)

14 18 54

0 1/NaNO, 0 1;NaNO; 0 l/NaNO, 0 1 /NaNO,

0008~0010 0021fOOO6s 0043&-0022 0019~0020

13 857 f 0 019 13867rtOO30 h

8167~0007 8165~0017’

13860~0016

8167&0#7

0 l/KNO,

0023*0012 0049*0024 0042iOO18 0032kOO28

1 2 3 4

HS HS HS

5 6 7 8

OY 8 (4) OY 9 (4) OY 10 (4) 0 Y, werghted mean of 5-7at

9

AZ

H S , werghted mean of I-3 at

11-14

9weIghted ziyof

11 10

AZ2 A

12 13 14

A.Z AZ AZ

11-14 11-14

I5

A Z, we&ted

Eik40f

6 7 12

Ol/KNOj 0 l/KNO,

(1) 9 and%

(1) (1)

at

7’

9 9 70

12-l~~t

0 l/KNO, 0 l/m%

0 l/KNO, 0 I /kWo, 0 5/KNo, 0 s/KNo, 0 s/KNo, 0 5/KNo,

1388kOlO

f

’

0052fO014 0030*0020 0045*0033 0026*0007 0040*0014 0023*0018 0028kOOI2

13874kOOO6

8256*0005

a AU error hnuts are three times the standard error of the mean value b See Table 1 c These numbers refer to the correspondmg paragraphs m Section 22, for further detads see also Sectlon 23 d These are the numbers of htrations carried out, Hnth the exceptton of entnes 3, 10, and 14, for wluch the number of mchvldual pH measurements 1s gwen ’ This IS a nuxed constant, 1 e , - log[OH-1, m other words, the negative loganthm of the product resultmg from the concentration of OH- and PK;, = PH,, the value measured for Hf IS oven f This IS a practical or mxed acuhty umstant (see SectIon 1) s Calculated via pomt-me evaluations of the tltratlon curves of HNO, [see also Sect10112 3 and paragraph (2) m Se&on 2 21 h Actually detennmed was the mflect~on point of the titration curve, this value tunes two gave pK& = 13 888 f 0 029 The above value was obtained via the correspondmg conversIon term A ’ See Section 2 3 J Ths value IS an estunate only, as It 1s the average of only SIXtltratlons, I e , two titrations with each electrode

H SIGEL ET AL

[7,13,14,17]) The mentloned result for the conversion term A means that from the negative logarithm of a practical acldlty constant as measured m the laboratory of H S at an ionic strength of 01 M and at 25”C, 002 pK unit should be subtracted If the correspondmg concentration constant 1s desrred It may be emphasized that the conversion term A = 0 02 has been fairly constant over many years, this 1s evident from the results (H S ) obtained for the deprotonatlon of H(ATPj3- the acidity constant, pKgAW, = 6 47 f 0 01, was obtained from 57 pairs of titrations over a period of about 20 years, 1 e , from 1965 to 1985 (see [181) Snmlarly, the results obtamed for H(ITPj3- and H(GTPj3-, 1 e , pKEITP, = 6 47 f 0 02 and pK$oTP, = 6 49 f 0 02, also show no dependence on time, these pK, values [191 have been repeatedly determmed m this laboratory since 1975 up to the present and the above results are the averages of 56 and 48 pairs of titrations, respectively Analogous observations regardmg the constancy of A were also made m the laboratory of AZ regardmg the acidity constants of protonated mudazole and mudazole derlvatlves However, even more remarkable 1s the fact that a sunllar constancy for the conversion term A 1s also observed m the laboratory of 0 Y despite the use of different kmds of combined glass electrodes and also of glass electrodes connected over the years wth different reference electrodes, m addition to the employment of various eqmpment for a period of about 17 years [7-91 A, = 0 054 f 0 019 (2~) for Z = 0 1 M &NO,) and 25 ’ C, and this value 1s stdl m satisfactory agreement with the present result m row 8 of Table 2 L4=0032*0028) 3 2 Companson of the present results wzth hterature data and concluswns regardang the conversion term A There are several aspects which appear worth emphaslzmg mtlally (1) The value of 8 173 given by Bates 1201 for the pH of a solution which is 0 05 molal m Trls and m Tns HCl(1 e , Z = 0 05 M) 1s very close to the practical acldlty constant M)glvenmthe PK&) = 8167~0007(1=01 fourth row of Table 2 (u> The value ApK, =

