A Very Low Pressure Reactor (VLPR) is constructed for the kinetic study of atom-molecule bimolecular elementary reactions. The basic principles and the versatility of the method are described. By using the VLPR technique the forward (k1) and the reverse (k-1) rate constants for Br atom reaction with trimethylsilane are studied; Br + $(CH_3)_3$SiH k1 ${leftrightarrow}$ k-1 HBr + $(CH_3)_3$Si. From the kinetic data and the entropy estimation the bond dissociation energy for Si-H bond in trimethylsilane is calculated to be 90.1 kcal/mole $({pm}1.1$ kcal/mole). The Arrhenius parameters for k1 are found to be log A = 10.6 l/mole·sec, $E_a$ = 4.4 kcal/mole respectively. For the comparison purpose analogous reaction for carbon compound ; Br + $(CH_3)_3$CH ${ ightarrow}$ HBr + $(CH_3)_3$C was also studied. The corresponding rate constant and equilibrium constant at $25^{circ}C$ are found to be 2.67 ${ imes}$ $10^6l$/mole${cdot}$sec and 160 respectively.