The Meaning of ph. UCLA School of Medicine, Harbor General Hospital Campus, Torrance, CA 90509

Transcription

1 A n n a l s o f C l i n i c a l L a b o r a t o r y S c i e n c e, Vol. 3, No. 3 Copyright 1973, Institute for Clinical Science The Meaning of ph M. MICHAEL LUBRAN, M.D., Ph.D. UCLA School of Medicine, Harbor General Hospital Campus, Torrance, CA ABSTRACT The principles involved in the definition of ph are discussed in relation to the actual procedures used in its measurement. The assumptions made in the operational definition of ph and the existence of a residual liquid junction potential when ph is measured using a glass electrode and calomel electrode result in an uncertainty of ±0.02 in the ph measured. While of small importance in most uses of ph, this uncertainty is of considerable importance when ph is used to calculate the activity or concentration of hydrogen ions, and when it is used in formulae such as the Henderson-Hasselbalch equation. The measurement of ph using a glass electrode-calomel electrode pair is a common procedure in the clinical laboratory. Recent improvements in the design and construction of these electrodes and of ph meters have permitted the reliable measurement of ph to ±0.002 in the range of ph of *4 to 9. This excellent reproducibility of ph measurements does not necessarily mean, however, that the accuracy of the ph measurement is equally precise. According to Mattock and Band,6 ph cannot be measured with an accuracy better than ±0.02. Bates,1 without quoting a figure, warns that no quantitative interpretation of measured ph values should be attempted unless the medium can be classified as a dilute aqueous solution of simple solutes. Blood and most other biological fluids are therefore excluded by this warning. The reasons for this lack of precise quantitative interpretation of ph measurements can be considered under three headings: the definition of ph; the standardization of ph; the measurement of ph. T he D efinition of ph S0rensen introduced the term ph (p standing for Potenz, i.e., power)9 as a device for the more convenient expression of hydrogen ion concentrations. He defined it as ph = logi0ch, chbeing the molar concentration of hydrogen ions. The concept of activity5 had been introduced a little earlier; eventually ph was redefined10 as ph = log10ah, where an was the activity of hydrogen ions given by one of the formulae a = yc, a = ym, a = fn, c, m and N being respectively the molarity, molality and mole-fraction of hydrogen ions and y, y and f the corresponding activity coefficients. Although this definition was theoretically sound, it was not really useful in practice, as it defined ph in terms of something that could not be measured, namely the activity of a single ionic species. Ions in solution always occur accompanied by ions of the opposite charge, so that the solution is electrically neutral. Thermodynamic theory shows that what is measurable is the mean

2 182 LUBRAN activity of the positive and negative ions. Thus, in a solution of hydrochloric acid, the mean activity would be V(aH+) (acioi the geometric mean being taken. If the concentration of hydrochloric acid were known, the mean activity coefficient could be calculated. Activity coefficients of a single ionic species can be calculated using arguments lying outside thermodynamic theory, which involve assumptions about the movement of ions in aqueous solutions and their electrostatic effects on ions of like and opposite charges. A widely accepted theory is that of Debye and Hiickel,4 who give the formula In fi = Zi2A Vi 1 + Ba Vi The left hand term is the natural logarithm of the activity coefficient on the molefraction concentration scale; Zi is the valency of the ion (1 in the case of hydrogen), I is the ionic strength of the solution, a is the ion size parameter, i.e. the sum of the radii of oppositely charged ions in contact and A and B are constants for a particular solution, which can be evaluated using complex formulae ( tables of A and B for uni-univalent electrolytes have been constructed). The ionic radius cannot be measured either with accuracy or precision and, therefore, the activity coefficient is imprecise and of unknown accuracy. In addition, the Debye-Hückel equation, although important, is derived from hypotheses involving many unverifiable assumptions. In order to obtain uniformity, Bates and Guggenheim2 proposed a convention which has been widely accepted for the calculation of yci in uni-univalent electrolyte solutions of ionic strength less than 0.1:, - A VÎ 106 To' m w i A varies with temperature and is at 37 C. As the product of the activities of hydrogen and chloride ions can be measured experimentally with precision, the activity of the hydrogen ions in hydrochloric acid can be calculated by this formula. The accuracy of the answer depends on the choice of the parameters and the validity of the equation used. The calculated ph is not the true (i.e., accurate) value of the ph, which is not known. However, it is possible to calculate the theoretical value of the ph of certain standard buffer solutions which can be used in the definition of an operational ph. For a solution X and standard buffer solution S of calculated ph (S), ph (X) = ph (S) + (Ex - E S)F RT E x and Es are the E. M. F. s in volts of the solutions when the same electrode pair is dipped into them. The constant F/ RT is at 37 C; each change in ph of one unit gives rise to a change of 61.5 mv at 37 C. Note that the ph given by this operational definition is not necessarily the accurate value of logioah; as will be shown, although the measurement can be repeated with great precision, its accuracy is ±0.02 ph units. Standardization o f ph The National Bureau of Standards has defined the ph of seven buffer solutions, covering the ph range to at 38 C. A standard phosphate buffer of ph at 37 C is suitable for standardization of ph meters used for measuring the ph or P002 of blood.3 Secondary buffer solutions of known ph can be calibrated in terms of the primary standards by direct comparison. However, it is important to appreciate that in spite of the three decimal places used to define the standard buffer solutions, their accuracy is about ±0.01 ph units, because of the assumptions made in the

