Ion Activities: An Historical and Theoretical Overview1 D. L. SPARKS2 ABSTRACT to any substance, in any phase, in any kind of mixture 0 A knowledge of ion activities in soil-water systems is essential to at equilibrium. The ratio/// in Eq. [1] can be given a proper understanding of the physicochemical behavior of soils and the symbol a and defined to be the relative activity, to the environment of plant roots in the soil. However, with the or, the thermodynamic activity of the substance: notable exception of soil acidity, perhaps no other topic in soil chem- a = [2] istry has provoked such fierce arguments as the meaning of ionic activities as they apply to the soil solution. The purpose of this paper The activity is a dimensionless quantity that serves is to present an historical and theoretical overview of the use of ion as a measure of the deviation of the chemical potential activities in soil chemistry. Attempting to incorporate ionic species from its value in the Standard State. By definition the into a thermodynamic analysis of the soil solution is a convenient activity of any substance in its Standard State is equal mathematical device, since an ionic species cannot be described in to 1. The combination of Eq. [1] and [2] produces the thermodynamic terms. Ionic species are strictly molecular or micro- expression scopic concepts. It is demonstrated in this paper that when ionic equilibria between aqueous solutions and solid phases are investi- = M° + RTlna [3] gated, the division of the electrochemical potential into a term in electrical potential (4>) and a term in chemical potential (M) is entirely Attempting to incorporate ionic species into a ther- arbitrary. Additionally, the early 1950s arguments of Jenny, modynamic analysis of the soil solution is a conven- Marshall, Peech, Coleman, Overbeek, and Babcock dealing with ient mathematical device, since an ionic species can- junction potentials, suspension effects, and mobilities of ions is re- not be described in thermodynamic terms. Ionic viewed. The importance of soil solution activities in relation to nu- species are strictly molecular or microscopic concepts. trient uptake and plant growth is also presented. Consider two teflon beakers, each of which contains Additional Index Words: thermodynamics, electrochemistry, an aqueous solution of 0.01 M Cu(NO3)2 along with a chemical potential, electrochemical potential, suspension effect. wire made of pure copper that is immersed in the solution. Each of the two identical copper wires, in Sparks, D.L. 1984. Ion activities: an historical and theoretical over- turn, is connected to one pole of a dry cell, such that view. Soil Sci. Soc. Am. J. 48:514-518. an electrical potential difference V exists between the wires. Within either wire, the reaction (Sposito, 1981) Cu2+ + 2e = Cu T HAS BEEN 32 YEARS since some of the giants of soil chemistry initiated intense discussions on the (or its reverse) takes place. This reaction can be de- Imeaning of ionic activities as they applied to the soil scribed by the expression solution. Perhaps no other topic in soil chemistry, with the notable exception of soil acidity, has provoked at equilibrium. In this case, n(Cu) = M°(Cu) and the such fierce arguments. Standard State chemical potential of copper metal in Yet in 1983, many of the questions posed by such the wire is zero by definition (Sposito, 1 981). Thus the illustrious soil and surface chemists as Jenny, Cole- expression above is reduced to man, Overbeek, Peech, Marshall, and Babcock remain 2 unresolved. Yet, no one denies the fact that a knowl- M(Cu +) = -2i4e) [4] edge of ion activities in soil-water systems is essential 2+ to a proper understanding of the physicochemical be- between the chemical potentials of Cu and the elec- havior of soils and ionic environment of plant roots tron in each wire. If N denotes the wire connected to in the soil. the negative pole of the dry cell and P denotes the wire connected to the positive pole, THEORETICAL ASPECTS OF ION N p ACTIVITIES n (e) - »(e) = -FV [5] The chemical potential of a substance can be ex- relates the electrical potential difference to the chem- pressed as (Babcock, 1963; Sposito, 1981) ical potential difference between the electrons in the two identical wires (F is the Faraday constant). The M = M° + RTlnf/f [1] combination of Eq. [4] and [5] gives = where M = chemical potential, M° chemical poten- fiN(Cu2+) - fip(Cu2+) = 2FV. [6] tial in the Standard State,/= fugacity,/" = Standard State fugacity, and R and T = universal gas constant Since an equilibrium exists with respect to the transfer and absolute temperature, respectively. Eq. [1] applies of Cu2+ between each copper wire and the solution of Cu(NO3)2 bathing it, Eq. [6] can be written in another 1 Published with the approval of the Director of the Delaware Agricultural Experiment Station as Miscellaneous Paper no. 1038. form Contribution no. 153 of the Dep. of Plant Science, Univ. of Dela- M*[Cu2+(aq)] - /tCu2+(aq)j = 2FV [7] ware, Newark, DE 19711. Presented at the Div. S-2 Symposium "Chemistry in the Soil Environment: Activities," Soil Sci. Soc. Am., 29 Nov. 1982, in Anaheim, CA. Received 6 Apr. 1983. Approved where N and P now refer to the aqueous solutions in 21 June 1983. which the copper wires labeled N and P, respectively, 2 Associate Professor of Soil Chemistry. are immersed. 