Ion Activities: An Historical and Theoretical Overview1

D. L. SPARKS2

ABSTRACTA knowledge of ion activities in soil-water systems is essential to

a proper understanding of the physicochemical behavior of soils andto the environment of plant roots in the soil. However, with thenotable exception of soil acidity, perhaps no other topic in soil chem-istry has provoked such fierce arguments as the meaning of ionicactivities as they apply to the soil solution. The purpose of this paperis to present an historical and theoretical overview of the use of ionactivities in soil chemistry. Attempting to incorporate ionic speciesinto a thermodynamic analysis of the soil solution is a convenientmathematical device, since an ionic species cannot be described inthermodynamic terms. Ionic species are strictly molecular or micro-scopic concepts. It is demonstrated in this paper that when ionicequilibria between aqueous solutions and solid phases are investi-gated, the division of the electrochemical potential into a term inelectrical potential (4>) and a term in chemical potential (M) is entirelyarbitrary. Additionally, the early 1950s arguments of Jenny,Marshall, Peech, Coleman, Overbeek, and Babcock dealing withjunction potentials, suspension effects, and mobilities of ions is re-viewed. The importance of soil solution activities in relation to nu-trient uptake and plant growth is also presented.

Additional Index Words: thermodynamics, electrochemistry,chemical potential, electrochemical potential, suspension effect.

Sparks, D.L. 1984. Ion activities: an historical and theoretical over-view. Soil Sci. Soc. Am. J. 48:514-518.

IT HAS BEEN 32 YEARS since some of the giants ofsoil chemistry initiated intense discussions on the

meaning of ionic activities as they applied to the soilsolution. Perhaps no other topic in soil chemistry, withthe notable exception of soil acidity, has provokedsuch fierce arguments.

Yet in 1983, many of the questions posed by suchillustrious soil and surface chemists as Jenny, Cole-man, Overbeek, Peech, Marshall, and Babcock remainunresolved. Yet, no one denies the fact that a knowl-edge of ion activities in soil-water systems is essentialto a proper understanding of the physicochemical be-havior of soils and ionic environment of plant rootsin the soil.

THEORETICAL ASPECTS OF IONACTIVITIES

The chemical potential of a substance can be ex-pressed as (Babcock, 1963; Sposito, 1981)

M = M° + RTlnf/f [1]where M = chemical potential, M° = chemical poten-tial in the Standard State,/= fugacity,/" = StandardState fugacity, and R and T = universal gas constantand absolute temperature, respectively. Eq. [1] applies

1 Published with the approval of the Director of the DelawareAgricultural Experiment Station as Miscellaneous Paper no. 1038.Contribution no. 153 of the Dep. of Plant Science, Univ. of Dela-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. Approved21 June 1983.2 Associate Professor of Soil Chemistry.

to any substance, in any phase, in any kind of mixtureat equilibrium. The ratio///0 in Eq. [1] can be giventhe symbol a and defined to be the relative activity,or, the thermodynamic activity of the substance:

[2]a =The activity is a dimensionless quantity that serves

as a measure of the deviation of the chemical potentialfrom its value in the Standard State. By definition theactivity of any substance in its Standard State is equalto 1. The combination of Eq. [1] and [2] produces theexpression

= M° + RTlna [3]Attempting to incorporate ionic species into a ther-

modynamic analysis of the soil solution is a conven-ient mathematical device, since an ionic species can-not be described in thermodynamic terms. Ionicspecies are strictly molecular or microscopic concepts.

