Chemical Data Fitting as a Powerful Chemometric Method

The art and science of extracting useful information from chemical data Chemometrics: Chemometrics methods: Soft-modeling methods: EFA, TFA, RFA, Calibration based methods (PLS, PCR), PARAFAC, etc. Hard-modeling methods: Chemistry based analysis of the data, Data fitting usually by linear or non-linear least squares

Occurrences of the keywords ‘chemometrics’ and ‘data fitting’ in a series of chemistry journals over the last 20 years. Chemometrics and Data Fitting Azadeh Golshan, Yaser Beyad and Marcel Maeder J. Chemometrics 2013, 27: 260–261

A general view to chemical equilibria systems. M + L ML 2M + L M 2 L H + L HL Mass action laws:  HL = [HL] / [H][L]  ML = [ML] / [M][L]  ML2 = [ML 2 ] / [M][L] 2 What are know the total concentrations of M, L and H. What we need to calculate are the equilibrium concentrations of all species, HL, ML, ML 2, L, H and OH. C M, tot = [M] + [ML] + 2[M 2 L] C L, tot = [L] + [LH] + [ML] + [M 2 L] C H, tot = [H] + [LH]– [OH] C M, tot = [M] +  ML [M][L] + 2  M2L [M] 2 [L] C L, tot = [L] +  LH [L][H] +  ML [M][L] +  ML2 [M] 2 [L] C H, tot = [H] +  LH [L][H] - K W [H] -1

The task is to calculate all equilibrium species concentrations in a solution, knowing the total concentrations of the components and the complete set of equilibrium constants. In general non-linear problems cannot be resolved explicitly, i.e. there is no equation that allows the computation of the result in a direct way. Usually such systems can be resolved numerically in an iterative process. There are three components with unknown concentrations and also three mass action equations A general view to chemical equilibria systems. C M, tot = [M] +  ML [M][L] + 2  M2L [M] 2 [L] C L, tot = [L] +  LH [L][H] +  ML [M][L] +  ML2 [M] 2 [L] C H, tot = [H] +  LH [L][H] - K W [H] -1

Different procedures for studying the chemical equilibria make different designs for changing the total concentrations of components A general view to chemical equilibria systems. The equilibria situations are completely dependent to the total concentrations of the components. The total concentrations of components are controllable variables, so the situations of the equilibria can be controlled by the chemists. How can we observe the effect of different procedures on situation of equilibria?

(1)TitrantTitrand H Total concentrations change log (β)

Total Titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total Titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total Titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total titration curve and concentration profiles

(1)TitrantTitrand H Total concentrations change log (β)

Total titration curve and concentration profiles

Intertwined Chemical Kinetics and Equilibria M + L ML 2M + L M 2 L H + L HL Kinetic Systems B + F P k4k4 A B C k3k3 k2k2 k1k1 Equilibrium Systems M + L ML 2M + L M 2 L H + L HL HL P Coupling of Kinetic and Equilibrium How such systems should be studied?

C M, tot = [M] +  ML [M][L] + 2  M2L [M] 2 [L] C time L, tot = [L] +  LH [L][H] +  ML [M][L] +  ML2 [M] 2 [L] C Time H, tot = [H] +  LH [L][H] - K W [H] -1 Intertwined Chemical Kinetics and Equilibria HL P The influences of kinetic reaction on mass balance system should be considered: Always the equilibrium constants should be fulfilled. Due to consumption of HA, the C H,tot and C L, tot will change with time d[HA]/dt =- k [HA]d[P]/dt = k [HA] Simply the task is just the calculation of total concentration of two components as a function of time

Procedure for modeling the intertwined kinetics and equilibria: C 0 M, tot C 0 L, tot C 0 H, tot Known [HL], [L], [H] and other equilibrium concentrations of all species can be calculated by Newton-Raphson method dC M, tot /dt = 0 dC L, tot /dt =- k [HA] dC H, tot /dt =- k [HA] Solving the system of ordinary differential equations produce the total concentration profiles of components at all times. Equilibrium concentrations of all species can be calculated based on known values of total concentrations.

EQKIN.m and ode_EQKIN.m files for modeling the intertwined kinetic and equilibria

M + L ML 2M + L M 2 L H + L HL HL P Coupling of Kinetic and Equilibrium log  ML = 3 log  HL = 4 log  M2L = 5 k = 0.1 log  HL = 6

Variation of total concentrations as a function of time:

Molecular charge transfer complex formation reactions:

Incorporating the Buffer Equilibrium: M + L ML 2M + L M 2 L H + L HL  HL = [HL] / [H][L]  ML = [ML] / [M][L]  ML2 = [ML 2 ] / [M][L] 2 H + B HB  HB = [HB] / [H][B] C M, tot = [M] +  ML [M][L] + 2  M2L [M] 2 [L] C L, tot = [L] +  LH [L][H] +  ML [M][L] +  ML2 [M] 2 [L] C H, tot = [H] +  LH [L][H] - K W [H] -1 C B, tot = [B] +   H [B][H] C B, tot = C B + C HB C H, tot = C H + C HB

c_0 = [15e-3 5e ]; H L M B

c_0 = [10e-3 5e ]; H L M B