Mole Ratio Data Research Articles

Multiwavelength spectrophotometric-thermodynamic studies of complexation reactions of newly synthesized triazenes with Hg2+, Pb2+, Zn2+, and Cd2+ in MeOH, EtOH, DMF, and DMSO

The complexation reaction of Hg2+, Pb2+, Zn2+, and Cd2+ cations with four newly synthesized triazene ligands was studied spectrophotometrically in nonaqueous solvents (MeOH, EtOH, DMF, and DMSO) at various temperatures. Stability constants (K1 and K2) and stoichiometries of formed adducts (1:1 and 1:2 ligand to metal ion) were calculated by computer refinement of experimental spectral mole ratio data by SQUAD program. The results indicated that the donor number, dielectric constant, the acceptor number of the solvents play an important role in the complex stability. Besides, the shape and size of the solvent molecules were significant factors in the studied reactions. Between log β1 and log β2, a linear relationship was illustrated for most of the complexes under different conditions. The Van't Hoff equation was used to calculate ΔG°, ΔS°, and ΔH° from the dependence of formation constants on temperature. After calculating thermodynamic data at different temperatures, a good linear correlation was obtained from the TΔS° − ΔH° plot resulting in the entropy-enthalpy compensation for complexation reactions.

Microencapsulation of Gac (Momordica cochinchinensis Spreng.) fruit oil in Ca-Alginate bead produced through Jetcutter

The Gac (Momordica cochinchinensis Spreng.) fruit oil was microencapsulated in Ca-Alginate bead by Jetcutter equipment. Experiments showed that the effects of emulsion preparation and equipment parameters were significant on particle size, microencapsulation yield, loading capacity and solids recovery efficiency of the device. At alginate concentration of 2.5%, the bead had a spherical size of 1.07 - 1.18 mm when the fluid flow was 14 mL/min and the rotation of the cutting disc was 400 - 800 rpm. Samples stored for 2 h after homogenization showed better microencapsulation yield (83 - 84%) and bead size (1.07 mm) than those stored for 24 h after homogenization (79% and 1.18 mm). When the loading capacity increased from 20% to 40%, the mole ratio (CaCl2-alginate) in the bead was reduced from 1.55 to 0.86. This mole ratio data can be considered to control and adjust CaCl2 concentration during the continuous operation of the Jetcutter.

Competitive 7Li NMR studies of the complexation of some metal ions with a novel heptadentate (N7) macrocyclic Schiff base ligand having two pyridyl units as pendant arms in acetonitrile and methanol mixture (50:50)

In order to investigate the stoichiometry and stability of a Li+ complex with new heptadentate (N7) macrocyclic Schiff base having two pyridyl units as pendant arms (MSb) in Acetonitrile and Methanol mixture (50:50), Lithium-7 NMR spectroscopy was employed. A competitive 7Li NMR method was also used to probe the complexation of Li+, Na+, K+, Rb+, Mg2+, Ca2+, Ba2+, Mn2+, Zn2+, Cd2+ and UO22+ ions with macrocyclic Schiff base (MSb) in the same solvent systems. The formation constants were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant of the resulting complexes. In this solvent, the stability of the final 1:1 complexes were found to vary in the following order:Zn2+-MSb > Mn2+-MSb > Cd2+-MSb > UO22+-MSb > Ca2+-MSb > Mg2+-MSb > Na+-MSb > Li+-MSb > Ba2+-MSb > K+-MSb > Rb+-MSb.

Complexation study of 4,13-didecyl-1,7,10,16-tetraoxa-4,13-diazacyclooctadecane (kryptofix 22DD) with the Co2+, Cr3+, Tl+, and UO2 2+ cations in acetonitrile, methanol, and their binary mixtures