Consider two teflon beakers, each of which containsan aqueous solution of 0.01 M Cu(NO3)2 along with awire made of pure copper that is immersed in thesolution. Each of the two identical copper wires, inturn, is connected to one pole of a dry cell, such thatan electrical potential difference V exists between thewires. Within either wire, the reaction (Sposito, 1981)

Cu2+ + 2e = Cu(or its reverse) takes place. This reaction can be de-scribed by the expression

at equilibrium. In this case, n(Cu) = M°(Cu) and theStandard State chemical potential of copper metal inthe wire is zero by definition (Sposito, 1 981). Thus theexpression above is reduced to

M(Cu2+) = -2i4e) [4]between the chemical potentials of Cu2+ and the elec-tron in each wire. If N denotes the wire connected tothe negative pole of the dry cell and P denotes thewire connected to the positive pole,

nN(e) - »p(e) = -FV [5]relates the electrical potential difference to the chem-ical potential difference between the electrons in thetwo identical wires (F is the Faraday constant). Thecombination of Eq. [4] and [5] gives

fiN(Cu2+) - fip(Cu2+) = 2FV. [6]Since an equilibrium exists with respect to the transferof Cu2+ between each copper wire and the solution ofCu(NO3)2 bathing it, Eq. [6] can be written in anotherform

M*[Cu2+(aq)] - /tCu2+(aq)j = 2FV [7]where N and P now refer to the aqueous solutions inwhich the copper wires labeled N and P, respectively,are immersed.

514

SPARKS: ION ACTIVITIES: AN HISTORICAL AND THEORETICAL OVERVIEW 515

Suppose now that the copper wires are removed verycarefully from the two solutions without perturbingthem. In that case, Eq. [7] still must relate the chem-ical potentials of Cu2+ in the two solutions of 0.01MCu(NO3)2. Thus, the value of M[Cu2+(aq)] will dependnot only on the chemical properties of the solution ofCu(NO3)2, which in this example are exactly the samein each beaker, but also on the electrical state of thesolution. This dependence on the electrical state doesnot exist for neutral species. Therefore, it is more pre-cise to call /i[Cu2"l"(aq)] the electrochemical potentialof Cu2+ in an aqueous solution and to denote it witha tilde, while reserving the name chemical potentialfor ju[Cu(NO3)2(aq)] and generally for /*, which refersto any neutral species (Sposito, 1981).

The possibility that the electrochemical potential ofan ionic species can differ between two chemicallyidentical aqueous solutions, by virtue of a differencein electrical potential, suggests that the formal defi-nition

M =ZF<t> + X° + RTln a [8]should be examined as to its general applicability toa species of valence Z that is subjected to an electricalpotential 0. The quantity X° is a function only of theStandard State temperature and pressure, as well as ofthe "purely chemical" nature of the substance whoseactivity is a. For a neutral species, Z =0 and Eq. [8]reduces unambiguously to Eq. [3], with X° = ju°. Inthe case of the two solutions of Cu(NO3)2 just dis-cussed,HN [Cu2+(aq)] = 2F<j>N+ X

Hp [Cu2+(aq)] = 2F<t>pRTln

°P + RTln (Cu2+)P

and/i" [Cu2+(aq)] - Jf [Cu2+(aq)J = 2JF(0"-00 [9]

which is consistent with Eq. [7]. Here again there isno ambiguity in the separation of ji into "purely elec-trical" and "purely chemical" parts. If, instead of twoO.QIM Cu(NO3)2 solutions, Eq. [8] is applied in turnto Cu2+(aq) in solutions of 0.1MCu(NO3)2 and 0.00 IMCu(NO3)2, the difference in electrochemical potentialof Cu2+(aq) is given by Eq. [10]:A" [Cu2+(aq)] - M' [Cu2+(aq)]

