Eur. J. Inorg. Chem. 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, 2005 ISSN 14341948 SUPPORTING INFORMATION Title: The Hidden Equilibrium in Aqueous Sodium Carbonate Solutions Evidence for the Formation of the Dicarbonate Anion Author(s): Klaus-Peter Zeller,* Paul Schuler, Peter Haiss Ref. No.: I040445
ph dependence of the 18 O-isotope effect on the 13 C-chemical shift The 18 O-isotope effect on the carbonate 13 C-chemical shift has been measured as δ = 0.018 ppm for a 0.44 M solution of 18 O-labeled carbonate in D 2 O. In the presence of one equivalent NaOD a smaller value of δ = 0.016 ppm has been obtained. Because of the hydrolysis equilibrium between 2 carbonate CO 3 and bicarbonate HCO3 /DCO3, which is rapid on the NMR time scale, the measured chemical shifts δ( 13 C) and 18 O-isotope effects δ( 13 C) are time averaged values according to the molar fractions of the two anions. In the presence of one equivalent NaOD the concentration of DCO 3 is suppressed, therefore δ( 13 2 C) = 0.016 ppm should be closer to the true value for CO 3. By way of structural analogy the δ( 13 C) for the bicarbonate ion should be comparable to the values found for formate ( δ = 0.025 ppm) [1b] and acetate ( δ = 0.027 ppm). [1c] Therefore, a slightly higher isotope effect may be expected for bicarbonate in comparison to carbonate. Indeed, under conditions where a noticeable amount of DCO 3 contributes a higher isotope effect of δ = 0.018 ppm is observed. The 13 2 C-chemical shifts of CO 3 and HCO3 anions measured in 0.5 M solutions of the potassium salts in D 2 O are reported as 168.3 and 160.4 ppm. [2] 2 The true value of CO 3 without the contribution of HCO 3 should be higher. We obtained for a 0.42 M Na2 CO 3 solution in 0.5 Na/D 2 O a value of 169.07 ppm (referenced to internal dioxane, 67.19 ppm). Schematic diagrams showing the relative amounts of 13 C 16 O 18 2 3n O n isotopomers in dependence of time The distribution for time zero is calculated from the initial weights of Na 13 2 CO 3 and Na 2 C 18 O 16 3n O n. The end point (after infinite time) corresponds to the statistical distribution of the oxygen atoms from the carbonate isotopomers and the solvent D 2 O. The diagrams between zero and infinite time are obtained from the peak heights in 26 13 C NMR measurements executed over 154 days. The solution was kept at 20 ± 0.5 C.
13 CO 3 13 C 18 O 3 0 (calculated from the initial weights of 13C- and 18O-labeled sodium carbonate) 8 h 2 d 7d 9 d 14 d 17 d 20 d 23 d 27 d 34 d 41 d 44 d 48 d 56 d 58 d 66 d 67 d 76 d 84 d
90 d 104 d 118 d 125 d 134 d 141 d 154 d 201 d* ) 315 d* ) end point (calculated for statistical distribition) * ) After submission of the manuscript occasional 13 C NMR measurements confirmed that the exchange process continues to approach the calculated end point ( 13 C 16 O 2 3 / 13 C 16 O 18 2 O 2 / 13 C 16 O 18 O 2 2 = 94.1:5.8:0.1) asymptotically. After 315 d a composition of 93.7% 13 C 16 O 2 3 and 6.3% 13 C 16 O 18 2 O 2 was determined.
Estimation of the rate constant for the addition of carbonate to carbon dioxide CO 3 k + CO CO3 2 C 2 O 5 An approximate linear relation (1) between log k and the pk a of the conjugated acid has been found for the addition of bases to ester carbonyl groups. [3] (1) log k = a pka + b Provided that similar relation holds for the addition of bases to CO 2, the rate constant log k 2 CO 3 can be roughly estimated by comparison with the known kinetics of the addition of and H2 O to CO 2. From equation (1) it follows: k - (2) log = a pk H O pk + k 2 H3O k - (3) log = a pk H 2O pk k HCO - 3 CO3 Combining (2) and (3) gives: pkh 2O pk + H3O (4) log k = log k log k log k 2 pk CO H 3 2O pk HCO 3 After rearranging equation (4) equation (5) is obtained: pkh O pk pk HCO H O pk 2 3 2 HCO3 (5) log k 2 = log k log k + log k CO 3 pk pk pk pk + H3O + H3O
With logk = 3.93, [4] log k H2 O = 3.18 (calculated from the pseudo first order rate constant k' = kh 2 O [ ] = 3.64 10 2 sec 1 ), [4] H 2 O = 15.73, pk = 10.33, and pk + = 1.74 we obtain: pk HCO 3 H 3 O k 2 55 mol 1 L sec 1 CO 3 This rough estimate is in acceptable agreement with the experimental rate constant of 114 ± 11 mol 1 L sec 1 given for the 18 O-exchange between CO 2 and CO 3 2. [5] [1] [1a] J. M. Risley, R. L. Van Etten, J. Am. Chem. Soc. 1979, 101, 252253. [1b] J. M. Risley, R. L. Van Etten, J. Am. Chem. Soc. 1980, 102, 46094614. [1c] J. M. Risley, R. L. Van Etten, J. Am. Chem. Soc. 1980, 102, 66996702. [1d] J. M. Risley, S. A. DeFrees, R. L. Van Etten, Org. Magn. Res. 1983, 21, 2835. [1e] T. L. Mega, R. L. Van Etten, J. Am. Chem. Soc. 1993, 115, 1205612059. [2] D. Stueber, D. Patterson, C. L. Mayne, A. M. Orendt, D. M. Grant, R. W. Parry, Inorg. Chem. 2001, 40, 19021911. [3] R. W. Alder, R. Baker, J. M. Brown, Mechanism in Organic Chemistry, Wiley-Interscience, London, New York, Sidney, Toronto, 1975, p. 312. [4] Gmelin, Handbuch der Anorganischen Chemie, 8. Auflage, Kohlenstoff, Teil C3, 1973, pp. 117137. [5] C. K. Tu, D. N. Silverman, J. Phys. Chem. 1975, 79, 16471651.