3 THE MEANING OF p H 183 calculation and measurement of their ph values. In the case of the NBS standards, their ph is defined at particular temperatures. The appropriate ph must be selected when calibrating ph meters for measurement at a particular temperature. In the case of blood, measurements are usually made at 37 C, but until a few years ago, 38 C was used in many European countries. There are two other important features of the NBS buffer standard solutions. The first feature is that they are molal solutions. Most biological measurements are made in terms of molarity; however, the resultant error is small unless the concentration of solutes in the biological solution is high. Thus, molal NaCl is molar. The second feature, however, may cause more serious error. It is that the ph s of NBS solutions have been measured using cells without liquid junctions, whereas in almost all cases, the ph of biological solutions is measured in cells w ith liquid junctions. Therefore, the ph of the standard solutions used in calibration will not have the defined ph value when used with the glass electrode and calomel electrode system. The magnitude of the error and its causes will be discussed in the next section. An alternative standard buffer solution exists, namely, the British Standards Institutions 0.05 molar potassium hydrogen phthalate solution.7 No attempt is made to calculate the theoretical ph of this solution; instead, its ph is defined as at 15 C and at 37 C. Secondary standards are measured in terms of the primary standard. Values for the ph of the same solutions on the NBS and BSI scales are close, but not identical. For example, the standard phosphate buffer is of ph at 38 C on the NBS scale and ph at 38 C on the BSI scale. This scale also differs from the NBS scale in that molar solutions are used instead of molal and measurements are made using cells with liquid junction. The BSI system thus more closely duplicates measurements of biological fluids than does the NBS system. However, with the BSI system as well as the NBS system, the accuracy of the measured ph is about ±0.02. In practice, either system of standards can be used, but they should not be interchanged in a series of measurements. M easurem ent of ph Using the Glass Electrode The most important source of inaccuracy (but not imprecision) of ph measurements lies in the method of measurement. The inaccuracy appears to be unavoidable, even with the most perfect technique, and is due to the existence of a residual liquid junction potential, the exact value of which cannot be measured. In addition, there is a small error due to the asymmetry potential of the glass electrode and an error of unknown magnitude (but probably small) due to assumptions in selecting the standard state of the electrode systems. These errors will be discussed. The glass electrode6 consists essentially of an inner reference electrode, usually Ag AgCl, immersed in an inner buffer solution containing a fixed and constant amount of chloride ion. The electrode and buffer solution are enclosed in a glass envelope, the bottom of which is made of a special glass responsive to hydrogen ions. The sensitivity of the glass electrode to hydrogen ions is probably due in part to ion-exhange with cations of the glass. The exact mechanism is not fully understood. However, the potential of each glass surface of the bulb is given by the Nemst equation where Eg is the standard zero potential of the glass. Eg, although not a constant, has a fixed value at a given temperature. The potential of the glass electrode when immersed in a solution containing hydrogen

