N inth Annual Summer Symposium-Analytical Problems in Biological Systems
Use and Abuse of pH Measurements ISAAC FELDMAN Division o f Pharmacology, Department o f Radiation Biology, School o f M e d i c i n e and Dentistry, . University o f Rochester, Rochester, Y.
N.
The development of the concept of pH from its invention by Serenson in 1909 to the present-day National Bureau of Standards’ pH scale is reviewed. The liquid junction potential problem involved in the use of the pH meter is discussed in detail. The magnitude of the error due to the junction potential depends upon the pH, ionic strength, nature of the solutes, nature of solvent, presence of colloids, temperature-in fact, anything t h a t affects the mobilities of charged particles. Whether the junction potential error can be ignored depends upon the use to which the pH measurement is put. Some estimates from the literature as to the probable magnitude of this error are presented and discussed. Under certain relatively simple conditions a n approximate relationship may be considered to exist between the pH meter reading and the hydrogen ion concentration. Under other conditions, the pH meter reading must be considered as simply a reproducible reference point having.no theoretical significance. Under some conditions, the meter reading cannot even be considered as a reproducible reference point. These points are developed in detail.
THE
original hydrogen ion exponent, pH, was invented by Sgrenson (S4)in 1909, for the sake of convenience in tabulating and discussing hydrogen ion concentrations. He defined it by t h r equation: 4
CH+ = l o - p H
(1)
or PI3
- log10 CH’
(2)
I n calculating p~ for a number of buffers, Sgrenson made use of the then-current form of the Nernst equation, (3) for the following cell: P t ; Hf, buffer IiCl salt bridge(0.11- calomel electrode (4) vheie E , and E , are the electromotive forces, corrected for liquid junction potrntials, for cells containing buffers having hydrogen ion concentrations Cn: and CH;, respectively, and a hydrogen pressure of 1 atm. When CH: equals unity, this equation becomes pHz
E , - Eo ~2.3 RT/F
(5)
Sgrenson determined Eo by measuring the electromotive force for cells containing hydrochloric acid-sodium chloride mixtures. I n calculating the hydrogen ion concentrations in these mixtures, he erroneously applied the Arrhenius belief t h a t even strong electrolytes dissociate incompletely. I n addition, a t t h a t time it was not known t h a t the electromotive force of cells depends on activities rather than concentrations. Consequently, there is
no direct relationship between Sgrenson’s p~ and the hydrogen ion activity or concentration. ACTIVITY pH, OR paH
I n 1924, Sgrenson and Linderstrgim-Lang (56) made use of the concept of activity by defining a new p H term, paH = - loglo U H +
(6)
where U H represents the hydrogen ion activity. Although the introduction of paH represents a great advance in chemical thinking, much confusion is encountered in its interpretation. T h e chief difficulty is the impossibility of measuring the activity of a single ionic species without resorting to nonthermodynamic assumptions. Indeed, many assertions are made t h a t single ion activities have no physical significance and are therefore meaningless. Consider the cell, Pt; Hg (1 atm.), HCL, A4gC1; Ag (7) +
for which the electromotive force, E , is given by
where EO is the electromotive force of the cell when the activity product, aa+aci-, is unity. Combining Equations 6 and 8 gives
+
E - EO paH = _ _ _ ~ loglo ac12.3 RT/F It is obvious from Equation 8 that the electromotive force of cell 7 depends on the product of the individual ionic activities and that the contribution due to each ion individually cannot be evaluated. Conversely, for this type of cell the electromotive force can be used to determine only the product (aH+aci-), which by definition equals the square of the mean activity, a*. Hence, Equation 9 is of no value in determining QUHv’ithout some independent means of determining aci -. S o r is i t possible to determine individual ionic activities simply by separating the hydrogen ions to be measured from the chloride of the reference electrode as in cell 4 This device introduces a neu- source of trouble-namely, the liquid junction potentials a t the ends of the salt bridge. The liquid junction potential which exists a t the boundary of two solutions differing in composition is due to a difference in the rates of diffusion of ions of opposite charge. Thus, Then hydrochloric acid diffuses across a boundary, the hydrogen ions move much faster than the chloride ions and tend to produce a positive charge in the solution into n-hich they diffuse. On the other hand, if sodium hydroxide is the migrating substance, the solution into which it migrates tends to become negatively charged, because the negative hydroxyl ions diffuse much faster than do sodium ions. Diffusing salts also produce junction potentials but not t o as large an extent as do acids or bases, because hydrogen and hydroxyl ions have much greater mobilities than do other ions. For cell 4, the electromotive force is given by,
