THE INFLUENCE OF URINARY IONIC STRENGTH ON PHOSPHATE PK2′ AND THE DETERMINATION OF TITRATABLE ACID William B. Schwartz, … , Norman Bank, Robert W. P. Cutler J Clin Invest. 1959;38(2):347-356. https://doi.org/10.1172/JCI103808. Research Article Find the latest version: https://jci.me/103808/pdf THE INFLUENCE OF URINARY IONIC STRENGTH ON PHOSPHATE PK2' AND THE DETERMINATION OF TITRATABLE ACID * By WILLIAM B. SCHWARTZf NORMAN BANKt AND ROBERT W. P. CUTLER (From the Department of Medicine, Tufts University School of Medicine, and the Medical Service of the New England Center Hospital, Boston, Mass.) (Submitted for publication August 4, 1958; accepted September 25, 1958) It is well recognized that the pK' value for the solutions by employing concentrations in the salt of a weak acid or base is significantly influ- mass law equation. Thus, the value of K in the enced by the ionic strength of the solution. In equation the case of phosphate, the theoretical value for K = [H+][A-] pK2 in an infinitely dilute solution is 7.181 at (1) [HA] 370 C. (1) and in a solution of ionic strength com- parable to that of plasma is approximately 6.8. remains constant over a wide range of concen- The small variations in ionic strength ordinarily trations. In the case of strong electrolytes or encountered in plasma would not be expected to the salts of weak acids, the dissociation constant produce significant deviations from this latter is not accurately predicted by the mass law value. However, in view of the wider range of equation if concentrations are employed. Ac- ionic strengths which occurs in urine, values dif- cording to current theory, this deviation from fering appreciably from 6.8 might be anticipated. ideal behavior is not the result of incomplete In the present study an attempt has been made dissociation but is accounted for by changes in to evaluate the relationship between pK2' phos- activities induced chiefly by interionic electro- phate and ionic strength in urine, and to define static forces. The variation from ideal behavior the usual range of values which might be encoun- is expressed by the activity coefficient, -y: tered in the course of acute phosphate loading a experiments. A method has been devised for (2) 7=-, the determination of phosphate pK2' in urine c and the experimental values have been compared where a is the observed activity and c, the con- with those for phosphate solutions of similar ionic centration. In general, y decreases with increase strength. The data suggest that under the con- in concentration and approaches unity at high ditions of the present experiments the behavior dilution. If y c is substituted in the mass law of phosphate in urine conforms closely to that equation, the change in K can then be predicted. predicted for simple phosphate solutions by the Thus for the reaction H2PO4- ± H+ + HP04=, Debye-Hfickel equation. It has further been the following equation may be written: demonstrated that the pK2' of phosphate in urine may vary significantly and that under some cir- aH+ '72. [HPO4=] cumstances failure to consider this variation may (3) 71.[H2PO4-] introduce appreciable errors into either the meas- urement or calculation of urinary "titratable In the logarithmic form, this becomes: acid." (4) pK2= pH + log [HPO4'] + log 1 THEORETICAL CONSIDERATIONS [HP04-] 72 The dissociation constant of a weak acid may or: be determined with reasonable accuracy for dilute * Supported in part by grants from the National Heart (5) pK2-log29 = pH Institute, National Institutes of Health, United States Public Health Service, and the American Heart Asso- + log pK2'. ciation. -[HP4] t Established Investigator of the American Heart Asso- ciation. pK2 is the theoretical value for an infinitely dilute $ Fellow of the Life Insurance Medical Research Fund. solution where 7y1 and 72 = 1. At any finite 347 348 WILLIAM B. SCHWARTZ, NORMAN BANK AND ROBERT W. P. CUTLER concentration, however, the observed pK (pK2') tions is a function of the ratio of the two forms )LI of phosphate (3). Bates and Acree (1) have will vary from pK2 by the term log studied the second dissociation constant of so- The relationship between the activity coeffi- dium phosphate solutions in which the fractions cient of an ion and ionic strength, Iu of the solu- of total phosphate as HPO47 were approximately tion may be expressed by the Debye-Hfickel 0.4, 0.5 and 0.6. These workers employed molal equation: concentrations and measured E.M.F., using hy- drogen and silver chloride electrodes and a tech- A Zi24 (6) - logl7i = nique which eliminated errors due to liquid junc- tion potential. Since the method commonly in work is pH measurement Zi is the valence of the ion. A