514 SPARKS: ION ACTIVITIES: AN HISTORICAL AND THEORETICAL OVERVIEW 515 Suppose now that the copper wires are removed very electrical potential difference becomes well defined. If, carefully from the two solutions without perturbing on the other hand, the ratio of activity coefficients them. In that case, Eq. [7] still must relate the chem- could not be represented accurately with some model ical potentials of Cu2+ in the two solutions of 0.01M expression, or, if the activity ratio for Cu2+ in the two 2+ Cu(NO3)2. Thus, the value of M[Cu (aq)] will depend solutions could not be measured, there would be no not only on the chemical properties of the solution of chemical significance to the separation of the electro- Cu(NO3)2, which in this example are exactly the same chemical potential into "purely electrical" and "purely in each beaker, but also on the electrical state of the chemical" parts as in Eq. [8]. This conclusion applies solution. This dependence on the electrical state does to the problem of defining the electrical potential dif- not exist for neutral species. Therefore, it is more pre- ference between an aqueous solution in the pore space cise to call /i[Cu2"l"(aq)] the electrochemical potential of a soil and a supernatant solution contacting the soil, of Cu2+ in an aqueous solution and to denote it with or the so-called Donnan potential. Unless the ratio of a tilde, while reserving the name chemical potential activity coefficients on the right side of Eq. [10] is well for ju[Cu(NO3)2(aq)] and generally for /*, which refers defined, the Donnan potential, 4>" — $', is without to any neutral species (Sposito, 1981). empirical significance. The possibility that the electrochemical potential of Sposito (1981) makes the above point well through an ionic species can differ between two chemically a consideration of the equilibrium between Cu2+ in identical aqueous solutions, by virtue of a difference an aqueous solution and in a solid phase [e.g., a solid in electrical potential, suggests that the formal defi- cupric electrode, or Cu2(OH)2 CO3(s), or Cu-mont- nition morillonite]. Even though £ [Cu2+(s)]-/i [Cu2+(aq)] may be well defined, there is no known experimental M =ZF<t> + X° + RTln a [8] means by which the terms in <j> and X° can be distin- should be examined as to its general applicability to guished from one another unambiguously. Therefore a species of valence Z that is subjected to an electrical the definition in Eq. [8] cannot be applied usefully to potential 0. The quantity X° i s a function only of the this example and only the electrochemical potential Standard State temperature and pressure, as well as of itself may be used to describe thermodynamic equi- the "purely chemical" nature of the substance whose librium. activity is a. For a neutral species, Z =0 and Eq. [8] The important conclusion one can draw from the reduces unambiguously to Eq. [3], with X° = ju°. In above examples is that an electrical potential differ- the case of the two solutions of Cu(NO3)2 just dis- ence between two phases of different chemical com- cussed, position cannot be defined thermodynamically. The N 2+ N electric potential is a concept that has meaning only H [Cu (aq)] = 2F<j> + X RTln when identical phases (e.g., two pieces of copper wire) p 2 p 2+ H [Cu +(aq)] = 2F<t> °P + RTln (Cu )P are under consideration, or when it is possible to de- termine unambiguously the ionic activity coefficient ratios in two aqueous solutions that contain the same and components. In all other situations and, in particular, /i" [Cu2+(aq)] - Jf [Cu2+(aq)J = 2F(0"-00 [9] when ionic equilibria between aqueous solutions and J solid phases are investigated, the division of the elec- which is consistent with Eq. [7]. Here again there is trochemical potential into a term in 0 and a term in no ambiguity in the separation of ji into "purely elec- X° is entirely arbitrary. trical" and "purely chemical" parts. If, instead of two O.QIM Cu(NO ) solutions, Eq. [8] is applied in turn DISCUSSIONS ON THE SUSPENSION 2+ 3 2 to Cu (aq) in solutions of 0.1MCu(NO3)2 and 0.00 IM EFFECT Cu(NO ) , the difference in electrochemical potential 2+3 2 The observation that when a mixture of soil and of Cu (aq) is given by Eq.