Multinuclear solid-state nuclear magnetic resonance studies (Re-185/187, Mn-55, As-75, and H-1 NMR) were undertaken on a series of polycrystalline inorganic salts incorporating diamagnetic XO4- groups, X being a half-integer quadrupolar nucleus. Exploiting data acquisition protocols that were recently developed for observing undistorted half-integer quadrupole central transitions, some of the largest quadrupole coupling constants reported to date by high field NMR were characterized (e(2)qQ/h approximate to 300 MHz). On repeating such measurements as a function of temperature, certain samples displayed reversible changes that could not be rationalized in terms of the usual temperature dependencies of the nuclear quadrupolar couplings. Instead, dynamic exchange processes between chemically or magnetically inequivalent sites had to be invoked. To quantitatively analyze these processes, the semiclassical Bloch-McConnell formalism for chemical exchange was extended to account for second-order quadrupole effects. Insight into the potential nature of the chemical dynamics was also obtained from quantum chemical calculations of the coupling parameters on model systems.