and B are con- employed biologic stants, dependent upon temperature and the with the glass electrode, these constants have been sodium phosphate solutions at solvent. a is the "interionic diameter." The restudied for the Furthermore, ionic strength of the solution, IA, is calculated by 370 C. using glass electrode. multiplying the concentration of each ion, Ci, molar concentrations have been employed in the by the square of its valence Z12 adding all such present study in order to obtain results which could be compared more closely with those of 2. JA = products, and dividing by 2i urine where concentrations are ordinarily meas- Substitution of 4.5 A for a and the appropriate ured and expressed on a molar basis. In addi- values for A and B (1) in Equation (6) yields an tion, linear constants have been determined for equation for each form of phosphate. The com- a wider range of phosphate ratios than studied bination of these equations gives: by Bates and Acree, in order to encompass the range found in urine. No attempt was made to log-=71 1.57-4C correct for liquid junction potential error in the (7) pH measurement of either phosphate solutions or urine. Equation (5) may then be rewritten: Within certain limits, the Debye-Huckel equa- 1.57.4 tion also predicts changes in activity coefficients (8)( )PpK2 1 + for solutions containing more than one electro- 1.49,Cu Kt .4i~FH2j] lyte. In dilute solutions, the activity coefficient =pH + log E[H'P04] = pK2 . of a given strong electrolyte is the same in all solutions of the same ionic strength (4). Thus In this form, the equation is valid to an ionic in an equimolar phosphate buffer solution whose strength of about 0.1. For ionic strengths above ionic strength is increased from 0.1 to 0.2 by the this, an additional term must be added which has addition of sodium chloride, the change in activ- been found to be linear with respect to ionic ity coefficient is simply that predicted by the strength (2). The expanded equation may be change in ionic strength (2). The effects of written: higher concentrations of NaCl have not previ- ously been studied, nor have data been available. (9) pK2- AhFIA + #JA on the influence of NaCl or other salts when phosphate is present in other than equimolar concentrations. = pH + log [H2PO4 -] pK' [HP0=] =p2 . METHODS The value of pK2 for phosphate solutions at A. Experimental determination of PK2' phosphate and linear constants in simple solutions 370 C., obtained by extrapolation to zero ionic strength, is approximately 7.181 (1). Thus if 1. Sodium phosphate solutions. Standard solutions were made so that the ratio of to was varied and ratio of are up H2P04- HPO4- the ionic strength phosphate over a range from 19/1 to 0.43/1. For convenience, these known and pH determined experimentally, the ratios may be expressed as fractions of total phosphate equation may be solved for P. The value of the present as HPO- and will be referred to as mole fractions linear constant, P, in the case of phosphate solu- in the remainder of this paper. The mole fractions, corre- IONIC STRENGTH, PHOSPHATE pK2 AND TITRATABLE ACID 349 sponding to the above ratios, ranged from 0.05 to 0.70 and equivalent to organic buffer present between approxi- were achieved by individual weighings of Na2HPO4 and mately pH 4.4 and 6.8. The pH after addition of alkali NaH2PO4. All solutions were made up in triplicate to a was taken as the value of pK2't. final molarity of 0.50. The ionic strength of urine specimens after addition of The following procedure was carried out in duplicate alkali was calculated by correcting the original electrolyte with each standard solution: Successive 1 ml. aliquots were concentrations for the change resulting from the addition added from a buret to a beaker containing 10 ml. of dis- of HCO and NaOH. H2PO4- and HP04 were assumed to tilled H20. By this means the molarity of the solution be present in equimolar concentrations and organic anions in the beaker was increased in a step-wise fashion from present between pH 2.7 and 6.8 were included in the 0.0455 to 0.2500. The pH was determined after each calculation and taken as univalent. increment. Substitution of pH and the appropriate values [H2P04-. for and (9) was then made C. Chemical measurements ,u log [HP04c]]in Equation and the equation solved for P. pH determinations were made with a Cambridge re- 2. Sodium phosphate solutions with added salts. The search model pH meter, using an external glass electrode effects of increasing quantities of NaCl and Na2SO4 on the and calomel reference electrode. All determinations were pK2' of phosphate was studied by utilizing 50 and 100 mM carried out in water bath maintained at 37 1 1° C.