[PK&,~, at Z= 0 5 M, row 12]- [PK&~~, at I=01 M, row 4]=(8256fOOO5)-(8167& 0 007) = 0 089 f 0 009 1s m excellent agreement vvlth the analogous difference found m a data compilation m the literature 1211, 1e , ApK, = 0 06 f 0 04 (estimated error limit), and also with related data [22] for other H+N acids for the same change m lomc strength (m) The values measured for the apparent ion product of water, at Z-01 (NaNO,, le, PK& =13860*0016 row4mTable2jand13874fO006at Z=05M (KNO,, row 12) are also in excellent agreement with previous results of 0 Y and A Z , e g , 13 88 or 13 91 (I = 0 1 M, KNO,, 25 o C) [7,8] and 13 885 (I = 0 5 M, KCl, 25 ‘C) [13,14] A further point which warrants attention m this connection 1s the fact that smular small values as observed now for the conversion term A and as listed m Table 2 have been observed before [12] Even values close to zero are known from Irvmg and co-workers [12,23,24] and, as mdlcated before, similar prewous data exrst from the laboratones of 0 Y [7-91 and A Z 113,141 Takmg everything together, it IS evident that the conversion term A for combmed glass electrodes, and also for glass electrodes used with a reference electrode, 1s fairly independent of (1) the orlgm and type of buffers used for cahbratlon, provided that the buffers are NBS based, (11) the type and ongm of the glass electrodes employed, (m) the equipment used, (IV) the kind of method used for the measurements, (v) the lomc strength, be it 0 1 or 0 5 M, and the mert salt used and (w) even the differences between different research laboratories are small Therefore, we consider the weighted mean of the results listed m rows 4, 8, 11 and 15 m Table 2, 1e , A = 0 028 f 0 028 (3~1, as a representative value for the conversion term A to be generally used at Z = 0 1-O 5 M and 25 ’ C (see also Sectron 4) 3 3 Comments regarduagthe converswn term A and the stab&y constants of metal zon complexes The conversion term A (Eqn 11, which allows a measured pH based on a cahbratlon Hrlth NBS buffers to be converted mto the correspondmg pH defined m terms of concentration, -loAH+] ( = ~[H]ca,c+nc m Eqn 11, is composed of the

PO?ENTIOMETRIC

pH TITRATIONS

actlvlty coeffiaent of the hydrogen Ion (7) and the residual liquid-Junction potential (AE,), 1 e , A = log y - AE, [12] It should be emphasized that log y and AE, shift the pH scale m opposite dlrectlons and therefore the conversion term A 1s usually smaller than a converslon term solely based on the actlvlty coefficrent (1 e , log 7) [12], and this fact 1s confirmed by the results summarazed m Section 3 1 and 3 2 In this connection it should also be mentioned that conversion terms of 0 11 and 0 15 pK umt, which correspond to the hydrogen ion actrvrtles (log y) m KCl solution at I= 0 1 or 0 5 M 1251, respectwely, and which are often employed [11,21,26], are clearly too large for most practical acldlty constants published m the last 30 years (see also Section 4) Another point to be made is that researchers cahbratmg then electrode systems with NBS buffers should not sunply subtract the mentioned 0 11 or 0 15 pK umt from their practical acldlty constants determmed and then pubhsh these values as concentration constants, examples of this procedure exist m the literature From our experience m talkmg to colleagues, It 1s apparent that d m a given study nothrng IS said about the cahbratlon procedure of the pH meter, then It 1s based on the NBS scale [2-61 or on closely related procedures [5,27], colleagues who use strong aads and/or bases for the cahbratlon of their pH meter generally state so It may be emphasized that cahbratlon of a pH meter (a) with buffers or (b) with a strong acid or base of known concentration so as to read dlrectly - lodH+l leads to tltratlon cunres [12] which “he parallel to one another and can be made to supernnpose exactly by a small dlsplacement along the pH ax&’ (see also Section 7 m 1511, of course, this small displacement corresponds to the converslon term A (Eqn 1) The reason why stabrhty constants of metal Ion complexes determined by potentiometnc pH titrations do not require a conversion 1281hes m the mentloned small parallel displacement, they are always defined as concentration constants Of course, the total mass balances have to be correctly calculated whatever method 1s used (see also Sectlon 3 4) Moreover, it 1s mterestmg to observe in the literature [29-321 that the stablhty

