Abstract
We have been evaluating third derivative quantities of the Gibbs free energy, G, by graphically differentiating the second derivatives that are accessible experimentally, and demonstrated their power in elucidating the mixing schemes in aqueous solutions. Here we determine directly one of the third derivatives of G, the partial molar entropy-volume cross fluctuation density of 2-butoxyethanol (BE) in the BE–H2O system, SV δ BE . The difference of the heats of compression were directly determined using two identical cells and applying the same pressure change to both cells concurrently. Both cells are filled with sample solutions having a small appropriate difference in mole fraction. The results indicated that this method is feasible with the prior knowledge of the thermal expansivity of the solution to within a few per cent accuracy. If the volumes of the two cells are identical within the order of 0.01%, the method provides the required results to within 0.1% without the thermal expansivity data. This success opens a possibility of evaluating the fourth derivative graphically, which is expected to provide much more detailed information about the molecular processes in aqueous solutions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Schellman, J.A.: Thermodynamics, molecules and the Gibbs conference. Biophys. Chem. 64, 7–13 (1997)
Prigogine, I., Defay, R.: Chemical Thermodynamics. Longmans, London (1954). Chap. XXIV
Koga, Y.: Mixing schemes in aqueous solutions of non-electrolytes: a thermodynamic approach. J. Phys. Chem. 100, 5172–5181 (1996)
Koga, Y.: Solution Thermodynamics and Its Application to Aqueous Solutions: A Differential Approach, pp. 89–173. Elsevier, Amsterdam (2007)
Koga, Y.: Solution Thermodynamics and Its Application to Aqueous Solutions: A Differential Approach, pp. 69–78, 117–130. Elsevier, Amsterdam (2007)
Westh, P., Kato, H., Nishikawa, K., Koga, Y.: Towards understanding the Hofmeister series (III): the effect of Na-halides on the molecular organization of H2O. J. Phys. Chem. A 111, 2072–2078 (2006)
Kropman, M.F., Bakker, H.J.: Dynamics of water molecule in aqueous solution shells. Science 291, 2118–2120 (2001)
Bakker, H.J., Kropman, M.F., Omta, A.W., Woutersen, S.: Hydrogen-bond dynamics of water in ionic solutions. Phys. Scr. 69, C14–24 (2004)
Omta, A.W., Kropman, M.F., Woutersen, S., Bakker, H.J.: Negligible effect of ions on the hydrogen-bond structure in liquid water. Science 301, 347–349 (2003)
Collins, K.D., Washabaugh, W.: The Hofmeister effect and the behavior of water at interfaces. Q. Rev. Biophys. 18, 323–422 (1985)
Koga, Y.: Fluctuations in aqueous methanol, ethanol and 1-propanol: amplitude vs. wavelength of fluctuation. Can. J. Chem. 77, 2039–2045 (1999)
Koga, Y., Tamura, K.: Fluctuations in water, aqueous tert-butanol and 2-butoxyethanol: amplitude and wavelength of fluctuation. Netsusokutei (J. Jpn. Soc. Calor. Therm. Anal.) 27, 195–204 (2000). ISSN 0386-2615. Available in a pdf file on request to the author, koga@chem.ubc.ca
Koga, Y., Westh, P., Sawamura, S., Taniguchi, Y.: Normalized fluctuations, H2O vs. n-hexane: site-correlated percolation. J. Chem. Phys. 105, 2028–2033 (1996)
Davies, J.V., Lau, F.W., Le, L.T.N., Lai, J.T.W., Koga, Y.: Thermal expansivities of aqueous solutions of 2-butoxyethanol in the water-rich region: transition of mixing scheme. Can. J. Chem. 70, 2659–2663 (1992)
Parsons, M.T., Westh, P., Davies, J.V., Trandum, Ch., To, E.C.H., Chiang, W.M., Yee, E.G.M., Koga, Y.: A thermodynamic study of 1-propanol–glycerol–H2O: effect of glycerol on molecular organization of H2O. J. Solution Chem. 30, 1007–1038 (2001)
Koga, Y.: Solution Thermodynamics and Its Application to Aqueous Solutions: A Differential Approach, pp. 267–268. Elsevier, Amsterdam (2007)
Koga, Y., Katayanagi, H., Davies, J.V., Kato, H., Nishikawa, K., Westh, P.: The effects of chloride salts of some cations on molecular organization of H2O: towards understanding the Hofmeister series (II). Bull. Chem. Soc. Jpn. 79, 1347–1354 (2006)
Westh, P., Inaba, A., Koga, Y.: Experimental determination of the third derivative of G: enthalpic interaction. J. Chem. Phys. 129, 211101 (2008)
Koga, Y.: Vapour pressures of aqueous 2-butoxyethanol at 25 °C: transition in mixing scheme. J. Phys. Chem. 95, 4119–4126 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s10953-010-9514-0
Rights and permissions
About this article
Cite this article
Koga, Y., Westh, P., Inaba, A. et al. Experimental Determination of Third Derivative of the Gibbs Free Energy, G II: Differential Pressure Perturbation Calorimetry. J Solution Chem 39, 431–440 (2010). https://doi.org/10.1007/s10953-010-9510-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10953-010-9510-4