REPORT
FOR
ANALYSTS
pH and the Modern Analyst
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VOL. 29, NO. 5, MAY 1957
·
15 A
REPORT FOR ANALYSTS
Basic to Dependable Lab Ware-VITREOSIL
and new measuring devices of increased stability are being developed contin ually. Fundamental difficulties re main, nonetheless, for the pH meter per sists in its incorrigible habit of express ing results on a scale that has no exact theoretical meaning. Because no really convenient practical way of measuring acidity on the scales that we find theo retically most satisfactory is known at present, the pH meter seems unlikely soon to become a casualty of technologi cal progress. The regrettable situation may be summed up in the following un certainty principle: "We can't under stand what we measure; we can't measure what we understand." De spairing of reform, the modern analyst must seek to recognize the limitations of pH numbers and to use these numbers most effectively. pH Units and Scales
The most exacting needs of laboratories throughout the world are most eminently and successfully m e t by Vitreosil ware (pure fused silica) produced to the high est standards of quality.
The analyst would like to have a means of determining quickly and ac curately the hydrogen ion concentration of solutions of unknown composition. The logarithm of the reciprocal of this
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quantity, termed pcH, in equimolar acetate buffer solutions is shown in Figure I. The curve of paH (the logarithm of the reciprocal of the hydrogen ion activity) lies considerably higher than that of pcH at ordinary concentrations, whereas psH, the clas sical pH value of S^rensen, is uniformly 0.03 to 0.04 unit lower than paH. Galvanic cells are oxidation-reduction systems, and the use of two electrodes is inescapable. Two arrangements of these electrodes are possible. The electrodes may both be placed in the same solution, whereupon the measured electromotive force (e.m.f.) is strongly dependent upon two ions. Alterna tively, one of the electrodes (the re ference) may be isolated in a suitable medium of its own which makes contact (the liquid junction) with the test solu tion through a "bridge," usually a saturated potassium chloride solution. There are then three loci of potential difference—namely, the two electrodes and the liquid-liquid boundary. In this arrangement, the measured e.m.f. is dependent primarily upon the amount of a single ionic species—e.g., hydrogen —present in the "test" solution, but the unknown changing potential at the liquid junction introduces a consider able uncertainty into the measurement. The pH cell is an arrangement of the second type. The only alternative would be to add a second ion in known concentration to the test solution, a very inconvenient measure at best and incapable of serving as a com pletely satisfactory pH method. For practical uses, then, one strives to make the liquid-junction potential constant, and to use the cell to determine differ ences of pH alone. If the residual liquid-junction potential were indeed nullified by this means, the e.m.f. would yield a relative activity of hydrogen ions, as the formal equations show. By definition, this activity, aH, is /HCH, where en is the hydrogen ion concen tration and / H is the activity coefficient of hydrogen ions. Granting for the moment that constancy of the junction potential has been attained, we are led to the operational definition of pH: pH = p H s +
Ε-Es 2.ZO2&RT/F
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16 A
·
ANALYTICAL CHEMISTRY
pH variation with temperature of NBS p H standards
where Ε is e.m.f. and the subscript 5 refers to the standard solution with which the pH cell is adjusted before the measurement, and 23Q2QRT/F has the value 0.05916 volt at 25° C. The operational definition has had an enormous influence in justifying the widest possible application of pH meas urements. In effect, it authorizes the conversion of every value of J? to a cor responding value of pH. Thanks to the high-impedance pH equipment avail-
REPORT FOR ANALYSTS
NEWEST OF
5
MICRO-MICROAMMETERS 412 Log Model indicates from
70'13 to TO''
ampere on a single six-decade scale
STABILITY, economy, and fast response are all combined in this versatile logarithmic instrument. Typical uses of the new Keithley 412 include reactor control, radiation monitoring, materials testing, and measurement of other widely varying micro currents from sources of one volt or more.