Complexation between 4,13-didecyl-1,7,10,16-tetraoxa-4,13-diazacyclooctadecane (kryptofix 22DD) and the Co2+, Cr3+, Tl+, and UO22+ cations in acetonitrile, methanol, and their binary mixtures was studied by conductometry at different temperatures. The experimental results showed the formation of 1: 1 [ML] complexes between the studied metal cations and the macrocyclic ligand in most solvent systems. The stability constants of the resulting 1: 1 complexes were determined by computer fitting the conductance–mole ratio data. The stability of the metal–ion complexes in pure acetonitrile at 15 and 25°C was found to decrease in the order: [Tl (kryptofix 22DD)]+ > [Co(kryptofix 22DD)2+] > [UO2(kryptofix 22DD)]2+. Along with 1: 1 [ML] complexes, 2: 1 [M2L], 2: 2 [M2L2], 2: 3 [M2L3], 1: 2 [ML2], and 1: 3 [ML3] complexes are likely to be formed in some of the solvent systems. The thermodynamic parameters (ΔSc0, ΔHc0) of the complex formation in the studied nonaqueous solvents, obtained from the temperature dependences of the stability constants of the complexes, showed that the process is athermic.

Conductometric studies and application of new Schiff base ligand as carbon paste electrode modifier for mercury and cadmium determination

ABSTRACTA new chemically modified carbon paste electrode by 2,2ʹ-((pyridine-2,6-diylbis(azanylylidene))bis(methanylylidene))diphenol (L) ligand has been made and used as a sensor for determination of trace mercury and cadmium ions with cyclic voltammetry (CV) and differential pulse voltammetry (DPV) methods. Complexation studies of the ligand with Cu2+, Zn2+, Hg2+, Ni2+ and Cd2+ ions by conductometric method in acetonitrile–ethanol mixture at 25°C show that the ML complexes have formed. The formation constants of complexes were calculated from the computer fitting of the molar conductance–mole ratio data, and the stability of the resulting complexes varied in order of Cd2+ > Hg2+ > Cu2+ > Zn2+ > Ni2+. Then a simple and effective chemically modified carbon paste electrode with L was prepared, and the electrochemical properties and applications of the modified electrode were investigated. Under the optimal conditions, the detection limit was 0.0494 μg L−1 and 0.0782 μg L−1 for cadmium and mercury ions, respectively, and the linear range for both metal ions were from 1 to 100 μg L−1. The electrode shows high sensitivity, reproducibility and low cost, and was successfully applied to determination of Cd2+ and Hg2+ ions in water samples with recovery in the range of 97–101%.

Thermodynamic study of β-cyclodextrin-dye inclusion complexes using gradient flow injection technique and molecular modeling

Gradient flow injection technique-diode array spectrophotometry was applied for β-cyclodextrin (β-CD)-dye inclusion complex studies. A single injection of a small amount of mixed β-CD-dye solution (100μl) into the carrier solution of the dye and recording the spectra gave the titration data. The mole ratio data were calculated by calibrating the dispersion pattern using a calibrator dye (rose bengal). Model-based multivariate methods were used to analyze the spectral-mole ratio data and, as a result, estimate stability constants and concentration-spectral profiles. Reliability was tested by applying this method to study the β-CD host-guest complexes with several dyes as guest molecules. Singular value decomposition (SVD) was used to select the chemical model and reduce noise. Molecular modeling provided the ability to predict the guest conformation-orientation (posing) within the cavity of β-CD and the nature of the involved interactions. Among those dyes showing observable spectral variation, the stoichiometric ratio of β-CD: dye (and log Kf) of methyl orange, fluorescein, phenol red, 4-(2-pyridylazo) resorcinol (PAR), and crystal violet were calculated to be 1:1 (4.26±0.01), 1:1 (1.53±0.08), 1:1 (3.11±0.04), 1:1 (1.06±0.12), and 2:1 (5.27±0.03), respectively. Compared with the classical method of titration, this method is simple and fast and has the advantage of needing reduced human interference. Molecular modeling facilitates a better understanding of the type of interactions and conformation of guest molecules in the β-CD cavity. The details of the proposed method are discussed in this paper.