69

constants of metal Ion complexes determmed by different groups for given hgand systems are often m excellent agreement, although this is not the case for the corresponding acldlty constants of the hgands 3 4 General comments regardrng potentwmetnc pH tztratrons and the determrnatlon of equrhbnum constants For the work from the laboratory of H S it may be emphasized that the ion product of water (pK&, Table 2) and the converslon term A (or the hydrogen ion actwrty coefficient y) do not enter mto the calculations for the (practical) aadlty constants and the stablllty constants of metal ion complexes because the drfferences in NaOH consumption between two correspondmg solutions are evaluated, 1 e , always solutions Hrlth and without hgand are titrated (see also the descnptlon regarding the pauwlse tltratlons for the Trls system m Section 2 3) [10,22,33-401 A further advantage of the mentioned procedure 1s (aside from not needmg pK& and A values) that acid or base nnpurltles m the solvents or m the metal salts, and also part of the systematic errors, cancel It IS evldent that this procedure 1s time consummg because the number of titrations 1s doubled m comparison Wlfh the smgle-titration procedure (see below) However, the effort 1s consldered worthwhile (especially for newcomers to the field) as this method 1s less error prone Clearly, single-tltratlon evaluations, wluch are apphed by most researchers, are as rehable as the above method provrded that addltlonal checks are made regardmg the purity of the solvents and metal salts, this IS done, of course, m the laboratones of 0 Y and AZ Further, m work devoted to the determmatlon of acidity constants of weak acids or the stability constants of metal Ion complexes, it IS evidently important that pK& and A, which enter mto the calculations m this procedure [161, are regularly checked and redetermmed However, whatever procedure 1s finally preferred by the mdlmdual researchers, and much depends here on expenence, m this type of work It 1s essentml that the experunents are carned out with the utmost care, and that possible pltfalls

70

H SIGELETAL

are ratlonallzed and avolded In addition, when usmg stablllty-constant results for structural mterpretatlons of complexes m solution, it may be recommended, whenever possible, to apply stab& &y-constant dtierences (see, e g , l-18,37,40]), as this procedure further mmumzes systematic errors

4 GENERAL TIONS

CONCLUSIONS

AND

RECOMMENDA-

From the expernnental results and the reasonings presented above, one has to conclude that several operationally different pH scales exist Indeed, although It may be considered unfortunate, It 1s a fact that at present (at least) three pH scales are evidently m use {m addltlon, special pH scales exist for the determmatlon of pH m blood and body flulds (see SectIon 8 m [51), and also for the determination of pH m sea water [41] and m highly saline waters [42]} (I) an actlvlty scale where the hydrogen ion activity is measured based on NBS [2-61 or sumlar [5,271 standards by carefully ehmmatmg the llquld-Junction potenteals of the electrode system via expenmental determmatlons, 01) a practical scale, which has unmtentlonally developed by convemence over the past ca 30 years, 1s based on now generally available combined glass electrodes (and “modern” equipment) together with NBS (or related) buffers used for cahbratlon, and (1111a concentratlon scale whrch uses strong acids and/or bases for cahbratlon and defines the pH-meter readmg m terms of -log[H+] Several pomts are evldent from the conclusions summarized m the preceding paragraph (1) Scales (1) and (111)may be converted mto each other by usmg known [WI (hydrogen) Ion actlvlty coefficients (2) Scale (u) IS clearly the least well defined one, and those usmg it are encouraged to determine for their experImental condltrons the conversion term A (Eqn 1) 1121as described m Sectlons 2 3 and 3 1, which allows, If desired, a converslon of data mto scale (m) and hence also mto scale 0) (3) Researchers who pubhsh concentratlon constants [scale (m)l ’ without provldmg the conversion term A for then expenmental