Figure 1. Comparison of pH numbers for ace tate buffer solu tions
KEITHLEY MODEL 412 able commercially, determinations of t h e e.m.f. of t h e glass-calomel assembly a n d of p H in soft solids, slurries, non aqueous media, a n d t h e like, a r e com monplace. T h e n u m b e r s obtained a r e useful for their reproducibility b u t o b viously bear hardly t h e remotest rela tion to hydrogen ion concentration. T h e propriety of calling t h e m " p H v a l u e s " is certainly questionable, al though t h e r e seems little d o u b t t h a t this practice will continue. Interpretation of pH Measurements T h e analytical chemist needs t h e answers to two i m p o r t a n t questions. T h e first is—can t h e measured p H ever be given a fundamental interpretation, a n d , if so, u n d e r w h a t conditions?— a n d t h e second—exactly h o w should t h e interpretation, when allowable, be made? T h e m e a s u r e m e n t of p H is a measure m e n t of a difference of e.m.f. If t h e l a t t e r is t o reflect t h e t r u e change of acidity, only one of t h e three possible sources of potential difference—namely, t h e glass electrode-solution interface— can change when t h e s t a n d a r d solution is replaced b y t h e " u n k n o w n . " T h e constancy of t h e liquid-junction p o tential is t h e kej- to t h e first question. F o r t u n a t e l y , t h e bridge of s a t u r a t e d potassium chloride solution is r a t h e r effective in bringing a b o u t this desired constancy. Xevertheless, t h e differ ence of potential across t h e liquidliquid interface is caused b y unbalanced diffusion of ions, a n d it can h a r d l y b e expected t h a t all u n k n o w n s will m a t c h
t h e s t a n d a r d s closely with respect t o ionic concentrations a n d mobilities. I n particular, t h e highly mobile hydrogen a n d hydroxyl ions, if present in t h e s t a n d a r d a n d u n k n o w n solutions a t dif ferent concentrations, have exagger ated effects. T h e same is t r u e of a n y ion present in high concentration or a n y molecular species in a m o u n t suf ficient t o alter t h e essentially aqueous character of t h e m e d i u m . T h e answer to t h e first question is, then, a qualified y e s : experimental p H values can be justifiably given a n inter p r e t a t i o n if (1) b o t h s t a n d a r d a n d u n k n o w n a r e dilute aqueous solutions ( < 0.2M) of simple ions, a n d (2) t h e p H is greater t h a n 2 a n d less t h a n 11, or m a t c h e s closely t h a t of t h e s t a n d a r d . T h e answer t o t h e second question facing t h e m o d e r n analyst—namely, how t o interpret experimental p H values when a n i n t e r p r e t a t i o n is allowable—is n o t readily found. I t requires first of all a n examination of t h e meaning of t h e p H s values assigned t o t h e s t a n d a r d solutions, for it is evident from t h e operational definition t h a t p H derives its character largely from p H s . One m u s t deal here with t h e great f u n d a m e n t a l problem of p H measure m e n t s : Although t h e p H measurement m a y yield w h a t is called a difference of hydrogen ion activity, aH, neither the l a t t e r n o r t h e single ionic a c t i v i t y co efficient, fa, h a s exact t h e r m o d y n a m i c significance. Hence, aH can neither be d e t e r m i n e d uniquely n o r applied exactly t o t h e chemical equilibria one deals with in calculating end points, ionic concentrations, dissociation constants,
LOG
MICRO-M1CROAMMETER
FEATURES include a single range of six decades from 10~13 to 10"7 ampere, accuracy of 0.2 decade, zero drift within 0.5 decade in eight hours, and response time of less than 2 seconds to 9 0 % of currents larger than 10 12 ampere with 5000 mmf across the input. IT'S SIMPLE to set up and use. The sole operating control is the on-off switch. It has only three calibration potentiometers, and reads out on a six-inch illuminated meter. C O N N E C T O R S furnished include a 216-volt tap for polarizing ion chambers and a single-ended 6-volt output that drives both 50-millivolt and 5-milliampere recorders. The instrument is furnished for bench or rack mounting. NEW CATALOG Β contains detailed data on the 412 and all other Keithley Instruments. A request on your company letterhead will bring your copy promptly.
K E I T H L E Y INSTRUMENTS,
INC.