1859
1860
ANALYTICAL CHEMISTRY
where E, is the algebraic sum of the two liquid junction potentials at the ends of the salt bridge; E: is E , for the hypothetical cell in which both CLH; and U C I ; are unity; and the subscripts b and 7 indicate that UH; refers to the hydrogen ion activity in the buffer solution v-hereas acl; refers to the chloride ion activity in the calomel half cell. Combining Equations 6 and 10 gives:
It is impossible to determine any one of the terms, E,, or
U H , ~ without
UCI;J
previously knox-ing two of these quantities. THERMODYNAMIC pH, OR ptH
I n an effort to get around this impasse it was advocated that p H be defined solely in terms of the most convenient method used for its determinatioIi-i.e., in terms of the electromotive force of a galvanic cell such as cell 4. Such a definition would be thermodynamically rigorous and therefore may be referred to as the thermodynamic pH, or ptH. Bjerrum and Unmack (9) and Guggenheim and Schindler ( 1 4 ) proposed as the fundamental definition, ptH =
E - Eo' - E , 2.3 R T / F
E = Eo
-F
l o g l o C & , , ~ R - ~ C=I -Eo - 2 3 RT log,,
CHCI
f2
(15) This equation holds for cell 7 and also for cell 16, P t ; H? (1 atm.), HCl(C1) I KC1 salt bridge I HCI(C2), AgCI; Ag (16) if the hydrochloric acid concentrations C, and CI are equal. When, however, CI # C2 or the right half cell contains a chloride other than hydrochloric acid, ~H:~cI;# f:. The failure to realize this latter inequality has probably led some chemists to the misconception that p t H equals -log,, UH -f*. Undoubtedly, also many chemists hold the mistaken belief that hIacInnes set up a p H scale in such a way that ft and j , are synonymous. It is true that RIacInnes, Belcher, and Shedlovsky ( 2 7 , 29), following Cohn's suggestion, used thermodynamic dissociation constants as a basis for their p H scale, but they did so in such a way that their p t H is only approximately equal to pH, or -log,, G"+ff,. RIacInnes and associates found empirically that, for certain dilute bufler solutions in cell 4,the quantity E:H could be selected such that a plot of the left side of Equation 17 u s . the square root of the ionic strength, p , was linear and gave an intercept equal to pK,, the negative logarithm of the thermodynamic dissociation constant of the buffer acid, H S .
in which Eo' is an experimentally determined constant. This 2.3 RT is equivalent to setting Eo' equal to (EO - E: - _F_ log,, ucl;) of Equation 11. Thus, it would be recognized that, even though they are not rigorously determinable, E: and acl- may be considered as constants for a given cell a t a given temperature. Hence, p t H would be a reproducible number dependent on the hydrogen ion activity if E , could be obtained. They proposed that E , be calculated by the Henderson equation (21). I n addition t o the fact that it would have to be performed for each p H measurement, such a calculation furnishes only a laboriously obtained approximation of questionable validity (4). The present-day thermodynamic definition ( 2 0 ) of p H lumps the junction potential term, E,, in with Eu'-i.e., ptH where E& = EO'
E - EEH ~2.3 RT/F
+ E , = Eo -
+E, -
2.3 RT
where f,, is the activity coefficient of the undissociated weak acid. Hence, for their solutions of ionic strength S0.01, if p t H = -log,, C H ~ the ~ * slope S of Equation 17 should equal the constant, A , of the Debye-Huckel equation, 19 and 20 (11, 20): loglofi =
7 logioacl;
As Harned and Owen have stated (ZO),' I . . .this equation completely defines a useful p H number, about which no confusion need arise unless an attempt is made to interpret it in terms of. . ." the hydrogen ion concentration. Unfortunately, however, the need does frequently arise nhen one nishes to know the hydrogen ion concentration. Hence, the p H cannot always be regarded simply as a variable which must be kept constant during a series of experiments. For this reason, beginning in 1928 with a suggestion by Cohn, Heyroth, and Nenkin (10) as t o a possible procedure, there have been several revisions of the p H scale in an attempt to equate, a t least approximately, the hydrogen ion concentration with the thermodynamic ptH. MacIY'IES pH
T o the theoretical chemist it would be most pleasing if the thermodynamic hydrogen ion activity coefficient, ft,in the formal expression p t H = - loglo U H = - log,, CH-.~S~
where S is an empirical constant, and Cx- and CHXare, respectively, the stoichiometric concentrations of buffer salt and acid corrected by the addition and subtraction, respectively, of the computed CH+. This Equation 17 is similar in form to 18, the rearranged logarithmic form of the dissociation constant of a n-eak acid.
