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

Abstract

Two experimental multi-component organometallic systems were studied, namely, (1) a non-reactive system consisting of [Mo(CO)₆], [Mn₂(CO)₁₀], and [Re₂(CO)₁₀] in toluene under argon at 298.15 K and 0.1 MPa and (2) a reactive system consisting of [Rh₄(CO)₁₂] + PPh₃ → [Rh₄(CO)₁₁PPh₃] + CO in n-hexane under argon at 298.15 K and 0.1 MPa. The mole fractions of all solutes were less than 140 × 10⁻⁶ in system (1) and less than 65 × 10⁻⁶ in system (2). Simultaneous in-situ FTIR spectroscopic measurements and on-line oscillatory U-tube density measurements were performed on the multi-component solutions. A newly developed response surface methodology was applied to the data sets to determine the individual limiting partial molar volumes of all constituents present as well as the reaction volume. The limiting partial molar volumes obtained for system (1) were 176.4 ± 2.5, 265.1 ± 2.4, and 276.8 ± 2.4 cm³ mol⁻¹ for [Mo(CO)₆], [Mn₂(CO)₁₀], and [Re₂(CO)₁₀], respectively and are consistent with independent binary experiments. The limiting partial molar volumes obtained for system (2) were 310.7 ± 2.7, 219.8 ± 2.2 and 461.5 ± 4.5 cm³ mol⁻¹ for [Rh₄(CO)₁₂], PPh₃ and [Rh₄(CO)₁₁PPh₃], respectively. In addition, a reaction volume Δ_rV equal to −17.0 ± 5.7 cm³ mol⁻¹ was obtained. The present results demonstrate that both partial molar volumes and reaction volumes can be obtained directly from multi-component organometallic solutions. This development provides a new tool for physico-chemical determinations relevant to a variety of solutes and their reactions.