Tracer diffusion of carbon tetrachloride, S‐trioxane, 12‐crown‐4, 15‐crown‐5, 18‐crown‐6 in acetonitrile, benzene, and chlorobenzene

Abstract

Tracer diffusivities measured with the Taylor dispersion technique are reported for carbon tetrachloride, s-trioxane, 12-crown-4, 15-crown-5, and 18-crown-6 in acetonitrile, benzene, and chlorobenzene across ranges of temperature. It is demonstrated that Stokes' law corrected with a microfriction factor successfully accounts for the diffusion behavior of even disk-shaped crown ethers. Solute and solvent molecules being effectively spherical in the context of Stokes' law, the tracer diffusion of crown ethers is found to be satisfactorily represented by a roughhard-sphere model for molecular diffusion. The degree of success increases with decreasing solvent polarity. The diffusion data for carbon tetrachloride are also used to extend the basis of the recently developed reduced equation for the tracer diffusion of nonelectrolytes in liquids over wide temperature ranges. EDUARDO YUMET, and SHAW-HORNG CHEN HANG-CHANG CHEN, Department of Chemical EngineeringUniversity of Rochester Rochester, NY 14627In liquid membrane separation and solid-liquid-phase transfer catalysis employing crown ethers, the rate of involved transport processes is determined by the diffusivities of crown ethers. One of the objectives of this paper is to measure the tracer diffusivities of a series of crown ethers in practically important solvents including acetonitrile, benzene, and chlorobenzene as a function of temperature. The other objective is to investigate the diffusion behavior of disk-shaped molecules in terms of Stokes' law. To provide a basis for studying size and shape effects, quasispherical carbon tetrachloride is also included as one of the solutes. A rough-hard-sphere theory is then tested once it is established that crown ethers behave effectively as spheres. The applicability of the recently proposed generalized equation for nonelectrolyte diffusion in liquids is extended with the new data reported here. CONCLUSIONS AND SIGNIFICANCEThe tracer diffusivities of carbon tetrachloride, s-trioxane, 12Crown-4,15-crown-5, and 18-crown-6 in acetonitrile, benzene, and chlorobenzene can be quantitatively predicted from Stokes' law with a correction factor for microfriction. The failure of Stokes' law, often quoted, can be attributed solely to the neglect of size discrepancies between solute and solvent molecules. Even the disk-like crown ethers appear to be spherical due to rapid molecular rotation. This is further supported by the success of a rough-hard-sphere theory in describing the tracer diffusion of crown ethers. The theory is capable of predicting the observed diffusivities to within 6,7 and 12% (absolute average deviations) in benzene, chlorobenzene, and acetonitrile; the less polar the solvent molecule, the more successful the RHS theory. The basis for applying Eq. 11 for predictive purposes has also been extended with additional binary interaction parameters for the new solute-solvent systems studied here.

Modification of the Stokes–Einstein Equation with a Semiempirical Microfriction Factor for Correlation of Tracer Diffusivities in Organic Solvents

“…The general trend in the empirical N S values is largely accountable with crown size, that is, the number of oxygen atoms as hydrogen-bonding acceptors, relative to the solvent’s van der Waals radius except the incremental N S values from 18-crown-6 to dicyclohexano-18-crown-6 in all three solvents, the reason for which is unclear at this time. In the absence of hydrogen bonding, the f t values of crown ethers in cyclohexane at 298 K and in benzene, acetonitrile, and chlorobenzene at 301 K follow the prediction by f t,C–C –1 = 1 + 0.695( r 1 / r 2 ) −2.234 with an average error of ±9%, typical of nonassociated solute–solvent systems included in Figure .…”

External vs. Internal Interactions in the Enantiodiscrimination of Fluorinated α‐Amino Acid Derivatives by Heptakis[2,3‐di‐O‐acetyl‐6‐O‐(tert‐butyldimethylsilyl)]‐β‐cyclodextrin, a Powerful Chiral Solvating Agent for NMR Spectroscopy

“…From the Stokes-Einstein equation [Equation (1)] the diffusion coefficient can be correlated to friction factor f, where k is the Boltzmann constant and T the absolute temperature. (1) The friction factor of spherical molecules can be correlated to molecular size by means of the hydrodynamic radius R H [Equation (2)], where η is solution viscosity and c represents a numerical factor that for medium-to largesized molecules is approximately 6, whereas for molecules with sizes comparable to those of the solvent it can be estimated from a semiempirical improvement [31][32][33] of the equation derived from the theory proposed by Wirtz and coworkers. [34,35] (2)…”