ANALYTICAL CHEMISTRY, VOL. 50, NO. 14, DECEMBER 1978
2137
Accurate Measurements of the Concentration of Hydrogen Ions with a Glass Electrode: Calibrations Using the Prideaux and Other Universal Buffer Solutions and a Computer-Controlled Automatic Titrator Alex Avdeef"' and Jerome J. Bucher Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94 720
Several universal buffer solutions, variably composed of 3-5 m M potassium acetate, potassium dihydrogen phosphate, ethylenediammonium dichloride, and Borax, were examined as a convenient and reliable method for calibrating a glass electrode to read true hydrogen ion concentration. From the results of 19 titrations, 25 'C, pH 2 to 12, I , 0.05 to 0.20 M (KCI), pH meter (adjusted with NBS pH, 4.008 and 6.865 buffers) readings, pH,, using a Beckman 39501 combination electrode, can be converted to -log [H'], p[H], by pH, = 1' S'p[H] where 1'= 0.2269 - 1.9491+ 7.75612, d1') = 0.019 pH and S' = 0.9657 0.47521 - 1.53212, ci(S') = 0.0022. At 1 0 . 1 M PH, = 0.110 -k 0.998p[H]. A FORTRAN computer program was coded to calculate A' and S'for any titration in the range 0 to 40 O C and 0 to 0.3 M (KCI), and for any Combination of the four buffer components. A microcomputer-controlled automatic titrator, programmed in BASIC, was used to collect the potentiometric data.
+
+
A convenient and reliable method for calibrating a glass electrode to read true hydrogen concentration is to measure a t least two solutions of accurately known hydrogen concentrations. Provided that the response of the glass electrode to log [H'] is linear in the region of interest. the pH, scale is defined in terms of true concentration. p [ H ] ( p [ H ] = -log,,[H+]: pH, = pH-meter reading after suitable calibration with NBS buffers). The strong-electrolyte buffer systems HC1 in water and K O H in water are perhaps the easiest to use. However, in the region p H 2.5-11.5, [H+]is not accurately known (since this is a buffer-free region). For the purpose of expanding the useful calibration range. one may choose a weak acid whose dissociation constants are accurately known. In t h e half-neutralization region (maximum buffering). t h e p [ H ] can readily be calculated from the dissociation constant. Acetic acid has been widely used for this purpose. Its most useful range is roughly p H 4 to 5 , Further extensions involve mixtures of weak acids with dissociation constants distributed uniformly over the entire useful pH range. Prideaux in 1916 ( 1 ) proposed the "universal" buffer solution (acetic acid, phosphoric acid, boric acid), henceforth abbreviated the APB buffer. In a later publication, Prideaux and LVard 12) replaced acetic acid by phenylacetic acid, and the latter mixture was used for calibration purposes (3,1). Other universal buffer systems have been described (1:(5). Even though these universal buffer mixtures have been known for a long time, their use for calibration purposes has been relatively scarce. (The control of pH was a more common application.) This may be due to two factors: (1)the dissociation constants may not have been known accurately enough over a useful range of ionic strengths and tempera-
' Present address. Department of Chemistry, Syracuse Cniversity. Syracuse. N.Y. 13210. 0003-2700/78/0350-2137$01 O O / O
tures. and (2) the routine computation of the hydrogen concentrations in such universal mixtures may have been too formidable in precomputer days. McBryde (6) discussed a useful procedure for p[H] measurements in the estimation of equilibrium constants. His empirical calibration results here confirmed by a more elaborate study by Hedwig and Powell (71, who proposed the simple relationship which was observed to be independent of ionic strength in the region I = 0.04 t o 0.20 M iXaC1). Here pH, corresponds to pH-meter reading (meter calibrated with NBS buffers) and the number in parentheses following the parameters is the estimated error in the least significant digit. The lack of ionic strength dependence wa5 remarkable (81. Heduig and Powell used HC1, acetic acid, and ethylenediamine. separately. to determine their relation. T h e present study was initially a n attempt to substantiate the observations of Hedwig and Powell for our particular electrodes and experimental conditions. Also we wished to re-examine the use of universal buffers for accurate p[H] determinations. Lye explored the use of the AP, APE, and ,4PB universal buffers (where A = acetate. P = phosphate, E = ethylenediamine, B = boric acid) with each component less than six millimolar in concentration. To our surprise. we find ineluctable support for ionic strength dependence of the glass electrode in the ionic strength range 0.05 to 0.20 M (KCl), contrary to the findings of Hedwig and Powell. Also we find that the APE uni-buffer does not accurately predict hh-drogen concentration. because of presumed ion-pair interactions of enH2*+and HP04"-. LVe find that it is possible to extend the accurate p [ H ] range of the glass electrode from 1.5 to 12.5, provided care is given to measurements in the extreme regions. For this purpose we have employed a computer-controlled automatic titrator of our own design. The method of collecting potentiometric readings by the autot itrator ensured some minimization of the deleterious effects of time-dependent changes of the asymmetry potential of the glass electrode (9). A versatile FORTR.AN computer program. G L treat the d a t a involving the universal buffer solutions. for I = 0.0 to 0 3 M (KCI) and t = 4 to 40 "C (conditions particularly useful to biologically-relevant studies).