4 184 LUBBAN ions is the difference between the potentials of the outer and inner membranes. Using i to denote the inner solution, o the outer solution, E glass electrode = (Eg )0 - (Eg ); + 2~ - y ^ T l o g ^ The inner solution has a stable hydrogen ion activity, therefore (ah)i is a constant. However, the standard zero potentials of the inner and outer glass surfaces are not identical and their difference (E g )0 (Eg )i is termed the asymmetry potential. If the asymmetry potential were constant, it would not give rise to error in the measurement of the operational ph, which involves calculation of the differences of E. M. F. when the electrode system is immersed in a standard buffer solution and the unknown solution. However, the asymmetry potential varies with differences in ph of the solution in contact with the glass and with temperature, among other factors. In order to reduce the error of the asymmetry potential to negligible proportions, the temperature of measurements must remain constant and the ph of the standardizing buffer must be close to that of the unknown, preferably within 1 ph unit. These conditions are usually obeyed in the measurement of blood ph, which fluctuates over a narrow range. They may be overlooked, however, in the measurement of the ph of buffer solutions or body fluids such as urine, gastric juice and duodenal aspirates, which vary over a much wider ph range. The glass electrode is theoretically a thermodynamically reversible electrode. For this condition to be obeyed in practice, the electrode must be matched to the ph meter according to the manufacturer s specifications. The zero point of the meter is affected by the construction of the glass electrode and the composition of the inner buffer solution. The same glass electrode, carefully washed between measurements, must be used for measuring the standard and unknown solutions. The slope ( R T /F) is a theoretical value, not attained in practice. It must be determined experimentally on each occasion a ph is measured. The use of two standard buffer solutions bracketing the ph of the unknown solution has been recommended.1 Calling these solutions 1 and 2, ph (X) = ph (SO + (ph (S,) - ph (Si)) (Ex (E* - EO EO If a direct reading ph meter is used, the scale is adjusted to show the ph values corresponding to the two standard solutions, the second being a check on the first; the unknown ph is then read directly on the scale. Although the instrument may record the ph to the third decimal place, the accuracy of direct reading instruments is, as a rule, not as good as that of potentiometric instruments in which EMF s are recorded. In the majority of cases, the convenience of the direct reading ph meter outweighs its lesser accuracy. Nevertheless, this inaccuracy must be considered in the interpretation of ph values. The calomel electrode serves as the reference electrode, the potential of which is assumed to remain constant during a series of measurements. However, the potassium chloride solution which forms the salt bridge is in contact through a ceramic plug with the solution being measured. A liquid junction potential is created at the interface of the two solutions of different composition. The EMF of the whole cell is thus E = E ret + Ej Eind where ref indicates the calomel electrode, ind the glass electrode and Ej is the liquid junction potential. This potential arises because of the difference in the mobilities of ions carrying opposite charges. Thus, Ej depends on the composition of both the

5 THE MEANING OF ph 185 reference electrode salt bridge and the test solution. Standardization is carried out with a standard solution and a liquid junction potential (E j) s is created. Unless the composition of the test solution is the same as that of the standard, it will give rise to a different liquid junction potential (E j ) x. In the operational definition of ph, the use of the term Ex Es implies that (Ej)s and ( Ej )x are equal and thus cancel out in the subtraction. However, as they are not equal, their difference creates a residual liquid junction potential AEj. The operational definition is, therefore, really ph (X) = ph (S) + (Ex ^3026+ RTEi)F Thus ph (X) is uncertain by an amount depending on the residual liquid junction potential. Ej cannot be measured with accuracy but can be calculated on the basis of certain assumptions. It may give rise to an uncertainty in ph as large as 0.01 ph units. The inaccuracy is reduced but not eliminated by using two standard buffer solutions bracketing the unknown. Another cause of inaccuracy of ph measurements arises through the variation of the standard potential of the cell with temperature. Not only is the slope altered but the position of the zero point changes. Most modern ph meters have temperature controls to correct this source of error. However, it must be appreciated that standard and test must always be measured at the same temperature, otherwise quite large errors can be introduced. This is particularly important when ph electrodes are inserted into the circulation of patients with induced hypothermia. Further uncertainties are introduced in the measurement of the ph of whole blood. Blood contains cells in suspension, which affect variables such as the residual liquid junction potential and the response of the glass electrode. Plasma has a ph about 0.01 higher than whole blood, extrapolated to the time of centrifugation.8 Further, plasma is not a simple aqueous solution of electrolytes, as are the standard buffer solutions. Although the effect of proteins on the accuracy of the ph determination is usually ignored, there do not appear to be data on the magnitude of the protein error. Certainly, proteins will alter the liquid junction potential and ionic strength, and therefore the activity coefficient. Interpretation o f ph In biology, ph is measured for a variety of reasons. In some cases the inaccuracy of the ph by ±0.02 is significant; in most cases it is unimportant. Thus, in making buffer solutions of known ph for providing standard conditions for enzyme assays, precision of measurement of ph is of more importance than great accuracy. Reaction rates are hardly affected by a small variation in ph. Similarly, titration end points and the measurement of the ph of body fluids such as blood or urine are sufficiently accurate, provided that no attempt is made to convert ph values to hydrogen ion concentrations. As ph s are logarithms, a small change in ph corresponds to a larger change in the activity. Thus, a ph change of ±0.02 (the uncertainty of ph measurement, excluding technical errors ) corresponds to ±4.7 percent change in hydrogen ion activity. If, in addition, an approximate value for the hydrogen ion activity coefficient is used, the error in the calculated hydrogen ion concentration will be much larger. The activity coefficient cannot be measured directly in blood. There do not appear to be data on the activity coefficient of hydrogen ions determined experimentally, using extra-thermodynamic assumptions, on solutions closely resembling plasma in electrolyte and protein composition. Another difficulty arises when attempting to convert blood ph into hydrogen ion con

