Experimental determination of the third derivative of G. I. enthalpic interaction.

The solute (i)-solute interaction in terms of enthalpy, H(i-i) (E)=N( partial differential(2)H(E)/ partial differentialn(i) (2))=(1-x(i))( partial differential(2)H(E)/ partial differentialn(i) partial differentialx(i)), the third derivative of G, was experimentally determined using a Thermal Activity Monitor isothermal titration calorimeter for aqueous solutions of 2-butoxyethanol (BE) and 1-propanol (1P). This was done using both calorimetric reference and sample vessels actively. We simultaneously titrate small and exactly equal amounts of solute i (=BE or 1P) into both cells which contain the binary mixtures at an average mole fraction, x(i), which differs by a small amount Deltax(i). The appropriate amount of titrant deltan(i) was chosen so that the quotient (deltaH(E)/deltan(i)) can be approximated as ( partial differentialH(E)/ partial differentialn(i)), and so that the scatter of the results is reasonable. deltaH(E) is the thermal response from an individual cell on titration, and we measure directly the difference in the thermal response between the two cells, Delta(deltaH(E)). The resulting quotient, Delta(deltaH(E))/deltan(i)/Deltax(i), can be approximated as ( partial differential(2)H(E)/ partial differentialn(i) partial differentialx(i)) and hence provides a direct experimental avenue for the enthalpy interaction function. We varied the value of Deltax(i) to seek its appropriate size. Since H(E) contains the first derivative of G with respect to T, the result is the third derivative quantity. Thus we present here a third derivative quantity directly determined experimentally for the first time.