Two series of sulfated silica-zirconia mixed oxides have been prepared and the densities of both Bronsted and Lewis acid sites calculated. Catalytic activity data were obtained for two Bronsted acid catalyzed reactions, the alkylation of toluene by styrene in the liquid phase and but-1-ene double bond isomerization in the gas phase, but no correlation could be obtained between activity and the number of Bronsted acid sites available. Using ab initio calculations for the sulfate structures and the determination of molar absorption coefficients for adsorbed pyridine which was used as a probe for both types of acid site, an understanding of the evolution of acid site densities as a function of sulfate loading has been established. Using this information, it is proposed that the active site for these reactions, which both involve a step involving protonation of the C=C group, must involve an adjacent Bronsted and Lewis acid site pair where the latter acts to initially adsorb the vinyl group prior to protonation.