>"-<t>') +RTln {[Cu2+]7[Cu2+]'}

[10]where " refers to the 0. IM Cu(NO3)2 solution,' refersto the O.OOIM Cu(NO3)2 solution, and ycu refers tothe single-ion activity coefficient. The left side of Eq.[10] is well defined because it is measurable, for ex-ample, by means of a volt-meter and a pair of suitableelectrodes. The molar concentrations on the right sideof Eq. [10] also are measurable. The extent to whichthe electrical potential difference, (<£" — 0')> whichcannot be measured directly, has chemical meaningdepends entirely on whether the ratio of single-ion ac-tivity coefficients, Y'cJYcu* m Eq. [10] can be eval-uated unambiguously. If, for example, this ratio canbe calculated accurately with the Davies equation, the

electrical potential difference becomes well defined. If,on the other hand, the ratio of activity coefficientscould not be represented accurately with some modelexpression, or, if the activity ratio for Cu2+ in the twosolutions could not be measured, there would be nochemical significance to the separation of the electro-chemical potential into "purely electrical" and "purelychemical" parts as in Eq. [8]. This conclusion appliesto the problem of defining the electrical potential dif-ference between an aqueous solution in the pore spaceof a soil and a supernatant solution contacting the soil,or the so-called Donnan potential. Unless the ratio ofactivity coefficients on the right side of Eq. [10] is welldefined, the Donnan potential, 4>" — $', is withoutempirical significance.

Sposito (1981) makes the above point well througha consideration of the equilibrium between Cu2+ inan aqueous solution and in a solid phase [e.g., a solidcupric electrode, or Cu2(OH)2 CO3(s), or Cu-mont-morillonite]. Even though £ [Cu2+(s)]-/i [Cu2+(aq)]may be well defined, there is no known experimentalmeans by which the terms in <j> and X° can be distin-guished from one another unambiguously. Thereforethe definition in Eq. [8] cannot be applied usefully tothis example and only the electrochemical potentialitself may be used to describe thermodynamic equi-librium.

The important conclusion one can draw from theabove examples is that an electrical potential differ-ence between two phases of different chemical com-position cannot be defined thermodynamically. Theelectric potential is a concept that has meaning onlywhen identical phases (e.g., two pieces of copper wire)are under consideration, or when it is possible to de-termine unambiguously the ionic activity coefficientratios in two aqueous solutions that contain the samecomponents. In all other situations and, in particular,when ionic equilibria between aqueous solutions andsolid phases are investigated, the division of the elec-trochemical potential into a term in 0 and a term inX° is entirely arbitrary.

DISCUSSIONS ON THE SUSPENSIONEFFECT

The observation that when a mixture of soil andwater is stirred and the solid particles are allowed tosettle that a higher pH is usually measured with theelectrodes placed in the supernatant solution thanwhen they are placed in the sedimented soil particles(Fig. 1) or the "suspension effect" was first noted byWiegner (1931). Earlier, Bradfield (1924) first dem-onstrated potentiometrically the "suspension effect"with electrodialyzed clays which constituted evidencefor the dissociation of H+ ions in colloidal clay sus-pensions. The suspension effect itself was not ques-tioned by anyone but its causes and implications havebeen given widely different interpretations.

In 1950, Jenny et al. touched off a controversy con-cerning the cause of the suspension effect and the re-sultant potential that was argued heatedly for four yearsby a number of eminent soil and surface chemists.Jenny et al. (1950) ascribed the potential difference toa "liquid junction potential," Ej. One would assumethat the use of KC1 in the salt bridge would eliminate

516 SOIL SCI. SOC. AM. J., VOL. 48, 1984

GLASS ELECTRODE

CALOMEL HALFCELL (SALTBRIDGE)

a) pH = 6.0

SUPERNATANT

SEDIMENT

b) pH = 5.0Fig. 1—Illustration of the suspension effect in colloidal systems.any junction potentials because the mobility of K+

and Cl~ ions in aqueous solution is very similar andtheory would predict a Ej would not arise. However,in cation exchange systems, Jenny et al. (1950) hy-pothesized that the mobility of K+ ions may be quitedifferent from that of Cl~ ions, giving rise to a Ej atthe KC1 bridge.

