Ion-Pair Complexation in Moderately Strong Aqueous Acids Lowell M. Schwattz
University of Massachusetts, Boston, MA 02125 Not long ago Russo and Hanania ( I ) contributed an article to this Journal pointing out that ion association in aqueous solution is often overlooked in undergraduate instruction. Their discussion and specific examples focused on solid ionic compounds with generic formula M.L(s). When dissolved in water, they exist as associated ion-pair complexes M.L(aq) as well as separate ions, written without electric charges: M(aq) and L(aq). I extend the discussion of aqueous ion pairing to compounds for which the generic formula is HB(s or l or g), where the cation M is specifically hydrogen H and the ligand L is the conjugate base B- of HB. Thus, we are looking a t protonic acids which, of course, need not be solids before dissolving in water. Conventional understanding is that a n aqueous solution of such an acid consists of separate ions: the hydronium ion H30t(aq) and the conjugate base anion B-(aq). When the acid is sufficiently weak and the concentration of solute is sufficiently high, undissociated acid HB(aq) is present as well. Except for a solvation sphere, the structure of the dissolved species HB(aq)is assumed to be the same as that in the undissolved compound, essentially a covalent HB bond. I am aware of only one previous mention in this Journal of ion pairing that involved the hydronium ion; Giguhre (2)suggested that aqueous hydrofluoric acid exists largely as H30t.F-(aq), which he calls a proton transfer complex.
may be called either ionization or dissociation because the formation of ions and the dissociation of those ions happen simultaneously. The two terms are synonyms and are often used interchangeably. Thus, the equilibrium constant K. for eq 1is sometimes called the acid ionization constant and sometimes the acid dissociation constant. But once ion-pair complexation is brought into the picture, the two terms can no longer be interchanged. We now must imagine an intermediate stage so that the process is in two steps.
Y
HB(aq)+H20 # H30t B?aq)
Kd
'# H30t(aq)+ B7aq) (2)
There are now two equilibria. If we regard the process as occurring from left to right, the formation of ions occurs first by the transfer of a proton from HB to a nearby Hz0 molecule followed by the dissociation of the resulting ion pair into free ions. Thus, the left-hand equilibrium constant Ki is properly called an ionization constant.
The right-hand constant Kd is a dissociation constant.
Dielectric Constant
The reason that ion pairing between H30t(aq) and B-(aq) has been largely ignored is clear: As pointed out by Russo and Hanania (1)and many others, a strongly solvating solvent with high dielectric constant, such as water, effectively reduces the short-ranee .- electrostatic attractions between cations and anions Thus, in water these well-iolvatrd ions diffuse about freclv in solution. Poorlv solvatina solvents with low dielectric constants are less effective in reducing shortrange interionic attractions, so catiodanion ion pairs are better able to form. For example, Kolthoff and Bruckenstein (3) could reasonably hypothesize the existence of ion-pair complexes in solutions of several acid solutes in glacial acetic acid solvent. Some three decades ago Eigen ( 4 ) suggested that aqueous ion pairs were transient intermediates in the mechanism of aqueous acid ionization, but stable ion-pair complexes H30t.B-(aq) (abbreviated as H.B) were not contemplated until more recently. Their existence originally arose as a means of explaining substantial discrepancies in the values of acid dissociation constants measured using different experimental methods. Equilibria
In the following discussion, all equilibrium constants are to be regarded as thermodynamic; solute species are written as activities. Activities of ionic species are then expressed as activity coefficients multiplied by concentrations. Within conventional understanding (intended here to mean that ion-pair complexes do not exist or are ignored) the process K.
HB(aq)+ H20$7 H30'(aq) + B-(aq)
(1)
where r represents the product of molar ionic-activity coefficients. Within this context the overall equilibrium described by eq 1remains K,, the acidity constant. Measurement Methods
Acidity constants can be found using many different experimental techniques. Whatever method is used, the objective is to evaluate the thermodynamic acidity constant for eq 1.
The equilibrium (eq 1)and acidity constant (eq 5 ) expressions as written are in the context of conventional understanding, that is, no ion pairing. An aqueous solution is prepared by dissolving a known quantity of monoprotic acid HB in pure water. (In some cases the solution also includes a strong acid, such as HC1, but the stoichiometries of these are simple modifications of the pure water case.) In the absence of other sources of either H30t or B-, both eqs 1 and 2 dictate that [H3Ot1 = [B-I. Suppose that the analytical concentration of HB is FB.By conventional understanding, FBis distributed into [B-I and [HB]. But if we admit the possibility of both un-ionized HB and a stable ion-pair complex, the conservation equation becomes FB = [BI + [HBI + [H.BI = [H,O'I+ [HBI + [H.B] (6) We mention here those experimental methods that have yielded suff~cientyreliable results to have been cited by investigators in discussions of ion-pair complexation. Furthermore, we divide these into two categories: methods that probe the concentration of free ions, and spectroscopic Volume 72 Number 9 September 1995
823
methods assumed to probe the concentrations of ion-pair complexes as well as free ions. From a historical perspectiverthe free-ion methods tend to use instrumentation that was available earlier and so are sometimes called "classical" methods, whereas the spectrophotometric methods use more recently developed instrumentation. Free-Ion Probes versus Spectroscopic Methods pH Potentiometry and Ion-Exchange Equilibrium
Free hydronium ion concentrations or activities are measured by pH potentiometry and by ion-exchange equilibrium (5).For examole.. the DH of the solution is measured with a pH meter fitted with glass and reference electrodes bv usine ~otentiometm.De~endinem o n how the meter is"calihritld, this measurement yieks either the activitv or the concentration of HnOt. If the meter is calibrated to read activity, the concentration can he readily estimated by a nonlinear calculation involving an activity coefficient correlation such as the Debye-Hiickel. Then the aciditv constant of a solution containing- ion-pair complexesderives from eqs 5 and 6 as
.
