Francis E. Crane, Jr.
Douglass College Rutgers, The State University New Brunswick, New Jersey
II
b There an Ahernathe to pH?
Surprising as it may seem, there have been many unsuccessful attempts over the years to replace the pH 'oncept. Most of these suggested substitutes are related to the hydrogen ion concentration [H+]in a more complicated manner than is pH itself. The reluctance of the scientific world to change from p H may be explained partly on that basis. The introduction of pH as a function of [H+]by Sorensen in 1909 was a significant event in the history of chemistry. I t eliminated the disagreeable task of working with very small decimals or with large negative exponential powers of ten when the [H+]is low, i.e., in weakly acid, neutral, or alkaline solutions. However, to some it may seem unfortunate that Sorensen defined his pH term as the negative logarithm of [H+]. This definition requires that as a solution becomes more acidic, IH+] increases whereas pH decreases. pH appears to be related inversely to [H+]and when [ H + ] is greater than unity, the pH is actually negative. This situation is difficult for some beginning chemistry students to comprehend. Some Alternative Proposals
Wherry and Adams ( 1 ) recommended in place of pH the use of a chemical potent,ial term, X,, defined as 7 - pH, and a specific acidity scale, "S.A.," defined as [H+]times lo'. Thus, when pH is less than 7 (in acidic solutions) XH is always positive and increases in direct relation to [H+]. Also, S.A. increases in direct relation to [H+]and is always greater than 1 in acid solutions. I n neutral solutions, when pH = 7 , X , = 0 and S.A. = 1. Later, Wherry (P) changed his nomenclature for the S.A. scale to the "active acidity" scale, and introduced an "active alkalinity" term especially for basic solutions. This alkalinity term, "A.A.," was defined as equal to the hydroxyl ion concentration times 10'. A.A. is equal to 1 at neutrality and becomes progressively more positive than 1 in alkaline solutions, whereas XU becomes progressively more negative. Wherry claimed a major advantage to be that his computations begin a t the neutral point. Clark (3) raised several objections to Wherry's terms, chiefly that the X , method involves an assumption, which is never used, regarding the nature of pure water; that Xn values are not directly derived from the potential of the normal hydrogen electrode; that the X , scale does not have a sufficient advantage over pH to warrant a change; and that Wherry's specific acidity scale is unfamiliar and puzzling, and obscures those logarithmic relationships which are valuable for students. Derrien and Fontes (4) proposed that acidity be expressed as the logarithm of [H+]in micro units per
liter. This term DF actually amounts to log lo7 [H+] in mole per liter concentration units. As a solution becomes less acid, the positive value of DF decreases until it becomes zero a t neutrality and progressively more negative as the solution becomes more alkaline. Another system, which claims the advantage of giving positive values for acidic solutions, zero for neutrality and negative values for alkaline solutions was described by Giribaldo (5). Instead of using [H+]to express acidity, the term log [H+] log [OH+] = log H+/OH- or log r was advocated. Also log r equals log [H+] - (log K , - log [H+]) in water solution. This simplifies to log r = 2 log [H+] log K,. Kolthoff (6) has commented a t length on the methods which were proposed up to 1926 to replace the pH method. He states that it is confusing to attach a special meaning to neutrality in biological systems as Giribaldo and Wherry had done. Also, no special meaning should be given to a pH of 7, because only pure water has this value. Kolthoff concluded that Sorensen's pH should be retained, and none of the new methods adopted. Specific disadvantages of the Giribaldo system were mentioned: (1) the values of r change as the square rather than the first power of the change in [H+];and (2) the log r scale is different a t each temperature due to the changing value of K,. Later, Giribaldo (7) claimed that his new pR values do not vary with temperature, while the theoretical pH does, owing to the varying dissociation of water. A unit of acidity named "hydron" was proposed by Gerstle (8). Because this unit is too large for practical purposes, he preferred the "decihydron" equal to of a hydron. The number of decihydrons, N d h , in a solut,ion = 10 log (aH+)l/(aa+)p where (an+), and (aR+)*represent respectively the hydrogen ion activity in the solution under investigation and that of the standard reference. As a practical standard of comparison, he suggested pure water at 22" C, in which = = lo-'. Thus Ndh = 70 10 log (an+). Advantages were claimed over the pH system: hydrogen ion activities have a more rational meaning; acidity and alkalinity are easily distiuguishable by the plus and minus signs; the numerical extent of the range has been increased, without resorting to small decimal values; and the zero poiut corresponds to the hydrogen ion activity of pure neutral water at 22' only. Miller (9) recommended that pH be expressed as an arithmetical quantity either as active acidity "A," or active alkalinity "Aoa." These terms were defined strictly on the basis of H+ and OH- ion concentrations. A t,ahle listing AR and Aon in familiar arithmetical and
-
+
dc
Volume 38, Number 7, July 7 96 7
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365
bases, the equations applicable a t the stoichiometric equivalence points would be as follows:
equivalent logarithmic terms was given. Catani (10) believes that both the pH and pR systems are inadequate, and proposed an rA (meaning reaction actual) system to replace them. The rA value was expressed as milliequivalents of ionic hydrogen per liter, with alkaline solutions given negative values. In 1952 Valentinuzzi and Lango (11) advanced additional reasons for adoption of Giribaldo's pR system. They claim that a constant numerical value of pR = 0 indicates neutrality independent of the temperature, and that the absolute value of pR is directly proportional to the deviation from neutrality. Also, several of the important formulas giving the pH of strong acids and bases, weak acids and bases, ampholytes, and buffer and salt solutions were changed into pR terms. Hitchcock (12) states that further work should be done to determine whether -log CEfE or -Cnfaz is more useful than pH as a measure of acidity or alkalinity, and whether simpler methods can be found for measuring these quantities (f is the activity coefficient).