(14)
were equal to some type of mean activity coefficient, Si. This attitude is understandable, as cell measurements provide only mean activity coefficients. For instance, the electromotive force and f* are accnrately connected by Equation 15.
-AZ: 4; 1 Bad;
+
where Zi is the charge on any given ion, and 2 , and Z - are, respectively, the charges on the cation and anion of a binary electrolyte; -4 and B are constants dependent on the temperature and dielectric constant of t,he solvent; and a, is an empirical constant related to the distance of closest possible approach between oppositely charged ions. The S values obtained by MacInnes and associates for acetate and chloroacetate buffers were only 12% higher than those predicted by the Debye-Hiickel theory. This discrepancy would imply a difference of less than 0.01 between p t H and pH, when p jO.01. Hence, it might appear true that their method '' yields p H values n-hich are not equal to -lOgloc'H+f, but are probably as close as they can be adjusted t o such equality using. . ." (2.9)the thermodynamic definition of pH. HoiT-ever, one must question their implication that their method ". . .will yield values of p H which are as useful as appears to be possible in the determination of ionization and other equilibrium conto st,ants," for in the ionic strength range of their solutions, 10- *,the Debye-Hyickel equation gives the same values for logmfk for a uni-univalent electrolyte as for the individual ionic activity coefficient term, lOgia.fH +. That is, in the region, p $0.01, where
1861
V O L U M E 28, N O . 1 2 , D E C E M B E R 1 9 5 6 the Debye-Huckel limiting law (numerators of Equations 19 and 20) is valid, pH, is equal t o paH. Their work, therefore, must not be interpreted as evidence for the validity of equating p t H with pH, a t higher ionic strengths. HITCHCOCK-TAYLOR pH
Hitchcock and Taylor (22) used an extended form of the DebyeHhckel equation, loglof
=
- A‘v$
- B‘p
(21)
to set up a p H scale on the basis of E g H values obtained over a higher ionic strength range, 0.01 to 0.1, than in the work of RIacInnes and associates. hloreover, the former workers studied polyvalent electrolytes, such as the tartrate, citrate, and phosphate buffers, in addition to the uni-univalent buffers studied by the latter. Replacing the last term of Equation 17 with the right side of Equation 21 and rearranging give Equation 22
E - k p K t - k loglo CX - - kA& CHX where k
=
=
EO,,
+ kB‘p
(22)
2.3 R T / F .
Culciilating A ‘ from the Deb!-e-Hiickel theory, Hitchcock and Taylor plotted the left side of Equation 22 against the ionic strength. If such a plot \\-ere linear, the intercept would be E : H . They obtained linear curves for the acetate and the glycollate buffers, but the phosphate and borate buffer plots showed curvature. The accuracy of the EgH extrapolation for the latter buffers is therefore questionable, but to an extent of less than 0.2 mv., corresponding to only 0.003 p H unit. The meaning of coefficient f in Equation 21, and therefore of the Hitchcock-Taylor p H scale, depends upon the means of obtaining d ’and B’. B’ is an empirical quantity, which may or may not be constant. Its value is a function of all the ions affecting E and its use therefore gives some sort of a mean activity coefficient nat,ure to f in Equation 21. For the uni-univalent buffers, the value of d ’ would be equal t o the Debye-Huckel constant, A , whether one attempted to compute f, or f + . However, for the phosphate buffer, Hitchcock and Taylor set A ’ = 3.~1. This latter equality would be applicable if Equation 21 w i s used to express the individual-ion activity coefficient ratio iri log,, ( ~ H P o ; / ~ H ~ P o :). Such a calculation n-odd throw fT, rather than f,, into the E ~ term. H At least for this particular biiffer, it ~ - o u l dseem then that their assigned p H is closer to paH than to pH,, for the effect of the last term of Equation 21 becomes very small as p approaches zero. Hitchcock and Taylor gave no data, other than their assigned pH, for the other polyvderit buffers xhich they studied. NATIONAL BUREAU OF STANDARDS pH, OR pHs
The p H scale established by the National Bureau of Standards workers, referred to as the pH, scale, is based upon measurements on cells without liquid junction (2-4, 6 , 16-18). The liquid junction problem will, of course, arise when the pH, scale is used as the reference by other workers 1% ho employ cells containing liquid junctions. The National Bureau of Standards method of assigning pH, valries consists of three steps ( 2 , 4). First, for each of three or more portions of the buffer solution with different small concentrations of added soluble chloride