Marshall (1950, 1964) believed that exchangeableH+ ions of clay ionized to a degree and the glass elec-trode responded to the ionized H+. He felt the pHshould decrease as the concentration of soil or clay inthe suspension rises, because the concentration of ion-ized H+ goes up as well. Marshall believed that for asystem consisting of sedimented clay and a superna-tant solution or a clay suspension separated from anequilibrium dialysate by a membrane, that there wasan electrical potential difference across the boundarywhich he called a Donnan potential. Marshall arguedthat the junction potential of an irreversible referenceelectrode would be the same in the soil suspension,soil solution, and in standard solutions. Therefore, anydifference in ionic activity between the suspension andsolution phases must be due to a difference in theelectrical potentials between the two phases.

Marshall (1964) felt the good agreement betweenionic activities calculated from potentiometric mea-surements, conductance measurements, and the rateof sugar inversions in clay suspensions supported theextrathermodynamic assumption of a constant Ej.However, one must view these conclusions with a cer-tain degree of suspicion. The increase of sugar inver-sion in clay suspensions as compared to the equilib-rium solution may have been due to the catalyticactivity of the clay surface rather than to increasedionic activity. The calculation of ionic activity datafrom Donnan equilibrium data or from mean salt ac-tivity measurements involves unverifiable extrather-modynamic assumptions which do not resolve the is-sue. Other investigators also concurred with Marshallthat the salt-bridge-clay junction potential should benegligibly small and considered the measured poten-tial was a Donnan membrane potential (Peech andScott, 1951; Low, 1954).

Jenny et al. (1950) had earlier hypothesized that themobility of K+ ions may be quite different from thatof Cl~ ions when one dealt with cation exchange sys-tems. This difference in ion mobility would give riseto a junction potential at the KC1 bridge. However,Marshall disagreed. He felt that when the KC1 of a saltbridge is so concentrated that it carries the greatestproportion of current across a boundary in a colloidalsystem, £,• must be small. Jenny et al. (1950) and Cole-man et al. (1950) attempted to counter this argumentby saying that K+ and Cl~ ions carried 95 to 100% ofthe current but the amount of current carried by K+,i.e., its transference number, was much greater thanthat carried by Cl~. Peech and McDevit (1950), how-ever, argued that ascribing the sole variation of theobserved transference numbers, viz., the decrease inthe transference number of Cl~ based on the assump-tion that the relative mobilities of K+ and Cl~ ionswere changed significantly in the presence of nega-tively charged colloids, was erroneous. Peech andMcDevit (1950) felt that Coleman et al. (1950) hadignored the fact that as the number of cations relativeto anions was increased due to dissociation of cationsfrom the clay, the proportion of total current carriedby cations must be increased. Also, they reasoned thatthe transfer number of ions in a solution containinga mixture of electrolytes tells nothing about the rela-tive mobility of ions.

In the wake of these intense arguments, Overbeek(1953) developed an equation relating the Donnan po-tential to the reduced mobility of counter ions. Therewas good agreement between Donnan potentials andthose calculated using Overbeek's equation. This wasalso later confirmed by Bower (1961).

Babcock and Overstreet (1953) and Overbeek (1953)used calomel half cells to measure Donnan potentials.They showed that even where transference numbersat the KC1 bridge were assumed to be equal, a calomelhalf cell does not measure a membrane potential in aDonnan system. If an emf was obtained for such acell, the authors reasoned this would indicate that thetransference numbers were not equal at all bridgejunctions.

Overbeek (1953) preferred to call the Donnan mem-brane potential a Donnan emf which was the sum ofall interface potentials including the Donnan poten-tial. He recognized well, along with Coleman andJakobi (1954), that for any electromotive cell, all thatcan be measured is the total potential. There is no apriori way in which the total potential can be dividedand the various potentials assigned to particular re-gions in the cell (Babcock et al., 1951). Thus, Over-beek concurred with Jenny and Coleman that most ifnot all of the Donnan potential was due to a liquidjunction potential resulting from the reduced mobilityof counter ions in the colloidal phase.

