Analytical solution the rate of disappearance of

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 08/25/2012 for the course CBE 430 taught by Professor Dumesic during the Spring '08 term at University of Wisconsin.

Ask a homework question - tutors are online