is determined by measuring the electromotive force of hydrogensilver chloride cells without liquid junction. B y combining Equations 8 and 23 it becomes evident that: PWH =
- loglo f~ +fc 1 - p ~
(24)
Secondly, these pwH values are plotted against the molality of added chloride to give a straight line, the intercept of Rhich corresponds to pwH when the buffer is infinitely dilute with respect to chloride (16). This intercept is designated as pwHo. If j & - represents the chloride activity coefficient in a solution of ionic strength equal to that of the buffer when infinitely dilute with respect to chloride, then for the buffer, -log10
fH
-CH =
PI1 Ha
log!, f E l -
(25)
Thirdly, the pH, is finally defined as ( -hglofE-CH’) in Equation 25 and is calculated from PRHO by introduction of a conventional, even though nonthermodynamic, scale of individual-ion activity coefficients. Several reasonable definitions have been proposed for a conventional individual-ion activity coefficient. Xone of them may be rigorously tested for validity. I n the words of Bates ( 4 ) , “the choice should be based for the moat part on convenience and ieasonableness in the light of what is known from the theory of ionic solutions.” On the basis of electrical conductance data, JIacInnes (28) concluded that it would be reasonable to assume (1) that the chloride activity in a solution of any univalent chloride is the same as in a solution of potassium chloride a t the same total concentration and ( 2 ) that in the latter solution the potassium and chloride ions have the same activity. Combining these two “MacInnes assumptions” with the definition of the mean activity coefficient of hydrochloric acid, one might estimate hydrogen ion activity coefficients by:
f~
= f&Jfci= f & c l / f ~ c ~where j ~ H C and I fmi refer t o mean activity coefficients of hydrochloric acid and potassium chloride in the particular solution under study. According to Guggenheim ( 1 3 ) the activity coefficient of an ion of a strong electrolyte, which dissociates into V + positive ions of charge 2 , and V - negative ions of charge 2-, is given by: +
B y this convention, then, the ionic activity coefficients of a single binary electrolyte are equal to each other and also to the mean activity coefficient, f,, of the electrolyte. Strictly speaking, neither of these assumptions is readilj, applicable t o a mixture of electrolytes, such as a buffer solution, in which the mean activity coefficients are not usually known. On the other hand, one may apply the Lewis and Randall hypothesis ( 2 6 ) that, “in dilute solutions the activity coefficient of any ion depends solely upon the total ionic strength of the solution.’’ Of course, it is now knoyn that this hypothesis may be used onl>for approximation purposes. For instance, in estimating activity coefficients in mixtures in which mean activity coefficients are unknown, it is frequently of value to employ as a first approsimation the mean activity coefficient of a given substance in its pure solution having the same ionic strength as the mixture. The terms “RIacInnes assumptions” and “Guggenheim assumption” are therefore used hereinafter to describe the applied mathematical device only. Khether the mean activity coefficient of a given substance in its pure solution or in the given mixture is used n-ill be evident from the folloning definitions: ~ E C (mixture) I refers to the mean activity coefficient of hydrochloric acid in the particular mixture indicated, whereas ~ H C I : H C I , refers to the mean activity coefficient of hydrochloric acid in pure hydrochloric acid solution having the same ionic strength as the mixture under et’itdy. The pH, values for the equimolal phosphate buffer, K H 2 P 0 4 : Na,HPO, = 1 : 1, have been calculated by Bates ( 2 ) as a function of ionic strength-i.e., molality of each phosphate X 4-using each of these three conventions. His results are shown in Figure 1. Using the Guggenheim assumption, jz.1- = ~ H C ~ , H C I , , curve G resulted. Curves 0 3 , 0 8 , and DL were obtained by applying the Debye-Hiickel equation using ( a i = 3) for curve
1862
ANALYTICAL CHEMISTRY
0 3 , ( a , = 8) for 0 8 , and the limiting-lam approximation (jgl- = )for D L . Application of the MacInnes assumpby the present author gave tions, using . ~ E C I ( H C I )and SKCI(KCI), curve M . The values assigned as the pH. values are represented by the dots and were calculated by Bates from Equation 19 using a value of 4.4 as the a, for chloride. The National Bureau of Standards ( 4 ) recommends using as a standard reference solution the mixture xhich is 0.02551 with respect to each phosphate and which therefore has E 0.1. The assigned pH, value is 6.86 zk 0.01 a t 25".