1H-NMR study of the stoichiometry and stability of the Ba2+, Sr2+, Hg2+, Pb2+, K+, Ag+, and Tl+ complexes with a new macrocyclic diamide in acetonitrile–nitrobenzene solvent mixture

Proton NMR technique was utilized to study the complexation reactions of a new macrocycle diamide with Ba2+, Sr2+, Hg2+, Pb2+, K+, Ag+, and Tl+ ions in % 50 (w/w) acetonitrile–nitrobenzene binary mixture. In all the cases, the chemical shifts of the single NMR signals due to the –O–CH2–CH2–O– and Ph–O–CH2– groups of the ligand were determined at 300 K. The exchange between free form of the macrocycle (I) and its complexes was fast on the NMR time scale and just a single population average 1H signal was observed. Formation constants of the resulting 1:1 complexes were determined by computer fitting of the chemical shift–mole ratio data. The stabilities of the resulting 1:1 complexes varying in the order Ba2+ > Sr2+ > Hg2+ > Pb2+ > Ag+ > K+ > Tl+ were determined. For two singlet groups of ligand (I) (Ph–O–CH2– and –O–CH2–CH2–O–), the values of the formation constants which were obtained from data fitting were found to be similar, but shift of the signal for Ph–O–CH2– group was larger than for –O–CH2–CH2–O– group. The theoretical studies on the structures and the energetic data of the five conformers of ligand macrocycle (I) and the complexes with Ba2+, Sr2+, Hg2+, Pb2+, Ag+, K+, and Tl+ have been performed by DFT-B3LYP/6-31G* method for ligand (I) and QM-PM6 method for the complexes. The comparison of the experimental and theoretical data with respect to the formation constants and the structures of the complexes have shown good agreement.

Competitive 7Li NMR study of the stoichiometry, stability and thermodynamic data for the complexation of Li+, Mn2+, Zn2+ and Cd2+ ions with two asymmetrical branched pentadentate (N5) amines containing pyridine moiety in ionic liquid–acetonitrile mixtures

Lithium-7 NMR spectroscopy was used to investigate the stoichiometry, stability and thermodynamic data of a Li+ complex with two asymmetrical branched amines, 3,6-bis(2-pyridylmethyl)-5-methyl-3,6-diazahexane-1-amine (A1) and 4,7-bis(2-pyridylmethyl)-6-methyl-4,7-diazaheptane-1-amine (A2) in 50–50 and 75–25wt% acetonitrile (AN)- [BMIM][PF6] (ionic liquid) mixture solution at various temperatures. A competitive 7Li NMR method was also employed to probe the complexation of Mn2+, Zn2+ and Cd2+ ions with A1 and A2 in the same solvent systems. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. There is an inverse relationship between the complex stability and the amount of ionic liquid in the solvent mixtures. The temperature dependence formation constant was used for the evaluation of the enthalpy and entropy values for the complexation reaction. It was concluded that in all complexes, except for lithium ion, the resulting complex enthalpy is stabilized and the ΔH compensates the TΔS contribution. In the all studied solvent mixtures, the stability of the resulting 1:1 complexes was found to vary in the order Cd2+>Mn2+>Zn2+>Li+.

Competitive 7Li NMR Study on the Mn2+, Zn2+ and Cd2+ Complexes of Two New Branched Hexadentate (N6) Amines Containing the Pyridine Moiety in Nitromethane and Acetonitrile Solutions

Lithium-7 NMR spectroscopy was used to investigate the stoichiometry and stability of a Li+ complex with two new branched amines, 4,7-bis(2-pyridylmethyl)-4,7-diazadecane-1,10-diamine (L1) and 4,8-bis(2-pyridylmethyl)-4,8-diazaundecane-1,11-diamine (L2), in acetonitrile and nitromethane. A competitive 7Li NMR method was also employed to probe the complexation of Mn2+, Zn2+ and Cd2+ ions with L1 and L2 in the same solvent systems. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data with an equation that relates the observed chemical shifts to the formation constant. In both solvents, the stability of the resulting 1:1 complexes was found to vary in the order Cd2+ > Zn2+ > Mn2+ > Li+.

