``Thermal Conductivity'' and Chemical Kinetics

A general expression is derived for the apparent ``thermal conductivity'' of reacting gas mixtures in which a single chemical reaction proceeds at a finite rate. In contrast to cases where reaction rates are either very high or very low, it is found that the ``thermal conductivity'' depends on the geometry and scale of the system—hence the quotes. This expression applies to the three geometries that can be described one-dimensionally: parallel plates, concentric cylinders, and concentric spheres. The results are limited to systems with small temperature differences, such as thermal conductivity cells, wherein reaction rate can be assumed constant. In addition to the scale and geometry, the ``thermal conductivity'' is determined by three types of constants having the dimensions of reciprocal length. Gas phase reaction is characterized by φ, which is proportional to the square root of the chemical reaction rate at equilibrium. (This is the total rate in either direction, not the net rate, which is, of course, zero.) Heterogeneous chemical reaction at the two bounding surfaces is characterized by ψ1 and ψ2, while χ1 and χ2 account for the temperature accommodation. The nature of the ``thermal conductivity'' is discussed for several specific systems. The expression is shown to approximate a numerical calculation of the effect of chemical reaction rate on stagnation point heat transfer. Experimental thermal conductivity data for the N2O4⇄2NO2 system are adequately described in terms of this theory. An upper limit for the rate constant for the bimolecular dissociation of N2O4 is estimated to be 5.3×109 cm3 mole—1 sec—1 at 296°K.