HW07solutionsF11

77 b equations 2 8 10 13 and 16 may be used to prepare

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Unformatted text preview: for the rate of formation of species E dE = k3 B dt Combination of equations 8 and 14 gives dE k1 k3 A0 Ⱥ −(k1 + k2 )t − k t Ⱥ = − e 3 Ⱥ Ⱥ e dt k3 − k2 − k1 Ⱥ Ⱥ Integration gives − (k + k )t Ⱥ − k t Ⱥ k1k3 A0 1−e 1 2 1− e 3 E= − Ⱥ Ⱥ k3 − k2 − k1 k1 + k 2 k3 Ⱥ Ⱥ or − (k + k )t −k t Ⱥ Ⱥ k1 A0 Ⱥ k3 − k3 e 1 2 − (k1 + k2 ) + (k1 + k2 )e 3 Ⱥ Ⱥ Ⱥ E= (k3 − k 2 − k1 )(k1 + k2 ) − (k + k )t Ⱥ ( k1 + k2 )e −k3 t Ⱥ k1 A0 k3 e 1 2 + = Ⱥ1 − Ⱥ k1 + k 2 k3 − k2 − k1 k3 − k2 − k1 Ⱥ Ⱥ Fall 2011 p. 7/7 B. Equations 2, 8, 10, 13 and 16 may be used to prepare the plots requested. The calculations were worked up on a spreadsheet and plotte...
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