~ H ~ P O ,= - j%o;-
using values of 3.76 and 0.01 for the parameters ai and p", respectively (16). The Sational Bureau of Standards ( 4 ) recommends as a standard either 0.05X or 0.05 molal potassium phthalate, both of which are assigned a pH, of 4.01 i.0.01 a t 25' C. Other Kational Bureau of Standard?-recommended buffers and their assigned pH, values can be found in Bates' book (4). Correspondence from Beckman Instruments, Inc., Fisher Scientific Co., and Hartman-Leddon Co., has informed this author that the Kational Bureau of Standards standards are used by them as the basis for assigning p H numbers to their buffers. PRACTICAL pH
For most of the p H measurements made by analytical or biological chemists, the glass electrode is employed as the indicator electrode and is connected by a potassium chloride salt bridge to a calomel reference electrode. Without going into the theory of the glass electrode, one may consider that it operates as a hydrogen ion electrode in that the surface potential of the glass,
RT Ec, is equal to (Eo - F log,
UH+);
SO
that for the cell used in
commercial p H meters, Glass electrode
MOLALITY
OF EACH PHOSPHATE
Figure 1. Relation of molality to pH of 1 to 1 phosphate buffers at 25' C. Computed with various estimates of ionic activity coefficient ( 8 , p. 657). See text for explanation of symbols
A t p 5 0.1 all three activity coefficient conventions (Guggenheim, MacInnes, and Debye-Huckel) furnish pH, values xhich agree within 10.01. The use of bromide or iodide cells (6) in place of chloride cells gave pH, values within 0.015 unit of the National Bureau of Standards assigned values a t p S 0.1. However, above p = 0.1 the p H , values depend significantly on the activity convention used. I n Figure 1, however, even at p = 0.2-Le., 0.05 molal in each phosphate- the National Bureau of Standards pH, differs by only 0.005 unit from that calculated using the MacInnes convention, but it is 0.02 unit lower than that obtained using the Guggenheim assumption. These differences result from the fact t h a t the a, used by the National Bureau of Standards to calculate .f& - is much closer to the ai for potassium chloride, 4.1, than to the ai for hydrochloric acid, -6. It should be evident that, in interpreting p H values in terms of C=+, it is necessary to decide which activity convention is to be used. Bates has plotted the pH, values for the phthalate buffer as a function of molality ( 2 ) . His graph is reproduced here as Figure 2. It is seen that even for 0.1 molar phthalate, application of the MacInnes and Guggenheim conventions gives pH, values which differ from the Kational Bureau of Standards pH, by only 0.002 and 0.01 unit, respectively. The National Bureau of Standards values, represented by dots, n-ere obtained with the aid of the Huckel extension (83) of the Debye-Huckel equation:
1) standard buffer or test
soh. I satd. KC1, HgzC12; Hg
(28)
the electromotive force is given by Equation 10. When a p H meter is standardized Kith a standard buffer, actually a potentiometer circuit is adjusted so that it is in balance when the reading on the output meter equals the p H number assigned to the buffer. The standard buffer is then replaced with a test solution-Le., the solution whose p H is desired-and the practical p H of the test solution is obtained, which is defined by Practical p H = pH,
Et - E , + 2.3 -__ RT/F
(29)
where E t and E, represent the electromotive force when test solution and buffer solution, respectively, are in the potentiometer circuit. From the point of view of the magnitude of the practical p H measured for a system, the differences betxeen the three modern 4 14
4 IO
4 06
4 02
3 98
"08 +G "M 9D3
3940
0 0 2 004 006 008
010
Molality
Figure 2. pH of potassium hydrogen phthalate at 25' C. Computed with various estimates of ionic activity coefficient ( 8 , p. 656). See text for explanation of symbols
p H scales ( MacInnee, Hitchcock-Taylor, and National Bureau of Standards) hold almost no signscance for a biological chemist. With one exception, the pH of standard buffers according to these three p H scales agree within the uncertainty of the National Bureau of Standards assigned values-i.e., within 0.01 from pH 3.5 to 9.2; 0.02 below p H 2.1; 0.03 near pH 13-and also within the limit of accuracy of commercial p H meters. The ex-
1863
V O L U M E 28, NO. 12, D E C E M B E R 1 9 5 6 ception is the 0.1 21 potassium tetroxalate buffer, m-hich was assigned a p H value of 1.45 by Hitchcock and Taylor and 1.52 by the Sational Bureau of Standards investigators. The p H values assigned to standard buffers on the original S@renson p~ scale are about 0.04 pH unit lorn-er than on the three more modern scales. An understanding of the various standardization scales, homever, is essential for intelligent interpretation of the meaning of the practical pH. The interpretation is discussed in a later section oi this paper.
