Consec_ABC_Gen_v7

Consec_ABC_Gen_v7 - Irreversible Two-step Consecutive...

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Unformatted text preview: Irreversible Two-step Consecutive Process: Generation and Visualization of Noisy UV-Vis Absorbance Data Dr. Kalju Kahn UC Santa Barbara, 2004-2010 This Notebook illustrates how to generate multi-wavelength absorbance data containing random noise for the irreversible process A fi k1 B fi k2 C. The lack of isosbestic point in the three-component system is illustrated. First, we generate concentration profiles for A, B, and C for 40 time points with 0.2 second spacing. The concentrations follow consecutive first-order kinetics. In[1]:= Remove @ "Global` * " D twostep = DSolve @ 8 concA @ time D == - k1 concA @ time D , concA @ D == A0, concB @ time D == k1 concA @ time D- k2 concB @ time D , concB @ D == 0, concC @ time D == k2 concB @ time D , concC @ D == < , 8 concA @ time D , concB @ time D , concC @ time D< , time D Flatten; Concentration Profiles In[3]:= cA = concA @ time D . twostep Simplify cB = concB @ time D . twostep Simplify cC = concC @ time D . twostep Simplify Out[3]= A0 - k1 time Out[4]=- A0 I - k1 time- - k2 time M k1 k1- k2 Out[5]= A0 I k1- - k2 time k1 + I- 1 + - k1 time M k2 M k1- k2 In[6]:= timeval = Table @ i, 8 i, 40 <D 5 N; cAtime = cA . 8 A0 fi 1.0, k1 fi 0.5, k2 fi 1, time fi timeval < ; cBtime = cB . 8 A0 fi 1.0, k1 fi 0.5, k2 fi 1, time fi timeval < ; cCtime = cC . 8 A0 fi 1.0, k1 fi 0.5, k2 fi 1, time fi timeval < ; cAdata = Transpose @8 timeval, cAtime <D ; cBdata = Transpose @8 timeval, cBtime <D ; cCdata = Transpose @8 timeval, cCtime <D ; In[13]:= Needs @ "PlotLegends` " D ListPlot @8 cAdata, cBdata, cCdata < , AxesLabel fi 8 "Time, s", "Conc" < , PlotLegend fi 8 " @ A D ", " @ B D ", " @ C D " < , LegendPosition fi 8 0.2,- 0.10 < , LegendSize fi 8 0.35, 0.35 < , PlotLabel fi "Concentration Profiles", LabelStyle fi 8 Medium, FontFamily fi "Helvetica" < , Background fi ColorData @ "Atoms", "He" DD Out[14]= 2 4 6 8 Time, s 0.2 0.4 0.6 0.8 Conc Concentration Profiles @ C D @ B D @ A D 2 Consec_ABC_Gen_v7.nb In[15]:= datatable...
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This note was uploaded on 01/09/2011 for the course CHEM 111 taught by Professor Kahn during the Fall '08 term at UCSB.

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Consec_ABC_Gen_v7 - Irreversible Two-step Consecutive...

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