water and its conjugates means that you must remember to include the activity of water and correctly decide to which standard state water must be referred for each of its several possible roles. If you want to evaluate the competition between water and some other acid for an added base, then the effective acidity of each acid is the product of its "intrinsic" acidity and its activity in solution. For water K ~ ~ ~ ~ ~ , (=H1 ,. O 8 10-I= )~ x 55.3 = L O X 10-l4 That is, for purposes of predicting the competition between water and another acid for an added base, the effective acidity of the water is correctly described by K,. Similarly, a base added to aqueous solutions containing H30t is in competition with water for protons from H30t. The water (which is the conjugate base of H30+)is present at an activity of 55.3 (if you are going to use the intrinsic acidity of H30+).Consequentlythe effective acidity of H30+ is reduced to
The "intrinsic" acidity of the H30+ion also presents pedagogic problems. It is difficult to explain to students that a process that involves no net change can have an equilibrium constant other than unity and thus a finite standard free energy change. Moreover the 55.3 value of the equilibrium constant appears to have little to do with the acidity of H30' but rather to be an artifact of two different standard states for water. We believe that the high probability of confusion and error inherent in using two different standard states for water far outweighs any advantage of "correctly" representing the intrinsic acidity and basicity of water. We would be less inclined to argue if it were proposed to refer water to a 1.0 m standard state at all times. Doing so would reduce all acidity and basicity constants by a factor of 55.3 and the "intrinsic" acidity constant for water would be equivalent to KJ(55.3)'. Thus the intrinsic activity of water would be seen to he less than that of alcohols (although the effective acidity of water in dilute aqueous solutions would be greater as a result of its high activity). However, the acidity constant for H30+would be unity on this scale (as it should be for an exchange process). W. George Baldwin C. Eugene Burchill
University of Manitoba Winnipeg, ME,Canada R3T 2V1 To the Editor: Baldwin and Burchill have misinterpreted the primary point of our previous article. We do not advocate the universal adontion of the K. values for water and the hvdronium ion derived in our paper. As correctly stated by Baldwin and Rurchill. these values use an unconventional standard state fo; water that results in equilibrium constants inconsistent with equilibrium constants derived using the conventional standard state. We agree that the use of two different standard states for water remesent an undesirable standard with concomitant confuskn and increased likelihood of error in usina these constants. While we do not advocate the adoption of the equilibrium constants derived in our article, we still feel these K's give a better indication of the "intrinsic" acidity of water and the hydronium ion than the conventionally derived values. The primary point of our paper, as stated in the title, is that for comparison with other acids, the unconventionally derived K. values give a better indication of the fundamental acidity of water and the hydronium ion, and for pur-
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poses of comparison only, it is these K, values that should be used to compare to equilibrium constants for other acids to determine relative acid strengths. Mark L. Campbell Boyd A. Waite
United States Naval Academy Annapolis, MD 21402
The Use of Equilibrium Notation in Listings of Standard Potentials
To the Editor: In a recent letter by Obline (1990,67, 184) an objection was raised against the use of equilibrium notation (with the double arrow: 5 as distinct from the single one: +) in tables of standard electrode potentials. I do not share this obiection: in my opinion, the real difficulty is due to the convention thai half-reactions must he written as reductions if the kfiven potential is to be called a (standard]electrode potential. his rule is confusing for two reasons. In the f r s t place it should not matter in which direction a chemical equilibrium equation is written. According to thermodynamics, once the system is in equilibrium neither reduction nor oxidation take place anymore. In a kinetic sense oxidation and reduction are proceeding in opposite directions in equal proportions and at an equal rate. The conclusion is the same:
are equivalent notations for the same equilibrium state. In the second place the definition of the electrode potential does not refer at all to reduction or oxidation processes. The electrode potential of a certain electrode is defmed as the cell potential of a symbolic electrochemical cell with the electrode in question placed on the right-hand side and a standard hydrogen electrode on the left-hand side. The cell potential is by definition the electric potential of the right electrode minus the electric potential of the left electrode, provided the measurement is performed in such a way that no electric current is gemmted through th.e cell. This last condition ensures that the whole cell is in eledrochemical equilibrium. Strictly speaking with a cell in this state it is not possible to refer to cathode (where reduction must occur) and anode (where oxidation must occur): The cathode~anodetermmology has to be reserved for galvanic cells (produonr!electric enerw) and electrolvtic cells (consuming electric energy), where the electriccurrent has a nonzero value by definition. For example consider the following cell: Pt, Hz (1atm)l H' (a= 1.0 M)I I c$+,~ 0HzO~I Cu(s) ~I Pt . The relevant half-reactions are on the left side: 2H' (aq)+ 24