12415Euclid Ave., Cleveland 6, Ohio Circle No. 17 A on Readers' Service Card, page 77 A VOL. 2 9 , N O . 5, MAY 1 9 5 7
·
17 A
REPORT FOR ANALYSTS and the like. I t is possible, however, to define arbitrarily the single ionic ac tivity coefficient and to establish in this way a conventional scale of aH that serves quite well. Perhaps the most logical procedure is to ascribe to the activity coefficient of a univalent ion the well-understood properties of the mean activity coefficient of a uni-univalent electrolyte in a similarly constituted medium. This approach was chosen as a basis for the establishment of the National Bureau of Standards pH stand
•':i;:l||ll;lti^
ards. These NBS reference materials, now six in number, enable pH measure ments to be standardized from 0° to 95° C. and over the pH range 1.6 to 12.4 at 25° C. In the procedure for the assignment of standard values (1), an alkali chloride is added in known concentration to the buffer solution, and the e.m.f. between hydrogen and silver-silver chloride electrodes in a cell without liquid junc tion is obtained. Standard potentials and fundamental constants being-
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18 A
·
ANALYTICAL CHEMISTRY
known, the e.m.f. is an unambiguous measure of — log(/H/ciCH), a quantity that has been termed pwH for con venience. The effect of the chloride on pwH is eliminated by a suitable ex trapolation, and /ci is made to disappear by introduction of the conventional definition of the single ionic activity coefficient. The result is a pH stand ard value, or pH s . Inasmuch as /H/CI is equivalent to / ^ , where f^ is the mean activity coefficient of hydrochloric acid in the buffer solution, p H s has" in reality the dimensions of —log f^cn, but it is often convenient to regard /^CH as the conventional hydrogen ion activity. The specific properties of the ions of strong electrolytes of a single charge type are different and, hence, so also are the mean activity coefficients of these electrolytes, even at rather low values of the ionic strength (μ). For example, the value of a, the "ion-size parameter" in the Debye-Huckel equation at 25° C , - l o g / ± = 0.508Vi/(1 + 0.328α\/μ), may vary from 3 to 6 for different strong uni-univalent electro lytes below 0.2M. Hence, a single con vention cannot yield exactly compar able p H s or pH values for differently constituted standards and unknowns, even under the most favorable circum stances. As μ decreases, the differences in / ± evidently also decrease. Ac cordingly, the NBS procedure selects standards of ionic strength 0.1 or less, where the assigned uncertainty of ±0.01 unit in p H s will allow a con siderable variation in the parameter a. A similar restriction to the application of measured pH \'alues to chemical equilibria is inescapable. Here again it is impracticable, or even impossible, to recognize specific differences of a secondary character, among the con stituents of the solution. Differences of electric charge are, however, of primary ' influence on the activity coefficients, and allowance must be made for them. If / ^ is the conventional definition of the activity coefficient of a single uni valent ion, the activity coefficients, /,-, of other ionic and molecular species of valence z; may be expressed by log /,· = z ^ l o g / ^ . This expression is con sistent with the ionic strength principle and with the valence relations of the Debye-Huckel limiting law. The manner in which measured pH values are employed in chemical equilib ria, when the favorable circumstances of the measurement justify this step, is now clear. The equilibrium is first formulated in its exact (thermodynamic) form, and the following substitutions are made: (1) — log fnCa is replaced by the experimental pH value; (2) the activity coefficients of the other species are expressed in terms of / ± ; and (3)
REPORT FOR ANALYSTS
/ ± is computed by the Debye-Huckel equation with an average value of 4 or 5 for a. The accuracy of calculations of this sort is evidently limited when ions of charge greater than ± 1 are involved. However, for certain equilibria, notably the dissociation of monobasic weak acids, this treatment may be very suc cessful, thanks to a partial cancellation of activity-coefficient corrections. In spite of these limitations, pH measure ments remain a most useful tool for the determination of equilibrium constants and other electrochemical data with moderate accuracy. Nonaqueous Media "This illustration is an authentic engratine, during ihe 1600's. For yo/it copy
