Experimental Determination of a Third Derivative of G. (III): Differential Pressure Perturbation Calorimetry (II)

Earlier we constructed a differential pressure perturbation calorimeter, in order to determine directly a third derivative of the Gibbs energy G, the partial molar entropy-volume cross fluctuation density of solute B, ^SVd_(B)\dot]^{\mathit{SV}}\delta_{\dot{\mathrm{B}}}, in a binary aqueous solution of B. Our attempt was basically successful, as described elsewhere (J. Solution Chem. 39:431–440, 2010). However, the uncertainty of the results for ^SV δ _B was several percent. One of the purposes of our direct experimental determination was to obtain a fourth derivative quantity graphically with some confidence. For this purpose, data of the third derivative quantity are necessary with uncertainties of less than one per cent. Various difficulties that we had on the first generation apparatus were attended to, and a new apparatus was constructed. The new experimental results for aqueous 2-butoxyethanol are found to be at least several-fold better. Hence, we were able to evaluate the fourth derivative quantity for the first time. The physical meaning of the fourth derivatives may become clearer in comparative studies when such data become available for aqueous solutions of other solutes including mono-ols and poly-ols. A project is underway to that effect.