5 H (g)
and on the right side:
cu2+(aq)+ 2% 5 Cu(4 The electrochemical cell reaction is 2H+(aq)+ Cu(s) + 2el f Hz(g)+ CU" (aq)+ 29., In these equilibrium equations care has been taken to ensure that the electrons in their different states are ex-
plicitly accounted for and differentiated with subscripts 1 (left)and r (right). It should be made clear to students that 1 and r refer & the electrodes of the symbolic cell, and not to the way the electrons are placed with respect to the $ symbol in the equilibrium equation, as one is used to in a thermodynamics context. One might write all or some of these three equilibrium equations the other way round. This would have no effect on the definition of the electrode potential of the Cu2+/Cuelectrode system. Leaving out the electrons or cancelling them, one would be left with the chemical equilibrium:
This equation is certainly not descriptive of the situation in the cell defined above. but would eventually become so after the cell has been shorkircuited so that ill electrons in the metal phase end up in the same thermod.mamic state and can be cancelled from the equation once zero-current conditions have been reestablished. The electrochemical and the thermodynamic IeWright conventions operate on completely different situations and should not be permitted to confuse students. A great deal of confusion is avoided if for cells in zero-current operation no reference is made to processes (reduction, oxidation) and derived concepts (cathode, anode). However, the references are there inthe literature and one would like to have a sensible argument to explain terms like reduction potential, etc. One might argue along the following lines. The IUPAC convention forces us to build a cell with the standard hydrogen electrode on the lcft. The convention also demands that with thiii cell in finite-current operation the external current must run from right to left. Therefore. in the circuit, electrons must be produced by oxidation on the IeRhand electrode (therefore called anode) and consumed hy reduction on the nght-hand electrode (therefore called cathode!. It is clear. however. that earlv introduction of the term "reduction" i i n o t likel; to be heipful to a good understandine of the electrode potential as an eauilibrium
countered redox titrations, and it seems that dedicated al-
would have to be written for these cases. -eorithms Finally, to assure "no approximations" for these redox titrations, any computational algorithm would have to take into account the changing ionic strength of the titration medium.
Donald C. Jackman Pfeiffer College Misenheimer, NC 28109 To the Editor:
In reply to Jackman's letter, I would like to make the following points.
1.Jackrnan is correct in his statement concerningdichromate titrations. In fact, our model only applies to redox systems such as
if a = b; this was pointed out at the beginning of our paper, when we set a = b = 1. We are still unable to propose a general solution for a + b. 2. Our model, contrary to Jackman's statement, can be applied to redox systems that are pH-dependent. In fact. even though we mentioned this i n t h e paper, perhaps we did not give this point the necessary emphasis. Let us consider, as a n example, the titration of Fez+with M n 0 4 in acid solution. The redox systems are
-
Maarten C.A. Donkersloot Eindhoven University of Technology 5612 AZ Eindhoven The Netherlands
EO1*and E,z* need to have their values determined under the same conditions (i.e., temperature, ionic strength, auxiliary reagents, indicating, reference and auxiliary electrodes, . . .) in which the titration is supposed to be performed, but a t several pH values. A plot ofE. measured versus pH will give E,* as the intercept on the Y axis. Then, if one wants to represent the system as
for a given pH value, one will have Algorithm for Plotting Titration Curves To the Editor:
Implicit in his claim of not introducinp any approximations-in treating redox titration curves.de MO;;~ [ISSO, 67, 2261 suggests that any redox titration sy3trm may be treatpd with hls aleorithm. Indeed. his aleorithm for dotting redox titratio; curves seems to be good for syst'ems that are not dependent on pH or product concentration, but is not applicable to those situations that the student mav more likely encounter than de Moura's chosen example. Students "are much more likely to encounter the iron(1IYpermanganate and the iron(II)/dichromate titrations in their actual laboratory experiences. In the former case, the equivalence point potential is dependent not only upon the formal redox potekials of the reactants but also pH (the actual term is 4 . 0 8 pH). In the latter case, the equivalence point potential is dependent upon the formal redox potentials of the reactants, the pH, and the concentration of the chromium(II1)ion produced (the actual term is -0.118 pH - 0.017 log LC$+]). The calculational algorithm of de Moura does not treat these more commonly en-
For the system Fe3+me2+ E, = E,*
For the system Mn04-/Mn2+,at 25 'C
where x is the pH of the solution. The values ofEO1and Eo2 are the ones to be used in our model. 3. During a given titration the temperature, the ionic strength, and the pH of the solution are supposedly kept constant. 4. In the titration taken as an example in our paper both systems are pH dependent. For both of then, one has at 25 'C: E, = ED*- 0.118 p H V Consequently, the reaction will apparently become pHindependent, since the two terms (-0.118 pH) will cancel out. However, I must admit, that in order to obtain the data for Figure 1of the paper, the pH was made equal to 0, and Volume 69 Number 3 March 1992
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