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 -