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A general method presented in Angew. Chemie Int. Ed. (DOI 10.1002/ange.201207403) for finding an approximate relationship between the molecular weights of small molecules (< 1000 g/mol) containing light atoms (sulfur or lighter) and their diffusion coefficients D, has recently been extended and presented in Anal. Chem (DOI: 10.1021/acs.analchem.7b05032) to apply to a wide range of common solvents and a range of temperatures. The method requires only the molecular weight of the solute, the name of the solvent and the temperature to yield an estimate of D (or the value of D to estimate the molecular weight) with an rms error of about 15%.
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References:
"Improving the Interpretation of Small Molecule Diffusion Coefficients"
"Quantitative Interpretation of Diffusion-Ordered NMR Spectra: Can We Rationalize Small Molecule Diffusion Coefficients?"