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CHEM 2PD3 ASSIGNMENT DUE: 5 APRIL, 2010 QUESTION 1 "Mechanisms governing the kinetics of a reaction in a homogeneous system differ from those

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CHEM 2PD3 ASSIGNMENT DUE: 5 APRIL, 2010 QUESTION 1 “Mechanisms governing the kinetics of a reaction in a homogeneous system differ from those governing the kinetics of a reaction in a heterogeneous system.” Is this statement correct? Justify your answer, including in the case of heterogeneous systems, differences between gaseous and liquid reactants. QUESTION 2 The unimolecular decomposition of A after it adsorbs onto a vacant site S on a surface. Write the three elementary steps of this decomposition, using the rate constants k 1 , k -1 and k 2 . Write the expression for the rate of the decomposition reaction. (C AS is the concentration of adsorbed species/m 2 , C s is the total concentration of active surface sites, θ is the fraction of surface sites occupied by A and C S is the concentration of vacant sites). Using the steady-state assumption, show that the rate of the reaction can also be written as: 2 1 1 1 2 k k c k c c k k A A s + + = ν [1] QUESTION 3 In the limiting case of [1], where the rate of decomposition is very small compared to the rate of adsorption and desorption, Show how θ can be written as the Langmuir isotherm (i.e. express θ in terms of the equilibrium constant of adsorption K). How does the rate of the reaction in this limiting case compare to [1]? Include an expression for the rate of the reaction in your answer. In this limiting case, what is the order of the reaction with respect to C A ? Does the order of the reaction with respect to C A remain constant for all values of C A ? Include a plot of rate versus C A in your response QUESTION 4 The rate of decomposition of acetaldehyde can be studied by measuring the P in a system at constant V and T. (a) Express the rate of reaction in terms of the rate of change of P. The overall reaction is: CH 3 CHO (g) CH 4(g) + CO (g) with mole numbers n 1 = n o - ξ ; n 2 = 0 + ξ ; n 3 = 0 + ξ . (b) Suppose that the decomposition is 2 nd order. Formulate the rate law in terms of the total P of the system and integrate the result to express P as a function of time.
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(c) How would you obtain the rate constant from the expression derived in (b). QUESTION 5 we drew a connection between thermodynamics and kinetics by considering IRREVERSIBLE thermodynamics. We derived an expression that related the rate of entropy production to the rate of the reaction. Discuss in your own words the key points that originate from this lecture. Are you convinced that we have formed a connection between thermodynamics and kinetics? QUESTION 6 What are the mains steps that must be taken into account when considering the kinetics of reactions at surfaces? What is the Nernst diffusion layer? Include a diagram in your response. Construct a labelled energy diagram contrasting the activation barriers of an uncatalysed and a catalysed reaction. Can this diagram be applied for surface catalysts? Write the three elementary steps for the unimolecular decomposition of A on a surface; write the expression for the reaction rate. QUESTION 7 The growth of a bacterial colony can be modeled as a first-order process in which the probability of cell division is linear with respect to time such as dN/N = kdt, where dN is the number of cells that divide in the time interval dt, and k is a constant. a. use the preceding expression to show that the number of cells in the colony is given by N = N o e k t , where N is the number of cell colonies and No is the number of colonies present at t = 0. b. The generation time is the amount of time it takes for the number of cells to double. Using the answer to part (a), derive an expression for the generation time. c. In milk at 37 o C, the bacteria lactobacillus acidophilus has a generation time of about 75 min. Construct a plot of the acidophilus concentration as a function of time for time intervals of 15, 30, 45, 60, 90, 120 and 150 minutes after a colony of size N o is introduced to a container of milk. You are given the following data for the decomposition of acetaldehyde. Initial concentration (M) 9.72x10 -3 4.56x10 -3 Half-life (s) 328 572 Determine the order of the reaction and the rate constant for the reaction. Consider the schematic reaction A ⎯→ k P a. If the reaction is one-half order with respect to [A], what is the integrated rate law expression for this reaction? b. What plot would you construct to determine the rate constant k for the reaction? c. What would be the half-life for this reaction? Will it depend on initial concentration of reactant?
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