THE CONSTANTS O F THE ACIDS The choice of the uii-buffer components (acetic. phosphoric. ethylenediamine, boric) was dictated by the apparent accuracy of the literature constants (determined with hydrogen electrodes, using junctionless references) and the wide range of ionic strengths and temperatures employed in their determinations. Our computer program has employed these constants in the forms of analytical expressions only as a function of temperature and ionic strength (IiCl). Water. T h e dissociation constant of water. pK,+'. as a function of temperature and ionic strength was calculated from c 1978 American Chemical Society
2138
ANALYTICAL CHEMISTRY, VOL. 50, NO. 14, DECEMBER 1978
t h e 17-parameter empirical expression of Sweeton, Mesmer, and Baes (10). T h e use of this constant was necessary when calculating p [ H ] in basic solutions of known [OH-] concentration. Also, some literature values of constants (boric acid, phosphoric acid, vide infra) were expressed in hydrolysis form and required pK,' for conversion to a more conventional form. At 25 "C, 0.1 M (KCl), pK,' = 13.787 (molar scale). Acetic Acid. T h e constants reported by Harned and Ehlers ( 1 1 ) a n d Harned and Hickey (12) were fitted to an empirical expression as a function of temperature (NaC1 medium) and ionic strength (KCl medium): log K = ___ 1240*8 3.6241 -
T 0.98281Z1/2/(1+ Z'") (1.4907
-
+ .01415T + (1.8284
log K , = 13.062 - 0.0379t (0.038t
-
2424.1
__
T
-
(molar units, t in
0.0018133T
+
-
where h = [H+], '/i = total hydrogen concentration, NL = number of buffer components, Li= concentration of the ith buffer component (i = A, P! E , B to designate the different buffers) and h, is t h e average number of protons associated with the ith buffer a t a particular p H . It'ith the further definitions 3, E 1:D, ~ , = o N H ~ , 3 1 L h ' ; G , E xj$,'h'; J , x J 2 d , ' h ' where NH,= number of dissociable protons on the ith buffer component, = [H,L!]/[L,][H]', and h, = G,;'D, one can restate Equation 6 as the polynomial function Fib) =
0
=(h-
T o solve for h iteratively by the present method,
"C) (3)
+ 2.336
-
+
0.06597911/2/(1 Z1") (1.2536 - 0.002149T)I (0.6002 -0.00067T)l' (RMSD = 0.0029) (4) 1842.5 log K , = ___
(6)
+ 0.0004166t2 +
2.9531'
This equation is not intended to be very accurate for I > 0.15 M and t > 40 "C. B u t this suffices for our calculation since the contribution to the determination of [H+]due to the third dissociation of phosphate (at 0.005 M) is overshadowed by the buffering of water a t p H > 11. Ethylenediamine. T h e constants for ethylenediamine were fitted to a n analytical form as a function of temperature and ionic strength, using the data of Everett and Pinsent (17):
T
METHOD OF CALCULATION Hydrogen Concentration. T h e computer program GLASb is coded to solve for [H+] for any combination of the four buffer components, including t h e case of water titration (no added buffers). T h e problem is that of solving a nine-order polynomial expression in [ H + ] by t h e Newton Raphson method of tangents 122), using 10'O' p H m ' as the initial [H'] value for the iterative process. T h e polynomial function is stated simplicitlq as
- 0.0052115T)Z 0.0049174T)11'2 (molal units, T i n I
