Cake :: Help & Info :: About the Cake simulator module

The CO oxidation reaction basically doesn't happen at room temperature, or without a catalyst, but at temperatures of 600 K - 700 K or above, and with Pt or a similar element, such as Ru or Rh, as a catalyst, the reaction likes to go to completion on the CO₂ side. The reason for this is the reaction mechanism. The uncatalyzed reaction mechanism requires either O₂ to spontaneously break apart, producing free oxygen that could then react with CO, or for there to be a three molecule effective collision between 2 COs and an O₂. Both of these things only happen at extremely high temperatures, since double covalent bonds are extremely difficult to break. However, in the catalyzed reaction mechanism, the O₂ can break apart much more easily by adsorbing (momentarily attaching) to the Pt surface: since Pt has a low electronegativity it attracts the individual oxygens more than they attract each other. After the O adsorbs, and some CO does as well, the O and CO react to form CO₂, which very quickly desorbs from the surface (reenters the air). This can happen because CO bonds oxygen more strongly than Pt. That is also why elements that are much less electronegative are not as good catalysts: they would simply oxidize, and wouldn't release the oxygen to the reaction. The reverse reaction happens much less abundantly than the forward reaction, since its activation energy is greater than the activation energy of the latter by the enthalpy.

A complete simulation of the catalyzed reaction would have to take into account the equilibria and rates of five different reactions -- CO and O adsorption, CO oxidation, and CO and O desorption (it can be assumed that the CO₂ desorbs completely). Such simulations have even been done. This simulation makes the assumptions that the rate limiting step of the reaction is always the CO oxidation step, and that reactant concentrations on the surface are directly proportional to those in the air. This leads to the following differential rate laws.

• The rate of the forward reaction (R_f) = k[CO][O₂]e^-E_a/(RT) where R is the gas constant, E_a is the activation energy, and T is the temperature in Kelvin.
• The rate of the backward reaction (R_b) = k[CO₂]e^{-(E_a + H)/(RT)} (The constants (k) were assumed to be the same) H is the ethalpy.
• d[CO]/dt = R_b - R_f = 2d[O₂]/dt = - d[CO₂]/dt

Since predicting the change of the concentrations over any arbitrary amount of time requires finding an integral over a system of 3 non-linear differential equations, the simulator module picks a suitably small epsilon value based on the magnitude of R_f - R_b and numerically approximates the integral.