By employing known e.m.f. values for cells reversible t o potassium and chloride ions and the MacInnes assumptions, Harned evaluated the ratio (UCI-)~/(UCI-)~. Inserting this ratio in
EI gave E , =
7 -
log,
!sq
which when subtracted from
EIIgave values for Ej in cell 11. His results are plotted in Figure 3.
LIQUID JUNCTION POTENTIAL ERRORS FOR AQUEOUS SOLUTIONS
From theoretical considerations (do), the junction potential across a boundary would be expected to be a function of pH, ionic strength, the nature of the diffusing ions, solvents, temperature, and, in fact, of anything which affects the mobility of an ion in solution. Because the pH, values assigned t o standard buffers are based upon cells without liquid junction, the original standardization of the p H meter is subject to an error due t o the junction potential term, E,, - Bys,subscripts referring to the fact that standard buffer is in the p H meter cell. This error is partially comwhich is pensated by the junction potential term, Ej, involved n-hen the test solution is placed in the cell of the meter. Thus, because E:' = E:,, the residual junction potential E , , - E,t inherent in the use of the p H meter, produces an error Apa( = residual E j X F/2.3 R T ) in the determination of the practical pH. One cannot calculate the magnitude of this error accurately. However, an indication under certain conditions may be obtained. Bates, Pinching, and Smith ( 7 ) determined the apparent pH, or pHj, for a number of test solutions in the cell with liquid junction; P t ; HP, test soln. 1 satd. KC1 I NBS phosphate buffer, H,; Pt (30) 4 , = mdmaddtd salt
For each of the same test solutions they determined pH, using hydrogen-silver chloride cells without liquid junction by the method already described. The difference, p H , - pH,, for each solution is equivalent to t'he 4 p E which would prevail if the p H meter were employed for the p H measurement using the phosphate buffer as standard. Their results may be summarized as follom-s: (1)p H j - pH, did not exceed 0.02 unit for any of their 12 buffers having pH, between 2.15 and 10.00; (2) p H j - pH. reached a magnitude of 0.03 unit for four of the six buffers studied having pH, 5 2.10; and (3) p H j - pH, exceeded 0.02 unit (0.05 a t p H 12.62) for three out of the six buffers having pH, 2 11. S o correlation between p H j - pH, and p can be drawn from their data. Hence the larger pH error below pH 2.1 and above p H 10 cannot be attributed to an ionic strength effect, but is probably a true p H effert. Severtheless, ionic strength has a real effect on spa. Its significance, however, depends on the accuracy required of the pH measurement. Some indication of its magnitude can be obtained from the electromotive force measurements of Harned ( 1 5 ) using cells I and 11.
+
), (I) Hg; HgZCI?, H C l ( / ~ ~ o ) l I c l ( ? ? ~ HU; Pt-Ptl Hz, HCl(>?to),HgzC12; Hg
(11) Pt; Hg, HCl(m0) 1 KCl sstd. I H'Jl(?n,) For cell I, E I =
+ l I C l ( m ) , H2;
Pt
RT - log, (aH-aclA n-here subscripts F ( a H -aCl -10'
s
and o refer t o the hydrochloric acid solutions with and without salt, respectively. For cell 11, EII
=
+ Ej.
