First_Order_UV_SVD_v7

First_Order_UV_SVD_v7 - Irreversible One-step First Order...

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Unformatted text preview: Irreversible One-step First Order Reaction: Generation and SVD Analysis of Noisy UV-Vis Absorbance Data Dr. Kalju Kahn UC Santa Barbara, 2004-2010 This Notebook illustrates how to generate and then deconvolute multi-wavelength absorbance data containing random noise for the irreversible process A fi k B . The main goal is to illustrate how to determine the number of species that contribute to absorbance change via singular value decomposition (SVD). The value of isosbestic point for two-component system is illus- trated. First, we generate concentration profiles for A and B for 30 time points with 0.2 second spacing. The concentrations follow first-order kinetics. Data Generation In[1]:= Remove @ "Global` * " D onestep = DSolve @ 8 concA @ time D == - k concA @ time D , concA @ D == A0, concB @ time D == k concA @ time D , concB @ D == < , 8 concA @ time D , concB @ time D< , time D Flatten; Concentration Profiles In[3]:= cA = concA @ time D . onestep Simplify cB = concB @ time D . onestep Simplify Out[3]= A0 - k time Out[4]= A0- A0 - k time In[5]:= timeval = Table @ i, 8 i, 30 <D 5 N; cAtime = cA . 8 A0 fi 1.0, k fi 0.693, time fi timeval < ; cBtime = cB . 8 A0 fi 1.0, k fi 0.693, time fi timeval < ; cAdata = Transpose @8 timeval, cAtime <D ; cBdata = Transpose @8 timeval, cBtime <D ; In[10]:= Needs @ "PlotLegends` " D ListPlot @8 cAdata, cBdata < , AxesLabel fi 8 "Time", "Conc" < , PlotLegend fi 8 " @ A D ", " @ B 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[11]= 1 2 3 4 5 6 Time 0.2 0.4 0.6 0.8 1.0 Conc Concentration Profiles @ B D @ A D In[12]:= datatable = Transpose @8 timeval, cAtime, cBtime <D ; PaddedForm @ TableForm @ datatable, TableHeadings fi 8 None, 8 "Time", " @ A D ", " @ B D " <<D , 8 3, 3 <D ; Spectra of Species Now we generate spectra for A and B. The spectrum of A is modeled as a Gaussian curve with a maximum at 280 nm, and the spectrum of B is modeled as a Gaussian curve with a maximum at 400 nm. The Mathematica function NormalDistribu- tion[ , ] generates the Gaussian distribution with mean and standard deviation . In[14]:= ndist280 = NormalDistribution @ 280, 30 D ; ndist400 = NormalDistribution @ 400, 35 D ; The function PDF[dist, x] calculates the probability density function of this distribution. We multiply the probability values with coefficients (100 and 90 below) to get reasonable units. You can think of these values as molar absorptivities in M- 1 cm- 1- units. In[16]:= pdf280 = 100 PDF @ ndist280, x D pdf400 = 90 PDF @ ndist400, x D Out[16]= 5 3 - H- 280 + x L 2 1800 2 Out[17]= 9 7 - H- 400 + x L 2 2450 2 2 First_Order_UV_SVD_v7.nb In[18]:= Plot A8 pdf280, pdf400 < , 8 x, 150, 500 < , PlotRange fi All, PlotLabel fi "Molar Absorptivity of A and B", AxesLabel fi 9 " , nm", " , M- 1 cm- 1 " = ,...
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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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First_Order_UV_SVD_v7 - Irreversible One-step First Order...

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