6 186 LUBRAN centration. Even if plasma and not whole blood ph were measured, the activity calculated from it refers to molal solutions. Although molal and molar concentrations of dilute solutions of electrolytes are numerically almost identical, this is not so for plasma which contains about 92 percent of water in healthy subjects and differing amounts in disease. Plasma water concentration must be taken into account when calculating ionic concentrations. A consequence of the inaccuracy associated with ph measurements is that small uncertainties are introduced into the values derived from the Siggaard-Andersen nomogram used in calculating Pc02 from ph. A change of 0.02 in ph corresponds to a 4.7 percent change in PCo2 (about 2 mm for normal values), probably not important clinically. However, it may be necessary to recalculate the values of the parameters of the Henderson-Hasselbalch equation in terms of the operational ph. The lesson to be learned from the above discussion is that ph is only approximately log ah; calculations depending on an exact knowledge of ah (as for example those using the Henderson-Hasselbalch equation) will yield only approximate answers when ph = log ah is assumed to hold. Although the magnitude of the error (±4.7 percent or ph ± 0.02) may not be great, or affect the clinical usefulness of the measurement, it is nevertheless important to be aware of the implications of the use of the operational ph scale and the measurement of ph using the glass and calomel electrodes. References 1. B a t e s, R. G.: Determination of ph. Wiley, New York, p. 57, B a t e s, R. G. a n d G u g g e n h e i m, E. A.: Report on the standardization of ph and related terminology. Pure Appl. Chem. 1: , B o w e r, V. E., P a a b o, M., a n d B a t e s, R. G.: Standard for the measurement of ph of blood and other physiological media. J. Res. Natl. Bur. Standards 65A , D e b y e, P. a n d H u c k e l, P.: The theory o f electrolytes. I. Lowering of freezing-point and related phenomena. Physik. Z. 24: , L e w i s, G. N.: Outlines of a new system of thermodynamic chemistry. Proc. Amer. Acad. 43: , M a t t o c k, G. a n d B a n d, D. M.: Interpretation of ph and cation measurements. Glass Electrodes for Hydrogen and Other Cations, G. Eisenman, ed., Marcel Dekker, Inc., New York, pp. 9-49, ph Scale, British Standard 1647, S ig g a a r d -A n d e r s e n, O.: Factors affecting the liquid-junction potential in electrometric blood ph measurement. Scand. J. Lab. Clin. Invest. 13: , S 0r e n s e n, S. P. L.: Enzyme studies. II. Biochem. Z. 2L , S0RENSEN, S. P. L. AND LlNDERSTR0M -LANG, K.: The determination and value of 7r. in electrometric measurements of hydrogen-ion concentration. Compt. Rend. Trav. Lab. Carlsberg 15:1-40, 1924.