RT 7log, ( u H - ) ~ (aH ' 1 0 ~
Figure 3.
E , estimated for cell I1 by Harned 1K. 1L. 1N. 2K. 2L. 2'V. 3L. 3N .
0.1 molal HCI DIU IiCl
4.v.
The p H equivalents of these data can be translated into A p a values. For instance, if a p H meter were standardized with 0.01 molal hydrochloric acid, the practical p H measured for a solution 0.01 molal in hydrochloric acid and 0.09 molal in sodium chloride would be in error by 0.045 pH unit. For a solution 0.01 molal in hydrochloric acid and 2 0 molal in sodium chloride, this error would be 0.065 pH unit. However, if the meter were standardized originally r i t h the (0 01 molal hydrochloric acid, 0.09 molal sodium chloride) solution, then A p for ~ the (0.01 molal hydrochloric acid, 2.0 molal sodium chloride) solution would be reduced to 0.065 - 0.045 or only 0 020 p H unit. Such deductions from curves 2K, 2 S , and 4 5 suggest that, if potassium chloride or sodium chloride is the predominant constituent in an aqueous solution having a pH between 2 and 12, the variation in A p due ~ to ionic strength is less than 0.04 pH unit R hen the ionic strength is increased from 0.05 to 3! The lithium chloride curves ( l L , 2L, and 3L) consistently show greater values for EII - E , than do the corresponding sodium and potassium chloride curves. This phenomenon is undoubtedly due to the fact that the mobility of the lithium ion differs
1864
ANALYTICAL CHEMISTRY Table I.
Approximate Ej at 25’ C.
[ F r o m Rlilaaao (4, p 41; 64)]
Left Boundary Soh. 1iV NaCl 0 1.Y NaCl 1 S HCI 0 O12V HC1 1.VKaOH 0 1 S NaOH
Right Boundary Soln. 0 . I N KC1 E ; , mv. pH equivalent -11 2 -0 19 -6 56 9 -45 -18
4 2
3 9
Right Boundary Soh. 3 . 5 F KC1 E ; , mv. pH equivalent -1 -0
11 0 94 0 16 -0 75 -0 32 -0
9 2
16 6 1 4 -10 5 -2 1
-0 03
- 0 00 0 28 0 02 - 0 18
-0 04
much more from that of the chloride ion than does the mobility of sodium or potassium ion. The great effectiveness of the universal practice of using saturated potassium chloride rather than a lower concentration in the salt bridge to decrease A p is~ evident from a comparison of some of Milazzo’s data (4,p. 41; 33) given in Table I. This table may also be used to emphasize an error in technique very frequently made. It is a fairly common practice to leave both electrodes soaking in distilled water when they are not in use. Such soaking, if prolonged, produces dilution of the salt bridge, R hich not only decreases the efficiency of the bridge in decreasing A”H but may even change the E , to such an extent that the potentiometer cannot be balanced with the standard buffer.
trary convention must be employed. This convention should be consistent with the convention used in the original assignment of pH, to the standard buffers. I n Figure 4 are presented values of -1og1ofHt calculated by various proposed conventions. Because of the junction potential error, the uncertainty of the assigned pH, of standard reference buffers, and the experimental error in the use of the p H meter, it is very unlikely that a measurement of the practical p H can be considered to be more accurate than within 0.02 unit for the simplest systems. Hence, it is evident from Figure 4 that it is immaterial Thich Convention is used to estimate f ~ a tt p 5 0.05. However, as p increases, the divergence of the curves increases. Because the niobilitj- of the hydrogen ion is five times the mobility of the chloride ion in aqueous solution, it seems justifiable to state that no individual-ion activity convention is reasonable that would allotv fH- must be determined. This coefficient measures the free energy of transfer of the solute from one solvent to another, so that f z of a solute in a given solvent relative to a standard state in another solvent equals T h e primary medium effect can reach tremendous values. For instance, relative to an infinitely dilute aqueous solution as the standard state, f m of hydrochloric acid a t low concentrations increases from about 2 in 207, dioxane to about 200 in 82% di-
JFfm.
