Laser flash photolysis of the hydrogen abstraction reaction of triplet benzophenone (3BP) from 2-propanol and 1,4-cyclohexadiene in supercritical ethane and fluoroform was investigate. Bimolecular rate constants based on bulk concentrations decrease with an increase in pressure along both isotherms studied. These results corroborate our previous studies in CO2 that show increased reaction rates due to enhanced local compositions of cosolvent around the 3BP solute. Analysis of the results includes prediction of the thermodynamic pressure effect on the rate constant, which suggests an increase in the rate constant with pressure, as well as the effects of increased local cosolvent concentrations about 3BP. Spectroscopic measurements of the local composition of 2-propanol about a solute in supercritical CO2 are used to explain the apparent discrepancy between experiment and prediction, providing reasonable evidence that the local environment can influence kinetically controlled reactions in supercritical fluids.