letters The Acid Equilibrium Constant Is Unity! To the Editoc
The recent paper by Ralph J. Thompson [I99467, 2201 leads us once more to tilt at windmills, and to assert that the acid eauilibrium constant. K.. for the hvdronium ion hasa valudequal to unity. This is the case whether you use the "concentration" or the "thermodynamic" approach ta .. defme the equilibrium constant. For the hydrogen ion exchange process H30+(aq)+ HzO(l)+ H20(1)+ H30t(aq) the reaction quotient
is identical to unity at equilibrium, whatever numerical value might be assigned to [HzOl. The "water term" cannot be omitted from one part of the expression for Q and not from the other; to do so would imply a different mle for water in the "forward" and the Peverse" reactions. The attempt to assign a non-unity value to this equilibrium constant is a consequence of misunderstanding the way in which the (nearly) constant concentration or activity of the solvent in a dilute solution (or of a pure solid or liquid in a heterogeneous system) is treated when formulating the conventional equilibrium constant expression. In the particular case of an (monoprotic)acid at low cancentration reacting with the solvent water, HA(aq)+ HzO(l)+ H30+(aq)+ A-(aq) if the reaction quotient has a constant value for all equilibrium states (whatever that constant value may be),
Combining these expressions lcads to the result given by Thompson for the general acidbase reaction,
This general expression includes all cases of (monopmtic) acid-base reaction in dilute aqueous solution, pmvided that you recognize that K.(H30+) = 1.0, Kb(OH-) = 1.0, K,(HzO) = K, and Kb(H20) = K, . Thus, for the trivial cases of the reactions oE Weak acid with solvent water as base, HA(aq)+H20(l)+ H30t(aq)+ A-(aq)
Weak base with solvent water as acid, B(aq)+ HzO(l)+ BW(aq)+ O K (aq) K= Kb(B) Kw = Kb(B) K,
and if the term &O] has a constant value (whatever that value may be), then the remaining quotient must also have a constant value.
Both the constancy of this residual quotient, K,, and its numerical value are independent of any particular number that might be assigned to the "water term" in the concentration quotient for K' since K'is never actually evaluated. The numerical value of the term involving water (whether a unit activity, or a concentration of 55.5 M, or a mole fraction of 1.0) is irrelevant-only its essential constancy is significant to the argument. Thus whether you use the "thermodynamic" or the "concentration" approach you come to the same conclusion-that terms involving solvent water may be omitted from the equilibrium constant expression for a reaction in dilute aqueous solution. However, to develop a quantitatively consistent set of equilibrium constants for reactions in dilute aqueous solution, the term involving water must be omitted in all cases. This is implicitly acknowledged by Thompson in his selection of equations to derive the equilibrium constant expression for the reaction of any (monoprotic) acid with any (monoprotic) base. Using the generally accepted Brgnsted model for these pmcesses: 514
Journal of Chemical Education
Strong acid (i.e., H@+) with strong base (i.e., OH-),
For the reaction of a strong acid ( H30+)with a weak base: H30Yaq)+ B(aq) + BH+(aq)+ HzO(l) 1.0 x Kb(B)- 1 K= K, K.(BH? That is, the equilibrium constant for this reaction is correctly shown to be the reciprocal of the acid equilibrium constant for the conjugate acid of the base. (The equilibrium constant proposed by Thompson for the reaction of a strong acid with aniline is not the reciprocal of the acid equilibrium constant for the auilinium ion). We agree with Thompson that the equilibrium constant for the reaction of any acid with any base, and the extent of their reaction with each other, should be included in any discussion of acid-base equilibria. However, using the values suggested by Starkey, et al. [1986, 64, 4731 for K.(H30+) and Kb(OH-)leads to inwrrect values of the equilibrium constants for the reactions of H30+and OH- with weak bases and weak acids, respectively. In addition, the expression proposed by Thompson to describe the extent of
