Carbon monoxide, CO, adsorbs on various metal oxides used in heterogeneous catalysis. For a particular metal oxide, the adsorbed volume, V, of C0 was measured as a function of its equilibrium pressure, pco), at a temperature of 300K. Analysis of the experimental results showed that a plot of P(coyV against Pco)was linear. (All volumes were corrected to stp.) (i) Based on the experimental results outlined above the adsorption of CO was found to fit a Langmuir isotherm model. Explain which type of Langmuir isotherm this data is consistent with (two or three sentences). (ii) The linear plot of pcoyV against p(co) was found to have: slope = 1.96 cm; intercept = 1.65 × 10³ Pa cm3. Showing your reasoning, use this information to calculate a value for the adsorption coefficient, b, for CO on the metal oxide at 300 K. (iii) If the enthalpy change of adsorption AadH, for CO on the metal oxide was found to be -55.0 kJ mol-, determine the value for the adsorption coefficient, b, for CO at 400 K. State any assumptions you make in your calculation. (b) A supported palladium catalyst is active for the oxidation of CO at room temperature as shown in Reaction 3.1: \mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g})=\mathrm{CO}_{2}(\mathrm{~g}) Under certain conditions, this reaction was found to involve competitive adsorption of the reactants, with CO being non-dissociatively adsorbed and oxygen undergoing dissociation and dual-site adsorption: \mathrm{CO}(\mathrm{g})+{ }^{*} \Leftarrow \frac{k_{\mathrm{a}}}{\overline{k_{\mathrm{d}}}} \mathrm{CO}(\mathrm{ad}) \mathrm{O}_{2}(\mathrm{~g})+2^{*} \leftleftarrows \frac{k_{\mathrm{a}}^{\prime}}{k_{\mathrm{d}}^{\prime}} \rightarrow \mathrm{O}(\mathrm{ad})+\mathrm{O}(\mathrm{ad}) The rate-limiting step is then a bimolecular surface reaction between CO(ad) and O(ad): \mathrm{CO}(\mathrm{ad})+\mathrm{O}(\mathrm{ad}) \rightarrow \mathrm{CO}_{2}(\mathrm{ad}) where carbon dioxide desorbs as quickly as it is formed. (i) For competitive adsorption of CO and O atoms the number of vacant surface sites available at any will be N(1-thetaco-theta o) where theta co and theta o are the fractional surface coverages of co and o respectively and N is the total number of sites available hence for the competitive adsorption of co that following expression can be derived by equating the shares of adsorption ans desorption of CO \theta_{\mathrm{CO}}=b_{\mathrm{co}} p_{\mathrm{Co}}\left(1-\theta_{\mathrm{co}}-\theta_{\mathrm{o}}\right) (ii) The Langmuir isotherms for CO and O (derived from Eqn. 3.5 and asimilar expression for 00), are given by the following expressions: \theta_{\mathrm{CO}}=\frac{b_{\mathrm{CO}} p_{\mathrm{CO}}}{1+b_{\mathrm{CO}} p_{\mathrm{CO}}+\left(b_{\mathrm{O}_{2}} p_{\mathrm{o}_{2}}\right)^{1 / 2}} \theta_{\mathrm{o}}=\theta_{\mathrm{co}} \frac{\left(b_{\mathrm{o}_{2}} p_{\mathrm{O}_{2}}\right)^{1 / 2}}{b_{\mathrm{co}} p_{\mathrm{CO}}} Given Equations 3.6 and 3.7 and considering the rate-limiting step inReaction 3.4, show that the theoretical rate equation obeys a Langmuir-Hinshelwood mechanism of the form: (i) Under certain conditions the experimental rate equation for Reaction 3.1,has the following form: r=\frac{k_{\mathrm{R}}\left(p_{\mathrm{O}_{2}}\right)^{1 / 2}}{p_{c_{0}}} where kr is the experimental rate constant. Show how this result can be rationalised in terms of the theoretical rateequation (Equation 3.8) that has been derived for the mechanism. (ii) What other experimental condition would enable reduction of the theoretical rate equation to be consistent with the experimental rate equation (Equation 3.9)? (One sentence.) r=\frac{k_{\theta} b_{c o} p_{\mathrm{CO}}\left(b_{\mathrm{O}_{2}} p_{\mathrm{O}_{2}}\right)^{1 / 2}}{\left\{1+b_{\mathrm{c} O} p_{\mathrm{CO}}+\left(b_{\mathrm{o}_{2}} p_{\mathrm{O}_{2}}\right)^{1 / 2}\right\}^{2}} \text { where } b_{\infty}=k_{\mathrm{e}} / k_{\mathrm{d}} \text { and is the adsorption coefficient for } \mathrm{CO} \text {. }

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