Nuclear magnetic resonance study of the stoichiometry and stability of several HgX2–acetylemethylentriparatolylphosphorane complexes in various acetone–dimethylformamide mixtures

The reaction of phosphorus ylide, acetylmethylenetriparatolylphosphorane (L) with HgX2 (X = Cl, Br, I and NO3) in equimolar ratios using acetone and dimethylformamide as solvents leads to binuclear products. 31P NMR spectroscopy was used to investigate the stoichiometry and stability of a HgX2 complex with CH3COCHP(p-tolyl)3 (L) in binary acetone–dimethylformamide mixtures of varying composition. In all cases studied, the variation of 31P NMR chemical shift with the [HgX2]/[L] mole ratio indicated the formation of 1:1 complexes. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In all mercuric salts used, the stabilities of the resulting 1:1 complexes varied in the order Hg(NO3)2 > HgCl2 > HgBr2 > HgI2. It was found that, in the case of all complexes, an increase in the percentage of dimethylformamide in the solvent mixtures significantly decreases the stability of the complexes.

A combined experimental and density functional theory study on the complexation ability of 15-crown-5 with Li+, Na+, K+, and NH4 + cations

The complexation processes among Li+, Na+, K+, and NH4 + cations with the macrocyclic ligand, 15-crown-5 (15C5) have been studied in acetonitrile–methanol binary mixtures at different temperatures using conductometric method. The stability constants of the resulting 1:1 complexes were calculated from the computer fitting of the molar conductance–mole ratio data at various temperatures. The values of thermodynamic parameters ( $$ \Updelta H_{\text{c}}^{^\circ } $$ and $$ \Updelta S_{\text{c}}^{^\circ } $$ ) for the formation of the complexes were obtained from temperature dependence of the stability constants of complexes using van’t Hoff plots. In addition, a theoretical study has been carried out using density functional theory to obtain the stability of the complexes and the geometrical structure of the 15C5 and its complexes with Li+, Na+, K+ and NH4 + cations in the gas phase. We compared the experimental data with those obtained by quantum chemistry calculations to investigate the effect of the solvent on complexation process.

Complexation studies of Mn2+, Zn2+ and Cd2+ ions with a series of tetradentate (N4) Schiff base ligands containing pyridine moiety in acetonitrile and nitromethane solutions by a competitive NMR technique using 7Li nucleus as a probe

Lithium-7 NMR spectroscopy was used to investigate the stoichiometry and stability of a Li+ complex with N1,N2-bis(pyridin-2-ylmethylene)ethane-1,2-diamine (L1), N1,N3-bis(pyridin-2-ylmethylene)propane-1,3-diamine (L2) and N1,N4-bis(pyridin-2-ylmethylene) butane-1,4-diamine (L3) in acetonitrile (AN) and nitromethane (NM) solutions. A competitive 7Li NMR method was also employed to probe the complexation of Mn2+, Cd2+ and Zn2+ ions with L1, L2 and L3 in the same solvents. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In both solvents, the stability of the resulting 1:1 complexes were found to vary in the order Zn2+>Cd2+>Mn2+>Li+. In addition, the stability of M–L complexes of M2+ with the Schiff base ligands found to vary in the order M2+–L1 > M2+–L2 > M2+–L3.

Synthesis, characterization and Nuclear Magnetic Resonance study of the stoichiometry and stability of several zwitterionic mercury(II) complexes in dimethylsulfoxide

The reaction of the non-symmetric phosphonium salts [PPh2CH2PPh2CH2C(O)R]Br2 (R=4′-biphenyl (L1); OCH2Ph (L2); 4-methylphenyl (L3); 2-naphtyl (L4); 3-nitrophenyl (L5) and [PPh2CH2PPh2CH2C(O)R]Cl2 (R=2,4-dichlorophenyl (L6)), with mercury(II) halides in 1:1 (for chloride and bromide) and 1:2 (for iodide) mole ratio in methanol under mild conditions afford the monomeric P-coordinated complexes, [HgCl2(Br)(Ph2PCH2PPh2CH2C(O)R)] (R=4′-biphenyl (1), OCH2Ph (2), 4-methylphenyl (3), 2-naphtyl (4), 3-nitrophenyl (5)) and [HgCl3(Ph2PCH2PPh2CH2C(O)C6H4Cl2)] (6), [HgBr3(Ph2PCH2PPh2CH2C(O)R)] (R=4′-biphenyl (7), OCH2Ph (8), 4-methylphenyl (9), 2-naphtyl (10), 3-nitrophenyl (11) and [HgBr2(Cl)(Ph2PCH2PPh2CH2C(O)C6H4Cl2)] (12)), [HgBr2(I)(Ph2PCH2PPh2CH2C(O)R)] (R=4′-biphenyl (13), OCH2Ph (14), 4-methylphenyl (15), 2-naphtyl (16), 3-nitrophenyl (17)) and [HgCl2(I)(Ph2PCH2PPh2CH2C(O)C6H4Cl2)] (18). These complexes were fully characterized by elemental analysis and IR, 1H, 13C and 31P{1H} NMR spectra. In addition, 31P{1H} NMR spectroscopy was used to investigate the stoichiometry and stability of all complexes in pure dimethylsulfoxide solvent. The formation constants of the resulting 1:1 complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. It was found that, in pure dimethylsulfoxide, the stabilities of the resulting 1:1 complexes vary in the order L3>L4>L1>L5>L6>L2 and HgCl2>HgBr2>HgI2.

