[HoshiKagakushya]

1. Question


 On a catalyst surface, the formation reaction of CO2 by the oxidation of CO with O2 proceeds in the following mechanism.

(1)  O2(g) + 2V <---> 2O(ads)  (equilibrium constant KO2)
(2)  CO(g) + V <--> CO(ads)  (equilibrium constant (KCO)
(3)  O(ads) + CO(ads) <--> CO2(g)  (rate constant k)

(g) denotes gas phase
O(ads) denotes Oxygen atom on absorption site
CO(ads) denotes CO on absorption site
V denotes vacant absorption site

Partial pressures of O2(g) and CO(g) are defined as PO2 and PCO respectively. Densities of O(ads), CO(ads), and V are [O(ads)], [CO(ads)], and [v] respectively. Fractional coverage of O(ads) and CO(ads) are defined are theta(Oxygen) and theta(CO) respectively.
Only reaction 1- 3 are considered and reaction 3 is the rate limiting step. More assumptions are that all adsorption sites are equivalent and a single adsorbate occupies an adsorption site at once.

Here are the questions

1. Show the adorption rate, ra, and desorption rate, rd, using all or parts of ka, kd, PO2, [V], and [O(ads)], where ka and kd denote the rate constants of adsorption and desorption in eqn (1).

2. Show KO2 and KCO using all or parts of the densities and partial pressures described above.

3. Show theta(Oxygen) and theta (CO) using all or parts of PO2, PCO, KO2, and KCO.

4. Derive the rxn rate rCO2 of eqn 3 using all or parts of k, PO2, PCO, K)2, KCO, and n.

5. Here, PCO dependence of rCO2 is considered under the condition of PCO >> PO2. Express rCO2 as a function of PCO in the two cases of a sufficiently low PCO (KCO x PCO << 1) and a sufficiently high PCO (KCO x PCO >> 1). In addition draw a rough sketch of the relation between rCO2 and PCO.

2. Relevant equations

The only equations that  I could think of are:
general rate laws

rate(r) = k x [reactant 1] x {reactant 2] x .
where k is the rate constant

* if at equilibrium, the concentration of the reactants must equal the concentration of products

Everything below was pulled from Atkins Physical Chemistry (8th ed) Ch 25 pgs 919 - 921
Raoult's partial pressure which relation partial pressure of pure solvents to solutions and concentrations

P (solution) = X x P (pure solvent)
* X = mol fraction of solvent  = (mol solvent)/ (mol solvent + mol solute)

Catalyst equations

theta = (# adsorption sites occupied)/ (# sites available)

rate of change of surface coverage (d theta/ d t) = K(ads) x P x N  x ( 1- theta)
rate of change of desorption (d theta/ d t) = - K(desorption) x N x theta
* N = total number of sites


3. The attempt at a solution

So my attempts are weak

for 1

ra = Ka x [V]
* here I think [O2] is constant so it is not taken into account of the rate of adsorption

rd = kd x [O(ads)]

For 2, 3, 4, and 5, I am honestly totally lost.

Thank you for advise on what to read to understand this and tips.

[curiouscat]

You  cannot assume PO2 as constant if you want an expression containing PO2.

[HoshiKagakushya]

You  cannot assume PO2 as constant if you want an expression containing PO2.

Well I was unsure, but I still think that the concentrations of O₂(g) and CO (g) are constant based on the information given. What equations are relevant for calculating the partial pressure of O₂?

[curiouscat]

You  cannot assume PO2 as constant if you want an expression containing PO2.

Well I was unsure, but I still think that the concentrations of O₂(g) and CO (g) are constant based on the information given. What equations are relevant for calculating the partial pressure of O₂?

ra = Ka x [V] PO2


Also, I think you need to raise [V] to an exponent of 2 based on stoichometry.

The concentrations may be fixed but your final expression for rate will contain them. Sorry my first post was confusing; all I meant is your rate expressions should have PO2 and PCO etc.

Another eqn. to use is a site balance on the surface. Sum of free and occupied sites is 1.

Finally as written I think you are wrong about saying "* if at equilibrium, the concentration of the reactants must equal the concentration of products"