J. Phys. Chem. B 2000, 104, 4723-4725
Thermodynamics of Ion Pairing in Lead Nitrate Solutions As Determined with Spectroscopy
4723 207Pb
NMR
Natalie Altounian, Alicia Glatfelter, Shi Bai, and Cecil Dybowski Department of Chemistry and Biochemistry, UniVersity of Delaware, Newark, Delaware 19716 ReceiVed: January 10, 2000; In Final Form: March 21, 2000
The temperature and concentration variations in 207Pb NMR shifts of Pb(NO3)2 in aqueous solutions are analyzed in terms of exchange between aquated lead ion and the Pb(NO3)+ ion complex according to the reaction PbNO3+(aq) ) Pb2+(aq) + NO3-(aq). The analysis gives an enthalpy of dissociation of -3.0 ( 0.2 kcal mol-1 and an entropy of dissociation of -11.9 ( 0.4 cal K-1 mol-1.
Introduction
Experimental Section
Lead exhibits a complex chemistry evident in its solution behavior.1 Over the centuries, the utility of materials arising from this diverse chemistry has led to the ubiquitous use of lead in many forms and its consequent dispersal in the environment. Unfortunately, many lead-containing materials are toxic, carcinogenic, or teratogenic. Concerns about safety have mitigated its use in certain applications. Still, important technological applications such as batteries and considerations of the chemistry attending proper removal and disposal of lead make the chemistry of lead-containing materials a topic of some ongoing practical interest. In this report, we focus on a particular process, namely, ion pairing in aqueous solutions of Pb(NO3)2 to form the complex Pb(NO3)+. Early conductometric measurements of solutions containing lead and nitrate2 suggested that ion pairs were formed, with an apparent equilibrium constant for dissociation of the complex Kdiss′ (298 K) ) 0.065 at an ionic strength of 0.200 m. The temperature dependence indicated a value for ∆Hdiss of 0.57 kcal mol-1 and for ∆Sdiss of -3.5 cal K-1 mol-1. Hershenson et al.,3 using polarography and spectrophotometric techniques, reported Kdiss′ to be in the range from 0.3 to 0.6. They, too, attributed the unusual electrochemical and spectrophotometric behaviors to an equilibrium between ions and ion pairs.4 Such associative behavior is not limited to lead and nitrate ions. It has been postulated to explain electrochemical anomalies for solutions of lead ions with other anions as well, particularly the hydroxyl ion.5 Careful analysis of NMR spectra of a nucleus exchanging among different environments yields information about the exchange process.6,7 For processes involving ion solvation, one can investigate the NMR spectroscopy of the solvent, such as water,4 but NMR investigation of the ion also provides direct evidence of exchange. 207Pb NMR studies of aqueous salt solutions8 at room temperature show a significant variation in the NMR chemical shift with concentration. In this study, we report temperature- and concentration-dependent 207Pb NMR shifts of Pb(NO3)2 solutions, from which we have determined equilibrium constants as a function of temperature and the enthalpy and entropy of dissociation of the ion complex in aqueous solution.
Pb(NO3)2 was purchased from Strem Chemicals and used without further purification. Solutions of Pb(NO3)2 were prepared by dilution with deionized water to concentrations of 0.050 m, 0.100 m, 0.150 m, 0.200 m, and 0.250m. 207Pb NMR spectra were obtained at 83.7 MHz with a Bruker DRX 400 spectrometer at temperatures between 295 and 350 K. As an external reference to calibrate the chemical shift scale, we used a 1.100 m solution of Pb(NO3)2 contained in a sealed capillary, the reported shift of which is -2965.7 ppm relative to tetramethyllead at 295 K.9 Measurements were performed with a 5-mm broadband inverse-detection probe. The 90° pulse width was 26.5 µs, and the relaxation delay was 1 s. Typically, signal averaging of 128 scans gave spectra with acceptable signal-tonoise ratios for all samples down to 0.050 m. Samples of different concentrations had different volumes, so intensities were not used to infer concentrations. All shifts are accurate to (0.1 ppm. Temperature was measured to a precision of (1 K. Discussion The NMR spectrum of lead in Pb(NO3)2 solution at all temperatures we investigated consists of a single sharp resonance. The shift is strongly concentration-dependent (Figure 1), as has been previously reported.8 The shifts determined here are somewhat more shielded than those in ref 8, although we define the same reference point and points near this reference are in close agreement. This most likely results from a subtlety of the definition of chemical shift that we have previously discussed.9 This effect, which is negligible for nuclei like 1H and 13C under standard operating conditions, can, depending on the precise spectrometer frequency, lead to discrepancies of tens of ppm in the apparent chemical shift for nuclei like 207Pb. At all temperatures, the shift is concentration-dependent (Figure 2). Generally, the resonance becomes more shielded as the concentration of lead nitrate is increased. As temperature increases at constant concentration, the shift also becomes more shielded. To analyze the NMR data of a lead nucleus undergoing rapid exchange between two forms in solution through the dissociation reaction
Pb(NO3)+ (aq) T Pb2+ (aq) + NO3- (aq)
10.1021/jp000130u CCC: $19.00 © 2000 American Chemical Society Published on Web 04/25/2000
(1)
4724 J. Phys. Chem. B, Vol. 104, No. 19, 2000
Altounian et al.
