Potter and Baron studied the reaction

CO + Cl₂ converts in COCl₂ at 1 atmosphere, using an activated carbon catalyst. Preliminary studies showed that the rate of reaction did not depend on the mass velocity of gases through the reactor.

Analysis of the rate data indicated that the reaction occurred by adsorption of Cl₂ and CO on the catalyst and surface reaction between the adsorbed complexes. It appears that the surface reaction, rather than the adsorption or desorption steps was controlling the overall reaction rate. Furthermore, preliminary adsorption measurements indicated that chlorine and phosgene were readily adsorbed on the catalyst, while CO was not. Hence, the adsorption equilibrium constants of carbon monoxide, although it was not zero, was considered negligible with respect to those for Cl₂ and COCl₂.

a) On the basis of this information, develop an expression for the intrinsic rate of reaction in terms of the bulk partial pressure in the gas phase. The reaction is irreversible.

b) Determine the best values for the adsorption equilibrium constant for Cl₂ and COCl₂ and the product from the following experimental data, where the temperature was 30.6C, the catalyst size was 6 to 8 mesh, and = Total concentration of active sites, moles/gram of catalyst, ks = specific reaction rate constant for surface reaction and K_CO = adsorption equilibrium constant for CO.

0.00414	0.406	0.352	0.226
0.00440	0.396	0.363	0.231
0.00241	0.31	0.320	0.356
0.00245	0.287	0.333	0.376
0.00157	0.253	0.218	0.522
0.00390	0.61	0.113	0.231
0.00200	0.179	0.608	0.206

Assume that the 6 to 8 mesh catalyst particles are small enough that the pore surface was fully effective.