The development of a response surface model for the determination of infinite dilution partial molar volumes and excess volumes from dilute multi-component data alone. Implications for the characterization of non-isolatable solutes in complex homogeneous reactive systems

The direct determination of partial molar volumes and reaction volumes in ultra-dilute non-reactive and reactive multi-component systems using a combined spectroscopic and modified response surface model approach

“…For the multi-component [Mo(CO) 6 ]-[Mn 2 (CO) 10 ]-[Re 2 (CO) 10 ]toluene semi-batch experiments, a recently developed experimental design 11 was used to obtain an optimal distribution of data points throughout the multi-component composition space.…”

“…[23][24] The determination of the partial molar volumes of the species present in the ultra-dilute multi-component solutions was achieved using a simplified form of a newly developed response surface approach to total molar volumetric data. 11 The reaction volume was calculated directly i.e. from the differences between limiting partial molar volumes of the products and reactants.…”

“…Given a set of appropriate experimental values for V m , the coefficients a i , a ij , and c ij can be solved, and finally, the infinite dilution partial molar volumes and volumes of interaction can be determined. 11 For the case of ultra dilute multi-component solutions of weakly or negligibly interacting solutes, changes to eqn (6) should be made. First, the bilinear and higher interaction terms can probably be neglected (eqn (7) and ( 8)).…”

“…10 Recently, a new and very general approach to the determination of partial molar volumes from multi-component solutions alone (without recourse to binary experiments) was developed and applied to a non-reactive highly-associating system. 11 This new approach relies on the application of a response surface model to the total molar volume of solution. Good experimental design ensured that the composition space was adequately covered and that optimal parameter estimation for the individual partial molar volumes could be achieved.…”

“…[Rh 4 (CO) 12 ] + PPh 3 → [Rh 4 (CO) 11 PPh 3 ] + CO (1) The concentration regimes were ultra-dilute. The mole fractions of all solutes were less than 140 × 10 −6 in system (1) and less than 65 × 10 −6 in system (2).…”