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# hw2 - CE 561 Homework 2(assigned due(1 Consider the network...

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CE 561 Homework 2: (assigned 9/9/09, due 9/14/09) (1) Consider the network of 1 st order reactions given by A 1 A 2 A 3 k k k A 4 k where for simplicity, we have given all four reactions the same rate constant and made all four reactions irreversible (note that a cyclic system of irreversible reactions with identical rate constants would be extremely unlikely to occur in practice, but it’s a nice problem). (a) Write this set of reactions in matrix form (i.e. 0 = A α ) (b) Write the rate equations in terms of the reaction rates in matrix form using the stoichiometric matrix (i.e. r dt C d T α = ). (c) Write the rate equations in terms of a matrix of rate constants and a vector of concentrations (i.e. C M dt C d = ). How are the matrices T α and M related? (d) Find an analytical solution to the rate equations (for C A 1 ( t =0)= C o , C A 2 ( t =0)= C A 3 ( t =0)= C A 4 ( t =0)=0) using the matrix method discussed in class. (e) If there are i A 1 molecules, j A 2 molecules, and k A 3 molecules in the system at time t

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