Multinuclear magnetic resonance study of N-phenyl-aza-15-crown-5 complexes with lithium, sodium and caesium ions in nonaqueous solvents

Nuclear magnetic resonances of 7Li, 23Na and 133Cs nuclei were used to study the lithium, sodium and caesium ion complexes with N-phenyl-aza-15-crown-5 (PhA15C5) in nitromethane (NM), acetonitrile (AN) and AN–NM mixture solutions. The chemical shift data indicated that these cations form 1 : 1 cation : ligand complexes with PhA15C5. The formation constants of the resulting complexes were calculated from the computer fitting of the chemical shift–mole ratio data. The results show that the complex formation constants of PhA15C5 with these cations vary in the order of Na+ > Li+ ≫ Cs+. Complexation of the lithium ion was also studied in binary AN–NM mixtures. It was found that the stability of the resulting complexes increases by an increase in the amount of NM in the solvent mixture.

Complexing ability of kryptofix5 with Ag+ in some binary mixed solvents at different temperatures

The stability constant (log Kf ) for complexation of 1,13-bis(8-quinolyl)-1,4,7,10,13-pentaoxatridecane (kryptofix5) with Ag+ has been determined conductometrically in acetonitrile–ethyl acetate (AN–EtOAc), methanol–ethyl acetate (MeOH–EtOAc), methanol–water (MeOH–H2O) and dimethyl sulfoxide–ethyl acetate (DMSO–EtOAc) solutions at different temperatures. A 1 : 1 [ML] complex was formed between the metal cation and ligand in most solvent systems. The stability constant of the resulting 1 : 1 complex was determined from computer fitting of the conductance–mole ratio data. The stability order of the (kryptofix5.Ag)+ complex in the studied binary mixed solvent solutions at 25°C was found to be MeOH–EtOAc > AN–EtOAc > DMSO–EtOAc. The results show that in some cases the stoichiometry of the complex formed between Ag+ and the ligand changes with the nature of the solvent and that solvation numbers of the metal cation and the resulting complexes change with temperature. The values of the standard thermodynamic parameters (, ) show that in all cases the (kryptofix5.Ag)+ complex is entropy stabilized, but the enthalpy, depending on solvent system, is stabilizing or destabilizing.

31P NMR study of the stoichiometry and stability of several mercury(II) halides with a phosphorus ylide in different solvents

31P NMR measurements were employed to monitor the stoichiometry and stability of complexes between HgCl2, HgBr2 and HgI2 with 4-methylbenzoylmethylenetriphenylphosphorane (L) in acetonitrile (AN), dimethylsulfoxide (DMSO), dimethylformamide (DMF) and tetrahydrofuran (THF) solvents of varying composition. In all cases studied, the variation of 31P chemical shift with the [M]/[L] mole ratio indicated the formation of 1:1 complexes. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In all solvents used, the stabilities of the resulting 1:1 complexes varied in the order HgCl2>HgBr2>HgI2.

