letters Standard States for Water Equilibrium To the Editor:
We are gratified that Campbell and Waite [1990,67,3861 recognize that our derivation of acid and base strength constants for water and its conjugates [1987,64, 10671is both "conventionally correct" and "thermodynamically rigorous". However they defend an alternative set of widely accepted values as being "most consistent" with the definition ofK. and Khvalues for other acids and bases. Here we would take issue. We consider that K. andKhvalues for Brmsted acids and bases in aqueous solution represent one data set describing the properties of solutes in dilute aqueous solution. There are several other sets (stability constants, standard electrode potentials, standard free enerfies, etc.) of eauilibrium and thermodynam~cdata for sohies in aqueous'solutlon. For all of these the convention has been adopted that the standard staw for water will be the pure solvent and thus the thermodynamicactivity ofwater will be equal to, or closely approach, unity for diiute aqueous soluti6ns. This is the case whether the role of water is as Brmsted acid. Brclnsted base. Lewis base. oxidizine aeent.. reducine ageit, stoichiometric requirement, or solvent. Any one of these data can be used in coniunction with anv other without concern for special (unconventional) standard states for water. While K, may not correspond to the "intrinsic" acid or base strength of water it does represent the effective acidity or basicity of water as it has been used to rank all other bases and acids. The Kth values of K, for water and H30f favored by Campbell and Waite are justified as correctly representing the "intrinsic" acidity of these species. (Similar arguments would require parallel Ku, values ofKb for water and OH3. By "intrinsic"they mean that in every case the acid or base specifically identified is always referred to a 1.0 m standard state, and that its conjugate base in the same system is also referred to a 1.0 m standard state. However this means that, when these intrinsic K. and Kbvalues are for water and its conjugates,water is referred to two different standard states in the same solution. In pure water or dilute aqueous solutions a t 25 'C the activity of water is equal to, or closely approaches, 55.3 (relative to a 1.0 m standard state) or 1.0 (relative to a pure water standard state). In such a solution, for the process HzO(aq)+ HzO(l)+ H30+(aq)+ OH7aq)
--
-
water as "intrinsic acid" must, according to Campbell and Waite, be referred to a 1.0 m standard state. On the other hand the water, which reacts as base, followingthe convention used for the definition of K, values, must be referred to a pure water standard state. (l.Orn atandard state)
Ku, =
a~30+
(1.0m standard state1
aHzO
aOH-
(1.0 m standard state)
K*
=
(1.0m standard state1 (1.0rn standard state1 a~30+ x aHp (1.0 m standard S t a t e ) (PYTe water standard state1
a~,o+
aHIO
To use these equilibrium constants in any quantitative calculations,you must explicitly include the actual activity of the water with respect to the nonconventional standard state (but only that water which plays the role for which the nonconventional standard state was specified).We believe that the most consistent consequence of using these "intrinsic" acid and base strength constants would be that the maioritv of chemists would use them incorrectlv most of the time: As a demonstration of this mobabilitv. consider the recent paper by Thompson [1996,67,2201:1n this article the value of an equilibrium constant for the reaction in aqueous solution is deduced to be K = 2.39 x lo6. The conventional equilibrium constant associated with this process is
--
1 KdkWW)
The difference is that Thompson used the valueKa(H30+) = 55.3 in the derivation of the equilibrium constant. In
using this value you must remember that it is based on a 1.0 m standard state for the water that is the conjugate base of H30+.The activity quotient has the form K=
a~e~5NHj ~ xo aC+i5w2 +
aH20
~ H
Using the "intrinsic" acidity of HsOt,
Using the "conventional" acidity of H30+,
In either case,
(p"m water standard state1
aH20
If all of the water is indistinguishable, then all of the water is capable of reacting in either capacity, and K, (conventional) Kth'
in dilute aqueous solution, the intrinsic acidity constant for H30+ requires that the water that reacts as base with H30+be referred to a pure water standard state. However, the water that is the conjugate base of H30+must be referred to a 1.0 m standard state.
55.3 x 1.0
Similarly, for the process + HzO(l)+ HzO(aq)+ H80t(aq) H30+(aq)
Either value of the equilibrium constant leads to the same result if you remember to include the activity of water, relative to the appropriate standard state, where necessary. Using the conventional values this creates no problem since the activity of water is always unity. The quantitative effectis the same as simply consistently omitting the activity of water. Using the "intrinsic" values for Volume 69 Number 3
March 1992
255
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-
256
Journal of Chemical Education
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-
