Rank Annihilation Factor Analysis for Kinetics Spectrophotometric Mixture Analysis

A P 1 k1k1 B P 2 k2k2 [A]=[A] 0 exp(-k 1 t) [P 1 ]=[A] 0 (1-exp(-k 1 t)) [B]=[B] 0 exp(-k 2 t) [P 2 ]=[B] 0 (1-exp(-k 2 t))

Rank Annihilation Factor Analysis for Kinetics Spectrophotometric Mixture Analysis

Spectrophotometric monitoring of pH-metric titration of mixture of metal ions and an acidic ligand Rank=3 [A] 0 =1 [B] 0’ =1.4 Rank=2 Unknown sample A P 1 k1k1 B P 2 k1k1 Standard sample A P 1 k1k1 [A] 0 =1 [B] 0’ =0

Rank=3Rank=2 - Rank Annihilation Factor Analysis

? Use RAFA for a mixture analysis based on kinetic spectrophotometric measurements

Simulation of two parallel first order reaction

Three are some problems in using RAFA for mixture analysis based on kinetic measurements

A + R P k k= 0.1 Second order reactions

Rank Analysis

Product concentration ratio A + R P k [A] 0 =1 [R] 0 =2 [A] 0 =0.5 [R] 0 =2 Analyte concentration ratio

Rank Annihilation Factor Analysis for Kinetics and Equilibria Study

[A] =[A] 0 exp(-k 1 t) [B] = [ exp(-k 1 t) - exp(-k 2 t) ] k 2 – k 1 [A] 0 k 1 [C] =[A] 0 - [B] - [A] A B C k1k1 k2k2 Consecutive Reaction:

D = (X A + X B + X C ) + E = (c A s A T + c B s B T + c C s C T ) + E DXAXA XBXB XCXC = ++ = ++ cAcA sATsAT cBcB sBTsBT cCcC sCTsCT D = C STST

R = D - X A = D - c A s A T The aim of RAFA is to find a suitable k 1 so that the rank of matrix F can be reduced by 1 from that of matrix Y through introduction of kinetic spectrum of species A DR C -A S -A T =- = XAXA cAcA sATsAT

Determination of rate constants of a consecutive reaction with known spectrum of reactant sAsA D R = D - X A = D - c A s A T c A =f (k 1 )

rafa_k.m Determination of rate constants of a consecutive reaction with known spectrum of reactant

Calling function rafa_k

k1k1 k2k2

Free study Why both rate constants can be calculated by removing only the reactant component Anal. Chim. Acta 454, 21-30, 2002

? Use rafa_k function for determination of rate constants for a consecutive reaction

consecutive.m file Creating the consecutive reaction kinetic model

Determination of rate constants of a consecutive reaction with known spectrum of product sCsC D R = D - X C = D - c C s C T c C =f (k 1,k 2 )

rafa_k2.m Determination of rate constants of a consecutive reaction with known spectrum of product

Calling function rafa_k2

? Use rafa_k2 function for determination of rate constants for a consecutive reaction with spectral rank deficiency

Second order kinetics and RAFA

A + B C k [A] + [C] = [A] 0 [B] + [C] = [B] 0 [B] 0 =  [A] 0 [B] + [C] =  [A] +  [C]  [A] - [B] + (  [C] = 0 Rank deficiency in concentration profiles Linear dependency

D = (X A + X B + X C ) + E = (c A s A T + c B s B T + c C s C T ) + E DXAXA XBXB XCXC = ++ = ++ cAcA sATsAT cBcB sBTsBT cCcC sCTsCT D = C STST

R = D - X A = D - c A s A T For correct k value DR C -A S -A T =- = XAXA cAcA sATsAT Rank® = 2 For incorrect k value DR C -A S -A T =- = XAXA cAcA sATsAT Rank® = 3Rank® = 2

Determination of rate constants of a second-order reaction with known spectrum of reactant sAsA D R = D - X A = D - c A s A T c A =f (k)

rafa_ks.m Determination of rate constants of a second-order reaction with known spectrum of reactant

Calling function rafa_ks

? Is it possible full resolving the second-order kinetic systems with RAFA?

? Use rafa_ks.m file and investigate in which rank deficient cases the k value of second-order reaction can be calculated with RAFA. i) s A = s B ii) s A = s C iii) s B = s C

second.m file Creating the second-order reaction kinetic model