Nothing more was done to resolve the suspensioneffect issue until the elegant work of Olsen and Rob-bins (1971). Through osmotic pressure and freezingpoint depression measurements, they concluded thatthe suspension effect was attributable to a junctionpotential at the interface between the suspension andthe supernatant solution which corroborated work ofJenny and his co-workers. They found that the freez-

SPARKS: ION ACTIVITIES: AN HISTORICAL AND THEORETICAL OVERVIEW 517

ing points of the slurry and supernatant solution wereidentical, providing evidence that the activity of ionsin the two media were identical.

What can one conclude from all of these differentviewpoints about the cause of the suspension effect?Perhaps Gast (1977) answered the preceding questionbest when he wrote: "At present there does not appearto be any rigorous way of resolving which of theseinterpretations is correct and the true significance ofthe Donnan potential remains in question. The con-sequence of this uncertainty is more than academicfor it enters into all measurements using a reversiblesingle ion electrode in conjunction with a referenceelectrode employing a salt bridge such as the calomelelectrode."

ION ACTIVITIES AND PLANT GROWTHOne of the main reasons for the initial interest in

measuring ion activities was to determine the validityof the "contact exchange theory" proposed by Jennyand co-workers (Jenny and Overstreet, 1939). Accord-ing to this theory, a plant root in the close proximityof a clay particle actually penetrates a zone (ion swarm)in which the activity of a cation may be 10 to 100times higher than the activity of a cation in the bulksoil solution. Most research workers agree that the ac-tivity of an ion is a better measurement of intensity(/) than is concentration. However, this is limited tosolutions only, and may stop when one is dealing withsuspensions.

There is a difference of opinion as to the drivingforce for ion uptake when roots are immersed in soilor clay suspensions. Is it a gradient in the chemicalpotential of the ion as given by Eq. [3] or is it a gra-dient in the electrochemical potential as denned byEq. [8]? Proponents of Eq. [3] found that uptake of anutrient was often higher when roots were submergedin a clay or resin suspension than when they wereplaced in a solution that was at equilibrium with thesuspension (Khasawneh, 1971). This was ascribed tothe greater cation activity in suspensions than in theirequilibrium dialysate. Proponents of uptake based onEq. [8] reported contradictory experimental evidenceshowing uptake by roots was equal from suspensionand from equilibrium dialysates (Khasawneh, 1971).

Olsen and Peech (1960) compared the rate of uptakeof Rb+ and Ca2+ by excised roots of barley and mungbeans from a suspension of clay or cation-exchangeresin with that from the corresponding equilibriumdialysate. The authors found that the rate of uptakeof Rb+ or Ca2+ by roots was exactly the same fromboth suspensions and equilibrium dialysates. The sig-nificance of this was that the composition of the soilsolution or of the equilibrium dialysate should com-pletely characterize the ion environment of plant rootsin soil-water systems, at any selected time.

Many attempts have been made to relate plantgrowth to ion activity in the soil solution. The earliestattempts dealt with soil pH and soil acidity in the1920s and early 1930s (Adams, 1974; Khasawneh,1971).

Adams and co-workers (Adams, 1974) were amongthe first to successfully relate the ionic activity of thesoil solution to plant uptake. Adams and Lund (1966)

1.0

0.8 -

fe 0.6o

0.4 -

0.2

NORFOLK SUBSOIL SOLUTIONDICKSON SUBSOIL SOLUTIONBLADEN SUBSOIL SOLUTION

0.0 1.0 2.0 3.0MOLAR ACTIVITY OF ALXIO"'

4.0

Fig. 2—Effect of molar Al activity on relative cotton root growth innutrient and soil solutions in situ. Figure taken from Adams andLund (1966).

measured the growth rate of cotton primary roots inculture solutions containing Al and in acid soils ofvarying Al contents. If culture solution Al and soilsolution Al concentrations were corrected to molaractivities, no difference in root growth rate in the twomedia at equal solution Al activities was observed (Fig.2). They found the "critical" value of solution Al forcotton roots was an A13+ activity of about 1p,M. Thedata points for all growth media fell on the same line.This critical value for soil Al was later verified byAdams et al. (1967) and by Richburg and Adams(1970).