Simultaneous separation and extraction of Ag(I), Pb(II) and Pd(II) ions by solid phase method and determination of these ions by flame atomic absorption spectrometry

A simultaneous preconcentration and separation method for determination of trace amount of dissolved Ag+, Pb2+ and Pd2+ ions by modified octadecyl silica membrane disks with DBzDA18C6 was developed. The adsorbed metal complexes were eluted from disk with 10 mL of 4 M KCl and determined by flame atomic absorption spectroscopy. Several parameters such as anion effect, pH of sample solution, type of eluent, amount of ligand, sample and elution flow rate were evaluated. The effect of diverse ions on preconcentration was also investigated. A precocentration factor of 110 can easily be achieved depending on the volume of the sample. For 100 mL of the solution the linear dynamic rang were found to be 30–1000, 140–6000, 60–900 μg l−1 for Ag+, Pb2+ and Pd2+, respectively. Based on three standard deviation of the blank the detection limit was obtained as 1.8, 8.0 and 4.2 μg L−1 for Ag+, Pb2+, Pd2+, respectively. The formation constants of Ag+ and Pb2+ ions with DBzDA18C6 at 25 °C were determined from the molar conductance–mole ratio data. This method was applied for the determination of Ag+, Pb2+ and Pd2+ in environmental water, tea and soil samples.

Complexation of 4′-Nitrobenzo-15-crown-5 with Zn2+, Mn2+, Cr3+ and Sn4+ Cations in Acetonitrile–Ethanol Binary Mixtures

The complexation reactions of 4′-nitrobenzo-15-crown-5 (4′NB15C5) with Zn2+, Mn2+, Cr3+ and Sn4+ cations were studied in acetonitrile–ethanol (AN–EtOH) binary solvent mixtures at different temperatures by the electrical conductometry method. The stability constants of the resulting 1:1 complexes were determined from computer fitting of the conductance versus mole ratio data. The results show that the selectivity order of 4′NB15C5 for the metal cations in the AN–EtOH (mol-%AN=76) binary solvent at 298.15 K is: Cr3+>Mn2+≈Zn2+>Sn4+, but the selectivity order changes with the composition of the mixed solvents. A nonlinear relationship was observed between the stability constants (log 10 K f) of these complexes and the composition of the AN–EtOH binary solvents. The corresponding thermodynamic parameters \((\Delta H_{\mathrm{c}}^{\mathrm{o}}, \Delta S_{\mathrm{c}}^{\mathrm{o}})\) were obtained from the temperature dependence of the stability constants using van’t Hoff plots. The results show that the values and also the sign of these parameters are influenced by the nature and composition of the mixed solvents.

Spectrophotometric study of complex formations between 1-(2-pyridylazo)-2-naphthol (PAN) and some metal ions in organic solvents and the determination of thermodynamic parameters

The complexation reactions between Ni 2+, Co 2+ and Zn 2+ metal ions with PAN in methanol (MeOH), acetonitrile (AN) and dimethyl sulfoxide (DMSO) were studied using a spectrophotometric method. The stability constants of the resulting complexes were determined from computer fitting absorbance mole-ratio data. The results revealed that the stability constants of complexes are varying in order of Ni 2+ < Zn 2+ < Co 2+ for all solvents. The values of the thermodynamic parameters (Δ H°, Δ S° and Δ G°) for complexation reactions were obtained from the temperature dependence of the stability constants.

Proton NMR probing of stoichiometry and thermodynamic data for the complexation of Na + and Li + ions with 15-Crown-5 in acetonitrile–nitrobenzene mixtures

Proton NMR was used to study the complexation reaction of Li + and Na + ions with 15-Crown-5 (15C5) in a number of binary acetonitrile (AN)–nitrobenzene (NB) mixtures at different temperatures. In all cases, the exchange between free and complexed 15C5 was fast on the NMR timescale and only a single population average 1H signal was observed. The formation constants of the resulting 1:1 complexes in different solvent mixtures were determined by computer fitting of the chemical shift mole ratio data. There is an inverse relationship between the complex stability and the amount of AN in the solvent mixtures. The enthalpy and entropy values for the complexation reaction were evaluated from the temperature dependence of the formation constants. In all the solvent mixtures studied, the resulting complex is enthalpy stabilized but entropy destabilized. Finally, the experimental results were compared with theoretical ones that were obtained from molecular modeling methods. Based on our results, it is most probable that Li +–15C5 in solvent stays in a rather nesting complex form with greater Log K f values, but Na +–15C5 forms a complete perching complex form with lower Log K f values.