This paper is the first part of a study reinvestigating the mechanism of the Belousov-Zhabotinsky (BZ) reaction of oxalic acid, which is the simplest organic substrate for a BZ oscillator. New experiments are performed to find the oscillatory region in 1 M sulfuric acid at 20 degreesC. The removal rate of the end product bromine by an inert gas stream is a critical parameter here: oscillations can be observed only in a window of that parameter. The "rate constant" for the physical removal of bromine is measured as a function of the gas flow rate and reactor volume; furthermore, the rate constants of three component reactions important in this system are also determined. These are oxygen atom transfer reactions to the oxalic acid substrate from Br(I) (hypobromous acid), from Br(III) (bromous acid), and from Br(V) (acidic bromate) compounds. In these second-order reactions, the partial order of each oxybromine species is 1. The measured rate constants are k(1) = 17 +/- 2 M-1 s(-1), k(III) = 4.2 +/- 0.5 M-1 s(-1), and k(V) = (7.47 +/- 0.1) x 10(-4) M-1 s(-1). In the case of the HOBr-oxalic acid reaction, however, an additional parallel reaction route was found that has importance at higher HOBr concentrations. In the mechanism of that new route, the active species is Br2O, and the reaction order is not 1 but 2 with respect to HOBr. The rate constant of this parallel reaction is k(I)((2)) = (1.2 +/- 0.2) x 10(5) M-2 s(-1). The k values measured here are compared with those reported earlier. A comparison of experimental results with computer simulations shows that free radicals play a negligible role or no role in the mechanism of the oxygen atom transfer reactions studied here.