Brenes and Pearson (1973) demonstrated that A13+

activity was a good index of Al toxicity for corn (Zeamays L.) and sorghum (Sorghum vulgare L.). Helyar(1978) also called attention to the use of Al activityas an index of Al toxicity for lucern (Medicago salivaL) and subterranean clover (Trifolium subterraneumL.). Pavan and Bingham (1982) conducted a solutionculture experiment with coffee seedlings (Coffee ara-bica L.). At a constant Al concentration, seedlinggrowth was reduced with dilution of the nutrient so-lution. This decrease in growth best correlated with

NUTRIENT SOLUTION

NORFOLK SUBSOIL SOLUTION

DICKSON SUBSOIL SOLUTION

0.0 0.2 0.4 0.6 0.8RATIO OF Co: TOTAL- CATION IN SOLUTION

1.0

Fig. 3—Effect of Ca: total-cation in solution on cotton root growthin nutrient solutions and soil solutions in situ. Figure taken fromHoward and Adams (1965).

518 SOIL SCI. SOC. AM. J., VOL. 48, 1984

an increase in the activity of A13+. An A13+ activityvalue of 1.2 X 10~5 was associated with a 10% re-duction of coffee seedling growth. This compared fa-vorably with values quoted by Adams and Lund (1966)and by Brenes and Pearson (1973).

Howard and Adams (1965), using soil solution data,found that Ca deficiency could also be found in non-acid soils. They showed that the critical Ca level forcotton (Gossypium hirsutum L.) root growth was thesame in culture solutions as in soil solutions in situ(Fig. 3). Subsequently, Adams (1966) and Bennett andAdams (1970a) found that Ca-deficient levels even inlimed soils were defined by this same quantitative re-lationship. However, the Ca-plant interrelation neces-sitated that soil solution cations be expressed as ionicactivities rather than ionic concentrations. The criticalCa level in soil solution was defined as:

flCa/S tfcationi =* 0-15

where a^ = molar activity of Ca2+, and 2 a ̂ ,ion; =sum of cationic activities. Thus, for each growth me-dium, there was a critical level of Ca activity belowwhich root elongation was reduced. However, thesecritical levels were different for different media.Changing the method of expressing the intensity of Cafrom concentrations to activities could not account forthe differences in the critical levels of Ca.

In studies with NH3, Bennett and Adams (1970),with soil solution and culture solution data, definedthe "critical" toxic concentrations of solution NH3 forcotton roots and sudangrass (Sorghum bicolor L.)seedlings. They further showed that the "critical" NH3concentration in soil solution was identical to the valuein culture solutions. However, a quantitative evalua-tion of the "critical" toxic concentration of 0.2 mMNH4OH, which applied to all systems, required thatthe electrolytic composition of the solutions be ex-pressed as ionic activities and not as ionic concentra-tions.

The soil solution experiments of Adams and co-workers were the first to show that some ionic effectson root growth were the same in culture solutions asin soil solutions in situ. The experiments further dem-onstrated the advantage of expressing soil solution andculture solution compositions as ionic activities ratherthan as measured concentrations. As Khasawneh(1971) stated: "There seems to be general agreementthat plant growth is related to nutrient ion activity inthe soil solution, but in many cases each soil has adifferent set of parameters that define this relation-ship. Data and conclusions cannot always be extrap-olated from one soil to another merely on the basis ofsolution ion activities-other parameters may beneeded."

ACKNOWLEDGMENTSThe author deeply appreciates the comments and sugges-

tions of Professor Hans Jenny, Univ. of California, Berkeley,and Professor R.A. Olsen, Montana State Univ. This paperis dedicated with immense admiration to Professor Jenny.