TY - JOUR

T1 - Experimental Determination of Third Derivative of the Gibbs Free Energy, G II

T2 - Differential Pressure Perturbation Calorimetry

AU - Koga, Yoshikata

AU - Westh, Peter

AU - Inaba, Akira

AU - Sou, Kalyan

AU - Tozaki, Ken-ichi

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - 3rd derivative of G

KW - Differential pressure perturbation calorimetry

KW - Thermal expansivity

KW - Aqueous 2-butoxyethanol

U2 - 10.1007/s10953-010-9510-4

DO - 10.1007/s10953-010-9510-4

M3 - Journal article

VL - 39

SP - 431

EP - 440

JO - Journal of Solution Chemistry

JF - Journal of Solution Chemistry

SN - 0095-9782

IS - 3

ER -