where
+
pH = ' 1 2 ( p K w P K ~ log [A-I cH = 16 - 'I2( p K w pKo log [A-I)
(7)
+ ++ +
cH = 16
then pH = 16 - cH
(3)
Journul of Chemical Educulion
(8)
- '/%( p K , + p K 4
(9)
'/z
(pKw
+ pK2 + log [A-%I)
(10)
Corresponding electrochemical equations also can incorporate the cH term in place of pH. For example, when hydrogen and calomel electrodes are used, the pertinent equation would be
When a glass electrode, whose potential is 0.6.5.5 volt, and a calomel electrode are employed, the measured potential is
+ +- 0.059 0.059 (16 - cH) eH
E = 0.655 E, or E = E, - 0.289
(13) (14)
I n the case of quinhydrone and calomel electrodes a similar expression results: E = constant
+ 0.059 cH
(15)
Acknowledgment
We are indebted to the Rutgers University Research Council for financial assistance, which made this work possible. Also, thanks are due Professor Frank H. McGar for a stimulating discussion, and the Misses Maryellen Marrow and Ethel Regenbere for assistance in searching the literature. Literature Cited WHERRY,E. T., AND ADAMS,E. Q., J. Wash. Amd. Sn'.,11, 19Rl1921). --- ~ - - - - , ~
WKERRY,E. T., Bull. Wagnw Free Inst. Sd., 2 , 5 9 (192i). CLARK,W. M., J. Wash. Acad. Sci., 11, 199 (1921). DERRIEN,E., and F O N T ~ SG., , Contpt. R a d . Sac. Biol., 92,503 (1925). GIRIBALDO, D., An. Soc. espaff.fls. qdirn., 22, 555 (1924). KOLTHOFF, I . M., Biocha. Z., 169,490 (1926). GIRIBALDO, D., An. jac. q h . farm. (Montevideo), 2, 3 119381. ~ ~ ~ ~ , ~ ( 8 ) GERSTLE,J., Trans. Electrochem. Soe., 73, 9 (1938). ( 9 ) MILLER,L. B., Paper Trade J., 109, 22 (1939). (10) CATANI,R. A,, Rev. Brasil. qziim. 15, 264 (1943). M., AND LARGO,R., Rev. Otto-Krause, 4, (11) VALENTINUZZI, No. 16,86 (1952). (12) HrTcKcocn, D. I . , Nntl. Bur. Stand. Circ. No. 524, 205 (1953).
The important equations in aqueous neutralization chemistry are usuallyexpressed in terms of pH. These equations can be transformed readily into cH nnits. For example, in titrations of various acids with various
+
- log [A-I
At the second equivalence point, if it is assumed that [A-2] - [OH-] S [A-2], the approximate equation would be
(1)
(1) (2)
+ log lH.41
+
It is simple to transform from cH to the conventional pH unit, if desired. Thus, the acidity concept can be introduced to the beginning student by means of the constant 16, which is easily remembered because it is the basis of the chemical atomic weight scale. Another suggested use of this teaching device may be as an exercise to clarify in the student's mind the various equations based on [H+] which are often expressed merely in terms of pH. It, will he noticed that euuation (3) ~,is reminiscent of the relationship between pH and pOH, which is equal to -log [OH-]. In water solutions of low ionic strength a t 25', pH = 14 - pOH. Thns:
/
(6)
where
For titrations of weak diprotic acids, H2A, by strong bases, if it is assumed that K1 HAH k - and that (H,A) S (A-=), a t the first equivalence point the approximate equation would be
CH has the advantage that it has a direct rather than an inverse relation to [H+] and is always positive unless the solution becomes extremely alkaline, i.e., where the [H+] is less than 1 X lo-" M. When the acidity decreases t o a [H+]=lO-'B, then CH decreases to 0. The neutral midpoint of the scale is 9. Also, cH is no more dependent on temperature than pH.
366
pH = 'Il ( p K w - pKs - log [ B i ] ) cH = 16 - 11: ( p K w - pKb - log [ B f l )
eH = 16 - pKi
Virtually all of the previously mentioned acidity systems were designed to replace the conventional pH term. A "cH" term is another way of expressing the [H+] in a solution. This term is designed to supplement pH but not to replace it, and is defined as:
Since cH = log [ H t ] 16 and pH = -log [H+]
9.00
where
cH = 16 -
+ 16
=
In buffer mixtures of weak electrolytes, HA, and their salts, A-,
A Further Alternative
cH = log [H+]
pH = ' j npKw cH = 16 - '/s pKw
-