Figure 3. ln K′ versus square root of m at various temeperatures: 295K ((), 310K (b), 330K (2), and 350K (9).
Figure 1. 207Pb NMR spectra of aqueous Pb(NO3)2 solutions as a function of concentration at 295 K: (from bottom to top) 0.05 m, 0.10 m, 0.15 m, 0.20 m, and 0.25 m. The resonance on the right-hand side of the spectrum is that of a reference solution (described in the text) used as a standard.
Figure 4. ln K versus 1/T for aqueous Pb(NO3)2 solutions.
TABLE 1: Thermodynamic Properties of the Dissociation of Pb(NO3)+ in Aqueous Solutions
Figure 2. Variation of the 207Pb NMR shift as a function of concentration at 295K ((), 310K (b), 330K (2), and 350K (9).
one must extract the equilibrium partitioning of lead from the variation of the exchange-averaged shift with concentration and temperature. The exchange-averaged shift is determined by the shifts, δA and δB, and lifetimes, τA and τB, of the independent species according to the equation6
δ)
(
) (
)
τA τB δ + δ ) RδA + (1 - R)δB τ A + τB A τ A + τB B
(2)
where R is the fractional time spent in form A in an equilibrium solution. To determine R, one must know, independently, the chemical shifts of the two species. For many exchanging systems, chemical shifts of the independent species, δA and δB, are typically found by observing the system under conditions of slow exchange, where each species is independently observed. For Pb(NO3)2 solutions, we have not been able to observe the individual species, so we determined the independent shifts at exchange-averaged limits, as was done by Harrison et al.8 We used -2860 ppm as the chemical shift of Pb2+(aq), a value near that reported by Harrison et al. from studies of a number of lead salt solutions. High NO3- concentrations shift the equilibrium in favor of the formation of the Pb(NO3)+ ion. Harrison et al.8 report the shift of this species to be -3028 ppm, very close to our value of -3030 ppm, derived from observation of solutions 0.050 m in Pb(NO3)2 containing various amounts of KNO3 up to 1.200 m. In the analysis that follows, we assume that the chemical shifts of the two species are temperatureindependent, with the observed dependence on temperature and
T (K)
K
∆G° (kcal mol-1)
∆S° (cal K-1 mol-1)
295 310 330 350
0.200 ((0.008) 0.147 ((0.006) 0.106 ((0.005) 0.081 ((0.004)
0.94 ((0.05) 1.18 ((0.06) 1.47 ((0.08) 1.75 ((0.09)
-11.7 ((0.2) -11.9 ((0.2) -12.0 ((0.2) -12.1 ((0.2)
concentration resulting from changes in partitioning between the two species. With a knowledge of these limiting shift values, eq 2 can be used to determine the equilibrium dissociation fraction, R, of PbNO3+ ions in a solution of concentration m. The apparent dissociation equilibrium constant, K′, is given by the equation
K′ )
R(1 + R)m (1-R)
(3)
Apparent equilibrium constants calculated from the NMR data are of similar magnitude to the reported equilibrium constant determined polarographically and spectrophotometrically for Pb(NO3)2 solutions at room temperature.3 Extrapolation of ln K′(m) versus the square root of m (Figure 3) to m ) 0 gives the equilibrium constant, K(T), at each temperature, as shown in Table 1. From the equilibrium constant at each temperature, ∆G°(T) is determined (Table 1). A van’t Hoff plot of ln K versus 1/T (Figure 4) gives ∆H° ) -3.0 ( 0.2 kcal mol-1. Assuming a temperature-independent enthalpy of dissociation, one calculates the entropy of dissociation, ∆S°, at each temperature, as shown in Table 1. The average value of ∆S° is -11.9 ( 0.4 cal K-1 mol-1, showing that this is not a strongly temperaturedependent quantity. A comparison of the NMR-derived thermodynamic quantities with those reported in the literature shows interesting features. The NMR-derived enthalpy of dissociation is different from the value (0.57 kcal mol-1) determined by conductometric measurements at an ionic strength of 0.200 m. We have observed that the apparent enthalpy of dissociation (not shown) determined
