Slowly Reacting Gas Mixture in a Heat Conductivity Cell

A hypothetical gas mixture composed of A2, B2, and AB which reacts bimolecularly, 2AB ⇌ A2 + B2, is placed in a thermal conductivity cell. The heat flux as well as the chemical and thermal profiles are calculated numerically for fast, slow, and intermediate reaction rates. Since the chemical composition is not in equilibrium with the local temperature, considerable calculational difficulties are encountered. An approximation scheme is given for estimating the behavior of such systems. It is found that for fast reactions, local equilibrium applies. If the rate of the chemical reactions is slow compared to the rate of diffusion (an exact criterion is given), the chemical composition within the cell becomes homogeneous throughout the cell. This composition is determined by the set of equations ∫ T CT HλRi dT=0,where λ is the coefficient of heat conductivity and ℛi is the net rate of production of molecules of the ith species. Conversely, from a knowledge of the steady-state chemical composition we may determine the chemical reaction rates. Calculations are made for a mixture of H2, I2, and HI. This system should be easy to study experimentally since the I2 concentration can be determined from optical absorption and the HI concentration can be determined from infrared absorption.