Kinetic investigations on the oxidation of pyrazine and four 2-substituted pyrazines viz., 2-methylpyrazine, 2-ethylpyrazine, 2-methoxypyrazine and 2-aminopyrazine by bromamine-B (BAB) to the respective N-oxides have been studied in HCl$O_4$ medium at 303 K. The reactions show identical kinetics being first-order each in $[BAB]_o\;and\;[pyrazine]_o$, and a fractional- order dependence on $[H^+]$. Effect of ionic strength of the medium and addition of benzenesulfonamide or halide ions showed no significant effect on the reaction rate. The dielectric effect is positive. The solvent isotope effect was studied using $D_2$O. The reaction has been studied at different temperatures and activation parameters for the composite reaction have been evaluated from the Arrhenius plots. The reaction showed 1:1 stoichiometry and the oxidation products of pyrazines were characterized as their respective N-oxides. Under comparable experimental conditions, the oxidation rate of pyrazines increased in the order: 2-aminopyrazine > 2-methoxypyrazine > 2-ethylpyrazine > 2-methylpyrazine > pyrazine. The rates correlate with the Hammett $\sigma$ relationship and the reaction constant $\rho$ was found to be -0.8, indicating that electron donating centres enhance the rate of reaction. An isokinetic temperature of $\beta$ = 333 K, indicated that the reaction was enthalpy controlled. A mechanism consistent with the experimental results has been proposed in which the rate determining step is the formation of an intermediate complex between the substrate and the diprotonated species of the oxidant. The related rate law in consistent with observed results has been deduced.