Ion Pairing in Lead Nitrate Solutions
J. Phys. Chem. B, Vol. 104, No. 19, 2000 4725
TABLE 2: Enthalpy and Entropy of Dissociation of Lead Complexes in Aqueous Solutions process PbCl+ f Pb2+ + ClPbBr+ f Pb2+ + BrPb(Ac)2 f Pb(Ac)+ + AcPb(NO3)+ f Pb2+ + NO3Pb(NO3)+ f Pb2+ + NO3-
∆H° ∆S° (kcal mol-1) (cal K-1 mol-1) reference -4.38 -2.88 -3.39 +0.57 -3.0 ( 0.2
-22.0 -16.4 -19.8 -3.5 -11.9 ( 0.4
2 2 8 2 this work
from the variation of ln K′(m) with temperature depends on concentration. In particular, its magnitude becomes smaller for higher concentrations. Thus, the present result is not inconsistent with the observed conductometric measurement of the enthalpy at finite ionic strength. The NMR-derived enthalpy of dissociation for the nitrate complex is similar to the dissociation enthalpies of PbCl+ and PbBr+ (Table 2), but these values were also determined conductometrically at a finite ionic strength.2 The NMR-derived entropy change, ∆S°, of -11.9 cal K-1 mol-1, is also somewhat smaller than the entropy changes reported for the PbCl+ and PbBr+ complexes, but it is much larger than the conductometrically determined value of -3.5 cal K-1 mol-1 reported for the nitrate complex.2 The present results for lead nitrate solutions are also similar to reported thermodynamic constants for the dissociation of a lead acetate complex in solution (Table 2).8 Thus, the NMR-derived thermodynamic parameters that characterize dissociation of the lead nitrate complex suggest that its dissociation behavior in solution is similar to that of the other three complexes of lead.
These NMR results provide an interesting insight into the ion-pairing process in aqueous solution. At finite concentrations, there is a sizable fraction of lead in solution that exists as the complex. As temperature increases, Pb(NO3)+ becomes more stable than the separately hydrated Pb2+ and NO3- ions in solution. This observation suggests that the effect of increasing the temperature is to weaken the bonding of water in the hydration sphere of the aquated ions, allowing the two to approach each other more easily through their mutual Coulombic attraction to form the ion complex. Acknowledgment. The support of the Petroleum Research Fund of the American Chemical Society under Grant 33633AC5 is gratefully acknowledged. References and Notes (1) Murrell, J.; Boucher, E. A. Properties of Liquids and Solutions; John Wiley and Sons: New York, 1982. (2) Nancollas, G. H. J. Chem. Soc. 1955, 1458. (3) Hershenson, H. M.; Smith, M. E.; Hume, D. N. J. Am. Chem. Soc. 1953, 75, 507. (4) Burgess, J. Ions in Solution; John Wiley and Sons: New York, 1988. (5) Sylva, R. N.; Brown, P. L. Trans. Faraday Soc. 1980, 1577-1581. (6) Kaplan, J. L; Fraenkel, G. NMR of Chemically Exchanging Systems; Academic Press: New York, 1980. (7) Maciel, G. E.; Simeral, L.; Ackerman, J. J. H. J. Phys. Chem. 1977, 81, 263-267. (8) Harrison, P. G.; Healy, M. A.; Steel, A. T. J. Chem. Soc., Dalton Trans. 1983, 1845-1848. (9) Neue, G.; Dybowski, C.; Smith, M. L.; Hepp, M. A.; Perry, D. L. Solid State Nucl. Magn. Reson. 1996, 6, 241-250.