[END
oxane (20). For an ethkl alcohol solution of hydrochloric acid, of hydrochloric acid is about 300 relative to the water standard (30). Even more startling are the ionic f m values estimated by Gutbezahl and Grunn-ald (15). They obtained 5 X lo4 and 2 X lo4 for hydrogen and ammonium ions, respectively, in ethyl alcohol relative to water as solvent but only 3.4 for the chloride ion in ethyl alcohol relative to the same standard state. McKinney, Fugassi, and Warner (30) suggested that an acidity scale could be set up in any solvent by the same procedures used to establish the pH scale for aqueous solutions. Although an enormous amount of work must be performed before such scales will be useful, a significant start in this direction has been made by Gutbezahl and Grunwald (15) and by Bates ( 4 ) .
fm
LITERATURE CITED
Babcock, K. I., Overstreet, R., Science 117, 686 (1953). Bates, R. G., Analyst, 77, KO.920, 653 (1952). Bates, R. G., Chem. Revs. 42, 1 (1948). Bates, R. G., “Electrometric pH Determinations,” Wiley, Yew York. 1954. Bates, R. G., J . Research Natl. Bur. Standards 39, 411 (1947). Bates, R. G., hcree, S.F., Ibid., 34, 373 (1945). Bates, R. G., Pinching, G. D., Smith, E. R., Ibid., 4 5 , 4 1 8 (1950). Beckman Instruments, Inc., South Pasadena, Calif., Beckman Bull. 225-A, 100-D. Bjerrum, N., Unmack, A,, Kgl. Danske T’idenskab. Selskab. Math. jus. Med. 9 , 1 (1929).
Cohn, E. J., Heyroth, F. F., Menkin, AI. F., J . Am. Chem. SOC. 50, 696 (1928).
Debye, P., Huckel, E., Physik. 2. 24, 185 (1923). Erikson, E. E., Science 113, 419 (1951). Guggenheim, E. 8.,J . Phys. Chem. 34, 1758 (1930). Guggenheim, E. A., Schindler, T. D., Ihid., 38, 533 (1934). Gutbezahl, B., Grunwald, E., J . Am. Chem. SOC.75, 565 (1953). Hamer, W. J., ilcree, S . F., J . Research Natl. Bur. Standards 32, 215 (1944). Ibid., 35, 381 (1945). Hamer, W.J., Pinching, G. D., Acree, S. F., Ibid., 36, 47 (1946). Harned, H. S., J . Phys. Chem. 30, 433 (1926). Harned, H. S., Omen, B. B., “Physical Chemistry of Electrolytic Solutions,” 2nd ed., Reinhold, Wew York, 1950. Henderson, P., 2. physik. Chern. 59, 118 (1907); 63, 325 (1908). Hitchcock, D. I., Taylor, A. E., J . Am. Chem. S O C .59, 1812 (1937). Huckel, E., Physib. 2. 26, 93 (1925). Jenny, H., Nielson, T. R., Coleman, N. T., Williams, D. E., Science 112, 164 (1950). Kielland. J.. J . Am. Chem. S O C 59. . 1675 (1937). Lewis, G. N., Randall, M.,“Thermodynamics,” 1st ed., p. 380, 1IcGraw-Hill, Sew York, 1923. AIacInnes, D. A , Cold Spring Harbor Symposia Quant Biol. 1 , 190 (1933). AIacInnes, D. A , , J . Am. Chem. SOC.4 1 , 1086 (1919). LIacInnes. D. d..Belcher. D . , Shedlovsky, T., Ibid., 60, 1094 (1938). LIcKinney, D. S., Fugassi, P., Warner, J. C., “Symposium on pH JIeasurement,” ASTM Tech. Pub. 73, 19 (1947). Marshall, C . E. Science 113, 43 (1951). Milasso, G., “Elektrochemie,” Springer-Verlag, Vienna, 1952. Mysels, K. J., Science 114, 424 (1951). S@renson,S. P. L., Biochem. 2. 21, 134 (1909). Spkenson, S. P. L., Linderstr$m-Lang, K., Compt. rend. traz . lab. Carlsberg 15, No. 6, 4 0 (1924). Van Uitert, L. G., Haas, C. G., J . Am. Chem. SOC.7 5 , 4 5 1 (1953). RECEIVED for review M n y 22, 1956. Accepted September 6, 1956. Based on work performed under contract with the U. S. Atomic Energy Commission a t the University of Rochester Atomic Energy Project, Rochester, N . Y . Figures 1 and 2 are reproduced by permission of the Society for Analytical Chemistry from The Analyst, 77, 653 (1952).
OF SYMPOSIUM]
