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Determination of dissociation constants of uniprotic acids with known spectrum of acidic or basic component

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HA A - + H + [HA] = C t [H + ] [H + ] + K a [A - ] = C t K a [H + ] + K a DX HA XAXA =+ c HA s HA = cAcA sAsA + R = D - X HA = D - c HA s HA T

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Determination of dissociation constants of uniprotic acids with known spectrum of acidic or basic component R = D - X HA = D - c HA s HA T c HA =f (K a ) s HA D

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rafa_Ka.m Determination of Pka value for an uniprotic acid with known spectrum of HA species

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Calling function rafa_Ka

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? Investigate the effects of extent of spectral overlapping on the determined pKa value by RAFA

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Di-protic Acids [H] 2 + K a1 [H] + K a1 K a2 C t [H] 2 [H 2 A] = [H] 2 + K a1 [H] + K a1 K a2 C t K a1 [H] 2 [HA] = [H] 2 + K a1 [H] + K a1 K a2 C t K a1 K a2 [A] = R = D - X H2A = D - c H2A s H2A T c H2A =f (K a1, K a2 )

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pK a1 = 3.0 pK a2 =4.0

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pK a1 = 3.0 pK a2 =4.5

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pK a1 = 3.0 pK a2 =5.0

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pK a1 = 3.0 pK a2 =5.5

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pK a1 = 3.0 pK a2 =6.0

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pK a1 = 3.0 pK a2 =6.5

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pK a1 = 3.0 pK a2 =7.0

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Determination of amount and pKa values of an acid in a mixture with known spectrum of its components

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HA A - + H + [HA] = C t [H + ] [H + ] + K a [A - ] = C t K a [H + ] + K a X HA XAXA D = + c HA s HA cAcA sAsA =+ R = D - X HA - X A = D - c HA s HA T - c A s A T Determination of amount and pKa values of an acid in a mixture with known spectrum of its components Interferences + +

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pH-metric titration of a mixture containing an acid with known spectrum of components D s HA sAsA R = D - X HA -X A = D - c HA s HA T - c A s A T c HA =f (C 0,K a )c A =f (C 0,K a )

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rafa_CKa.m Determination of concentration and Pka values for an uniprotic acid with known spectrum of HA and A component

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Calling function rafa_CKa

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? Use RAFA_CKa and determine the amount and pKa values of a known acid in an unknown mixture

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Rank Annihilation Factor Analysis for Spectrophotometric Study of Complex Formation Equilibria Anal. Chim. Acta 486, 109-123, 2003

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M +nLML n M +nLML n [M] [L] [ML n ] K f = n [M] [L] [ML n ] K f = n C L = [L] + [ [ML n ] C M = [M] + [ [ML n ] K f [L] n+1 + (nK f C M –K f C L ) [L] n + [L]–C L =0 [ML n ] =K f C M [L] n / (1+K f [L] n )[M] = C M / (1+K f [L] n ) One-step complex formation equilibria

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X MLn D = XLXL + cLcL sLsL c MLn s MLn =+ R = D - X L = D - c L s L T + Interferences c L = f(K f,n) Rank Annihilation Factor Analysis for Spectrophotometric Study of Complex Formation Equilibria

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One step complex formation (n=2) M +2LMLM +ML 2 [L] [M] [ML 2 ] C L =0.001K L =10 6.5

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rafa_MLn.m Determination of stoichiometry and formation constant values for an MLn complex with known spectrum of ligand

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n=1 n=2 n=3 n=4 n=5

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? Create the data for ML 3 system and use RAFA for determination of Kf and its stoichiometry.

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MLn.m Simulation of MLn complex formation system

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Calling function MLn

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[M] [L] [ML] K1=K1= [ML] [L] [ML 2 ] K2=K2= C L = [L] + [ML] + 2 [ML 2 ] C M = [M] + [ML] + [ML 2 ] K 1 K 2 [L] 3 + (K 1 (1+K 2 (2CM –CL)))[L] 2 + (1+K 1 (C M –C L ))[L]–C L = 0 ML + L ML 2 M + L ML Two successive step complex formation

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A = A L + A ML + A ML2 + R = L [L] T + ML [ML] T + ML2 [ML 2 ] T + R = E C T + R Two successive step complex formation R = D - X L = D - c L s L T c L = f(K 1, K 2 )

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Determination of dissociation constants of uni-protic acids without known spectrum

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1 2 5 4 3 5 4 1 2 3 1 1 1 1 1 5 2 0.2 0.5 1 0.1 0.2 0.3 0.4 0.1 0.3 0.4 0.2 0.1 0.2 0.3 0.4 0.1 0.3 0.4 0.2 0.6 0.3 0.2 0.15 0.12 1.7 0.8 0.5 0.35 0.26 2.3 1.1 0.7 0.5 0.38 1.4 0.8 0.6 0.5 0.44 = 0.6 1.7 1.6 1.5 1.4 1.3 2.3 2.2 2.1 2.0 1.9 1.4 1.6 1.8 2.0 2.2 = 1 2 5 4 3./ 1 2 5 4 3 A simple mathematical rule

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1 2 5 4 3 5 4 1 2 3 1 2 5 4 3./ 1 1 1 1 1 5 2 0.2 0.5 1 0 0 0 0 0 3.26 0.26 -1.54 -1.24 -0.74 1 2 5 4 3 5 4 1 2 3 3 2 4 5 1./ 0.33 1 1.25 0.8 3 1.66 2 0.25 0.4 3 -0.746 0.198 0.538 -1.212 -1.062 1.538 -0.076 1.924 -0.276 0.174 Mean centering Rank = 2 Rank = 1 Rank = 2

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HA A - + H + [HA] = C t [H + ] [H + ] + K a [A - ] = C t K a [H + ] + K a DX HA XAXA =+ c HA s HA cAcA sAsA =+ D’ = D./ c HA Determination of dissociation constants of uni-protic acids Mean centering (D’) c HA = f(K a )

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Titration of an uni-protic acid or a mixture containing an uni-protic acid

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Rafa_mcKa.m Determination of dissociation constants of uni-protic acids

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Calling function rafa_mcKa

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? Use mean centering based method for determination of acidity constant of an uniprotic acid in a mixture

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Determination of dissociation constants of di-protic acids without known spectrum

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c HA =f (K a1, K a2 ) Determination of dissociation constants of di-protic acids without known spectrum D’ = D./ c HA Mean centering (D’)

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Rafa_mcH2A.m Determination of dissociation constants of di-protic acids

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Calling function rafa_mcH2A

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? Use mean centering based method for determination of acidity constant of an di-protic acid in a mixture

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