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Question Catalyst equation help (redone)

A catalyst consisting of palladium on an α-Al2O3 support, Pd/α-Al2O3, has been used for the oxidation of CO at room temperature:

Equation 1 CO(g) + ½O2(g) = CO2(g)

Under certain conditions, the oxidation reaction was found to involve competitive adsorption of the reactants with CO being non-dissociatively adsorbed and oxygen undergoing dual-site adsorption:

Equation 2 ka CO(g) + * ↔ CO(ad) kd

Equation 3 ka’ O2(g) + 2* ↔ O(ad) + O(ad) kd’

The rate-limiting step is then a bimolecular reaction between CO(ad) and O(ad):

Equation 4 CO(ad) + O(ad) → CO (ad)

Carbon dioxide can be assume to be weakly adsorbed and, as a consequence, desorbs as quickly as it is formed.

(i) For the competitive adsorption of CO show that the following expression can be derived by equating the rates of adsorption and desorption of CO:

Equation 5 θCO = bCOpCO(1 – θCO – θO)

Where θCO and θO are the fractional surface coverages of CO and O, respectively. The quantity bCO (= ka/kd) is the adsorption coefficient for CO and pCO is the partial pressure of CO. (Hint In your working you should represent the total number of adsorption sites by N and provide expressions for both the rate of adsorption and the rate of desorption of CO.)

(ii) Equation 5 can be used in a more detailed analysis of the mechanism to derive the following two expressions:

Equation 6 θCO = (bCOpCO) / (1 + bCOpCO + (bO2pO2)1/2)

and

Equation 7 θO = θCO((bO2pO2)1/2 / bCOpCO)

where b02(= ka’ / kd’) and pO2 are, respectively, the adsorption coefficient and partial pressure of O2.

Given Equations 6 and 7, in conjunction with the information about the rate-limiting step at the start of this question, show that the theoretical rate equation takes the form:

Equation 8 r = (kθbCOpCO(bO2pO2)1/2) / {1 + bCOpCO + (bO2pO2)1/2}^2

(iii) The experimental rate equation for the CO oxidation reaction, under conditions for which the mechanism given in part (ii) is valid, takes the form:

Equation 9 r = (kR(pO2)1/2) / pCO

How can this result be rationalised in terms of the theoretical rate equation (Equation 8) that has been derived for the mechanism?

mark1402 in Chemistry about 7 years ago
Question Catalytic cyles involving radicals

This question is concerned with various processes that contribute to the loss of ozone in the lower stratosphere at mid-latitudes (about 30° to 60° north or south of the equator).

The ‘standard’ catalytic cycles involving radical species such as ClOx and HOx do not operate effectively in the lower stratosphere, because there is insufficient atomic oxygen at these altitudes. Instead the major cycles in the lower stratosphere have the net effect of catalysing the following reaction:

Equation 1

2O3(g) = 3O2(g)

An important part of the ‘natural’ system controlling ozone abundance in the lower stratosphere is represented by the catalytic cycle involving the HOx (HO• and HO2•) radicals:

Equation 2

k1

HO• + O3 → HO2• + O2

Equation 3

k2

HO2• + O3 → HO• + 2O2

net: 2O3 → 3O2

At 210 K, k1 = 1.0 x 10^-14 cm3 s^-1 k2 = 1.0 x 10^-15 cm3 s^-1

The principle source of HOx radicals is water vapour transported up from the troposphere. At about 20 km in the mid-latitudes, the total volume mixing ratio of HOx from this source can be taken as:

x(HOx) = x(HO•) + x(HO2•) = 6.0 ppt = 6.0 x 10^-12

(i) The partitioning between HO• and HO2•, and hence the ratio [HO•]/[HO2•], is largely determined by Equations 2 and 3. By applying the steady state approximation to HO• show that:

Equation 4

([HO•] / [HO2•]) = k2 / k1

(ii) For a given atmospheric constituent, A, the mixing ratio (by volume), x(A), is defined as:

Equation 5

x(A) = [A]/[M]

where [A] is the concentration of A and [M] is the total number density of air at a given altitude. Using this information and that given earlier in the question, determine the mixing ratios of HO• and HO2•, that is x(HO•) and x(HO2•), in the mid-latitude lower stratosphere at 210 K.

In addition to the HOx cycle, several other cycles involving ClO• and BrO• contribute to in-situ ozone loss in the mid-latitude lower stratosphere. In this region levels of ‘active’ chlorine and bromine radicals are influenced by heterogeneous reactions of reservoir molecules taking place on the surface of aerosol particles.

(iii) Explain briefly the significance of the term ‘reservoir molecules’ and the part such species play in both mid-latitude and polar stratospheric ozone chemistry. Note detailed examples of chemical equations for the processes are not required and your answer must be in your own words. (No more than 150 words.)

(iv) For the physical conditions in the mid-latitude lower stratosphere, heterogeneous reactions of bromine reservoir molecules (e.g. HBr and BrONO2) are more rapid than those of the corresponding chlorine compounds and hence levels of HO• and BrO• have been seen to increase. Moreover, because of the reaction of HO• with HCl, the increase in [HO•] is expected to lead indirectly to an increase in the concentration of the ClO• radical. Explain very briefly why this should be so. (Two or three sentences only.)

mark1402 in Chemistry about 7 years ago
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