HW07solutionsF11

# Analytical solution the rate of disappearance of

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Unformatted text preview: nonlinear terms (reactions other than first order), then it would only be solvable with numerical tools. Your estimate of the ratio of time needed for numerical:analytical solutions may be as low as 1:4 and as high as 1:infinity. Analytical Solution: The rate of disappearance of phenyl salicylate (A) is given by − dA (1) = (k1 + k2 ) A dt Separation of variables and integration give (2) The rate of appearance of species B is given by dB (3) = k1 A − k3 B dt Combination of equations 2 and 3 gives (4) This linear differential equation can be solved with the aid of an integrating factor, k dt kt e ∫ 3 = e 3 Thus (5) where the constant of integration C1 can be determined from the initial condition (B0= 0). Thus −k t ( k − k −k )t B = e 3 k1 A0 ∫ e 3 1 2 dt + C1 [ =e = −k3t (k 3 − k1 − k2 )t Ⱥ k1 A0e Ⱥ + C1 Ⱥ Ⱥ k 3 − k1 − k2 Ⱥ Ⱥ − (k...
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