&
where we use the notation KAfree ion) to s~ecifvthat the expression is derived for. n f&-ion probe methid. Suhstitution d the two equilibrium equations reqs 3 and 41yields K,K, K,(free ion) = -
1+y
In the conductimetric method, electric current is carried, within a solution, by charged particles, that is, free ions. In solutions of acid HB, the conductance is proportional to the concentration of H30tand B-. And with [H3Ot1 = [B-I, the conductimetric method yields the same stoichiometric information as does pH potentiometry. Thus, the acidity constant expressions written as eqs 7 and 8 applies also to conductimetry. Raman Spectrum The Raman spectrum of a n acid solution consists of many hands assignable to the individual solute species, but a particularly sharp and intense band characteristic of ionized species is used for measurement (6). By conventional understanding this band yields the concentration [BI, but if an ion-pair complex is present, the ionized hand is characteristic of both the complex and B- so that the measurement actually yields the sum [B-I + [H.Bl. An investigator unaware of the ion pair equates this sum to [H3Ot1 and calculates [HB] in the denominator of eq 5 by subtracting the sum from FB..Thus, the acidity constant calculated from Raman spectroscopy is
' H NMR Spectroscopy
In 'H NMR spectroscopy the chemical shift contributions are assumed to be the same as from hydrated protons i n H30f and hydrated protons in the ion-pair complex H3Ot.B-(7). Thus, 'H NMR measurement yields the sum [H3OC1+ [H.Bl. But an investigator having conventional understanding believes this sum to be [H3Ot1. Because 824
Journal of Chemical Education
[H30t] = [B7, this situation is exactly equivalent to that involved in Raman spectroscopy, so eq 9 applies to 'H NMR as well. Discrepancies Due to Method It is not ~ossibleto eliminate all s~eciesconcentrations from eq 9 dy substituting Ki and Kd of eqs 3 and 4, as was done in deriving eq 8 from eq 7, but a corresponding equation is
Comparison of eqs 8 and 10 reveals that &(free ion) and K,(spectr) measured in the same solution cannot be equal. Because all parameters and concentrations in these two equations are positive, &(free ion) must be less than KiKd and &(soectr) must be =eater than KKd. -. . .Therefore.,if s i c nificant ion pairing exists, an acidity constant measured from a Piven solution usine a s~ectrosco~ic method will be greater than an acidity constant measured from the same solution using a free-ion method. It also follows that an ohsewed discrepancy in this same direction can be rationalized by hypothesizing ion-pair complexation. Covington et al. (7) were apparently the first to propose that discre~anciesin aqueous acidity constants measured by different methods were attrib&ahle to ion pairing. These discrepancies did not seem to occur with truly weak acids but rather only with acids of moderate strength, defined arbitrarily as having Ka values approximately between lo-' and 10". In particular Covington et al. (7)used Raman and 'H NMR spectroscopy to measure the acidity constants of trichloro- and trifluoroacetic acids. For trichloroacetic acid, they obtained a value of about 4 i 2 which, regardless of the large uncertainty due to activity coefficient uncertainties, was a n order of magnitude greater than the most reliable classical measurement made by that time. Similarly, for trifluoroacetic acid the acidity constant of 6 f 2 was much greater than values measured by other techniques. Bonner and coworkers (8.9) later re~ortedrefined measurements of acidity constants of triclkoroacetic acid that corroborated the work of Covington et al. (71, establishing that the acidity constant measured by Raman spectroscopy (K, = 2.2 f 0.1) exceeded by an order of magnitude that measured by ion-exchange equilibrium. Bonner and coworkers (8,9) agreed with Covington et al. (7) that the large disparities were attributable to ion pairing in trichloroacetic acid. Bv contrast. Bonner and Pritchard (8) conclude that iodic acid, which is similar in strength to tricbloroacetic, does not appear to form ion pairs because the acidity constants measured both by Raman and free-ion methods agreed. However, Leuchs and Zundel(l0) report that their study of the IR spectra of aqueous HI03 solutions does reveal evidence of ion pairing. At least one investigator (11)did not accept the hypothesis that ion pairing was the cause of experimental discrepancies in the trihaloacetic acids. Gilkerson and Kendrick (11) argued rather that the discrepancies could be attributed to differences in solute concentrations and ionic activity coefficients used with the different methods.
.
-
-
- .
Photometry Another classical technique attempts to measure pH by detecting the absorption of light by a n acid-base indicator added to a solution of HB. This has been variously called the indicator (7). ontical (8).colorimetric (12). or photometric (13)method.~iypicalexperimental is as follows. An indicator is selected whose W or visible spectrum does not overlap that of tlie HB system and which changes
color with pH in a range near the pK, of HB. A series of standard solutions is prepared containing a fixed concentration of this indicator and a range of k
