33. Read the paper: Gold Is Smaller than Silver. Crystal Structures of [Bis(trimesitylphosphine)gold(I)] and [Bis(trimesitylphosphine)silver(I)] Tetrafluoroborate by A. Bayler, A. Schier, G. A. Bowmaker, and H. Schmidbaur (J. Am. Chem. Soc., 1996, 118, 7006-7007). Explain how the authors determined the radii of Ag(I) and Au(I), why they had to go to some effort to accomplish this, and why they believe gold is smaller than silver. How do the radii proposed by the authors for Ag(I) and Au(I) compare to literature values?
The authors prepared analogous complexes of Ag+ and Au+ using the bulky trimesitylphosphine ligand, crystallized the complexes, and then determined the crystal structures. Using the M-P distance and the established radius for P gave them the radius for the metal. Using this method, they find Ag+ to be larger than Au+ in a two-coordinate, covalent environment, i.e., the authors did not report ionic radii. The bulky ligand is essential to prevent any nearest neighbor interactions between the metals that may alter the measured radius. A comparison of the covalent radii of Ag0 (1.53 Å) and Au0 (1.43 Å) shows the same pattern of gold being smaller than silver. In contrast, the ionic radius for Ag+ (6-coordinate, 1.29 Å) is much smaller than the ionic radius for Au+ (6-coordinate, 1.51 Å). Thus, the conclusion that gold is smaller than silver depends upon the bonding environment.