conditions prevent the correct use of their data by those who calibrate their instruments m terms of NBS buffers [scale (u)] (4) The pK, values determmed for a gwen system (HA + A-+ H+) decrease m the order for the scales (I) > (11)> (1111, the overall difference at Z = 0 1 and 0 5 M (25 ’ C> for a pK, value expressed m scales (I) and (1111 being 0 11 and 0 15 pK unit, respectively [11,251 (5) The practical scale (I& developed due to convemence, and possibly “Ignorance” (cf , e g , [43]), 1s certamly the one most commonly used, especmlly m dally routrne work and among nonspeaahsts One of the reasons for this sltuatron IS that compames sellmg combined glass electrodes have a tendency to state that their electrodes measure the “hydrogen ion activity” Indeed, by talkmg to colleagues, many from bmchermcal laboratories, who apply acldlty constants from the literature m their own expernnental work, It became evldent that most of them simply calibrate the pH meter with commercial buffers (wlthout grvmg a thought to “mixed” or concentration acidity constants), m other words, they use the practical scale (11) Therefore, It IS the mtentlon of H S to pubhsh practical aadlty constants also m the future, as much of his work deals Hrlth hgands of bloloacal mterest As described m Section 3 1, the published pK, values [10,18,33-401 from the laboratory of H S may be converted into concentration constants by subtractmg 0 02 pK urut, this conversion term A wrll be checked from time to tune and If necessary will be revised In contrast, 0 Y and AZ are pubhshmg acldlty constants defined m terms of concentration, as indicated m Section 1 Of course, interconversions mto all scales are possible wltb the acldlty constants from all three mentloned laboratones as the conversion terms A are known (see, e g , Table 2) ’ A problem regardmg concentration constants that should at least be mdlcated [l] IS that electrode cahbratlons urlth strong acid and strong base “ are only really usable m the -log[H+] ranges of about 23-2 9 and 108-113 Sadly, most workmg tltratlons where one 1s researchmg metalhgand complexmg, for example, are Hrlthm the cahbratlon “bhnd spot” of -log[H+] 2 9-10 8 and so supplementary titrations are necessary ” 111, e g , as described m Sectlons 2 2 and 2 3 mvolvmg H(Tr@/Tns and the TITFIT program [17]

POTENTIOMETRIC

pH TITRATIONS

Fmally, one has to face the fact that the conversron term A and an exphclt defimtlon of pH are mlssmg m many publications However, it would be false to compare values from such pubhcatlons directly v&h those based on scale (I), 1e , on the smgle ion actlvlty coefficients of H+ In addltlon, it would be equally false (as dlscussed above, and m Sectlon 3 3) to use these same activity coefficients to calculate concentration constants [scale WI Yet it 1s clear that with pubhcations that do not give a value for A one 1s m pnnclple left with guesswork However, combined glass electrodes seem to be standardized to a large extent nowadays and the A terms evidently do not vary too much for dtierent systems Therefore, based on the expenence described m this study, we recommend for those cases where no expermental mformatlon 1s given by the authors the use of the conversion term A=003 for Z=Ol-05 M at 25°C (see also Section 3 21, the estnnated uncertainty being f0 02 log unit Tentatively we recommend the same value of A also for the range Z = l-2 M, because the actlvlty coefficients at these lomc strengths [11,25] tend to approach agam that of Z = 0 1 M To conclude, d a conversron of a pK, value from the concentration scale (m) mto the practical scale (11)1s destred, the conversion term A should be added, consequently, for the conversion of a pK, value from the practxal scale (u) mto the concentration scale (m), A should be subtracted

The technical assistance of MS Rota Baumbusch, Ms Susan Kaderh, Dr Akxa Odam and Mr Tatsuo Yqlma m carrymg out potentrometrlc pH measurements 1s gratefully acknowledged The financial support of this research by the SWSS National Science Foundation (H S and A Z 1 and the Ministry of Education, Science and Culture of Japan (0 Y 1 1s also appreciated

REFERENCES 1 P W Lmder, R G Tomngton and D R Wllhams, Analysis Usmg Glass Electrodes, Open Umverslty Press, M&on Keynes, 1984

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72 30 L G SQCn and A E Martell, Stab&y Constants of MetalIon Complexes, Supplement 1 (Special Pubhcatlon No 251, Chermcal Society, London, 1971 31 D D Perrm, Stabdlty Constants of Metal-Ion Complexes, Part B (IUPAC Chenucal Data Serves, No 221, Pergamon, Oxford, New York, 1979 32 E Hogfeldt, Stablllty Constants of Metal-Ion Complexes, Part A (IUPAC Chemical Data Series, No 211, Pergamon, Oxford, New York, 1982 33 H Slgel and H Brmtzmger, Helv C&m Acta, 47 (1964) 1701, K Kahmann, H Slgel and H Erlenmeyer, Helv Cbnn Acta, 47 (1964) 1754 34 H Sigel, Chlmla, 21 (1967) 489, H Sigel, K Becker and D B McCormick, BlochIm Biophys Acta, 148 (1967) 655

H SIGEL

ET AL

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