1. Rank Annihilation Factor Analysis for Kinetics Spectrophotometric Mixture Analysis

2. 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))

3. Rank Annihilation Factor Analysis for Kinetics Spectrophotometric Mixture Analysis

4. 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

5. Rank=3Rank=2 - Rank Annihilation Factor Analysis

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

12. Simulation of two parallel first order reaction

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

20. A + R P k k= 0.1 Second order reactions

21. Rank Analysis

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

23. Rank Annihilation Factor Analysis for Kinetics and Equilibria Study

24. [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:

25. 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

26. 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

27. 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 )

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

29. Calling function rafa_k

32. k1k1 k2k2

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

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

35. consecutive.m file Creating the consecutive reaction kinetic model

40. 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 )

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

42. Calling function rafa_k2

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

49. Second order kinetics and RAFA

50. 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

51. 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

52. 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

53. 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)

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

55. Calling function rafa_ks

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

60. ? 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

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