Determination Of Equilibrium Constants Research Articles

Reversed-phase ion-pair liquid chromatographic method for determination of reaction equilibria involving ionic species: Exemplification of the method using ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions

A reversed-phase ion-pair liquid chromatographic method is presented for the determination of reaction equilibria involving ionic species of the same charge sign as reactant and product compounds. It has been demonstrated that ion-exchange chromatography or reversed-phase ion-pair chromatography is a useful tool for the determination of equilibrium constants of chemical reactions involving ionic species such as metal complexation reactions. Previous work with these methods has been based on the assumption that the limiting retention factors of the reactant and product species are constant independent of concentration of the chemical species (X) in the mobile phase, which reacts with the analyte compound. However, when all the reactant and product species are ions of the same charge sign as that of the species X, it is virtually impossible to apply these methods to the equilibrium constant determination because the retention factors of both the reactant and product species may depend on the concentration of X. In this study, an alternative approach was developed that estimates the limiting retention factors of ionic species from the dependence of the retention factor on the ionic strength of the mobile phase. Ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions were used as model reactions to test this method. The equilibrium constants determined by this method are in good agreement with those obtained by a UV–visible spectrophotometric method.

Simultaneous determination of equilibrium constants and enthalpy changes by titration calorimetry: Methods, instruments, and uncertainties

Calorimetric methods have been used to determine equilibrium constants since 1937, but no comprehensive review of the various calorimeters and methods has been done previously. This article reports methods for quantitative comparison of the capabilities of calorimeters for simultaneous determination of equilibrium constants and enthalpy changes, for determining optimal experimental conditions, and for assessing the effects of systematic and random errors on the accuracy and precision of equilibrium constants and enthalpy changes determined by this method.

Optimization of supercritical extraction of nimbin from neem seeds in presence of methanol as co-solvent

Mathematical modeling and optimization of the extraction of nimbin from neem seeds using supercritical carbon dioxide with methanol as co-solvent is the subject of this study. At first a correlation for Sherwood number (Sh) as a function of Reynolds number (Re) and Schmidt number (Sc) was proposed using a Genetic Algorithm (GA) technique. This correlation was compared to previous correlations and was found to give the most accurate results. Moreover, optimum conditions (temperature, pressure, solvent flow rate and particle diameter) which maximizes the extraction yield have been determined using GA. At the next step, methanol was used as a co-solvent and the dynamic equilibrium constant of solute between the solid phase and the solvent was estimated. By applying the new determined equilibrium constant, good agreement between the model and experimental data was observed.

ChemInform Abstract: Determination of Equilibrium Constants for Ligand Exchange Reactions of (TcNX4)- (X: Cl, Br) by Means of EPR.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Free energy of formation for green rust sodium sulphate (NaFe II6Fe III3(OH) 18(SO 4) 2(s))

In a recent study, sulphate-bearing green rust ( GR SO 4 ) was shown to incorporate Na + in its structure (NaFe II 6Fe III 3(OH) 18(SO 4) 2(s); GR Na, SO 4 ). The compound was synthesised by aerial oxidation of Fe(OH) 2(s) in the presence of NaOH. This paper reports on its free energy of formation ( Δ G f 0 ) . Freshly synthesised GR Na, SO 4 was titrated with 0.5 M H 2SO 4 in an inert atmosphere at 25 °C, producing dissolved Fe 2+ and magnetite or goethite. Solution concentrations, PHREEQC and the MINTEQ database were used to calculate reaction constants for the reactions: 2 NaFe II 6 Fe III 3 ( OH ) 18 ( SO 4 ) 2 ( s ) + 12 H + ( aq ) ⇆ 9 Fe 2 + ( aq ) + 2 Na + ( aq ) + 4 SO 4 2 - ( aq ) + 3 Fe II Fe III 2 O 4 ( s ) + 24 H 2 O ( l ) , K = 10 54.5 ± 3.0 and NaFe II 6 Fe III 3 ( OH ) 18 ( SO 4 ) 2 ( s ) + 9 H ( aq ) + ⇆ 6 Fe 2 + ( aq ) + Na + ( aq ) + 2 SO 4 2 - ( aq ) + 3 α - FeOOH ( s ) + 12 H 2 O ( l ) , K = 10 42.5 ± 3.7 . From the determined equilibrium constants and published Δ G f 0 values for the other compounds, we derived Δ G f 0 = −6366 ± 18 kJ/mol for anhydrous GR Na, SO 4 . The solubility product at 25 °C and atmospheric pressure is K = 10 −210.5±3.2. It is not yet known if the extent of Na + incorporation in GR SO 4 depends on formation pathway; it cannot be excluded that both Na-free GR SO 4 and GR Na, SO 4 exist. If so, uncertainty in Δ G f 0 determined from acid titration is such that the E H–pH stability fields of the two phases are statistically indistinguishable for Na + concentrations as low as ∼30 μM (2 SD level; 0.036 M SO 4 2− concentration). In sea water, where Na + and SO 4 2− concentrations are high, but soluble Fe 2+ is low, GR is expected to form where local conditions increase concentration gradients, such as for corrosion of metallic iron and steel. Another example of an environment that would provide GR Na, SO 4 -favourable conditions is a degrading concrete and steel radioactive waste storage facility, where groundwater is saline. Green rust is a well-known sink for redox-active trace components, making it a compound that should be considered in risk assessment modelling of groundwater quality. Phase stability is critical in such simulations.

Some critical aspects in the determination of binding constants by electrospray ionisation mass spectrometry at the example of arsenic bindings to sulphur‐containing biomolecules

The influences of reactant concentrations, solvent type, acid strength, pH conditions and ionic strength on the determination of apparent gas-phase equilibrium constants K using electrospray ionisation mass spectrometry (ESI-MS) were elucidated. As example serves the interaction of the tripeptide glutathione (GSH) with phenylarsine oxide (PAO). It was shown that rising initial concentrations of both reactants were not adequately compensated by increasing signal intensities of the reaction products in the mass spectra. The equilibrium constant for the formation of the phenylarsenic-substituted peptide species decreased from 1.42 x 10(5) +/- 1.81 x 10(4) l micromol(-1) to 1.54 x 10(4) +/- 1.5 x 10(3) l micromol(-1) with rising initial GSH concentrations from 1 to 10 microM at fixed PAO molarity of 50 microM. K values resulting from a series with a fixed GSH molarity of 5 microM and a PAO molarity varied from 10 to 100 microM remained in a narrower range between 4.59 x 10(4) +/- 2.15 x 10(4) l micromol(-1) and 1.07 x 10(4) +/- 4.0 x 10(3) l micromol(-1). In contrast, consumption numbers calculated from the ion intensity ratios of reaction products to the unreacted peptide were not influenced by the initial reactant concentrations. In a water-acetonitrile-acetic acid mixture (48:50:2, v:v), the consumption of 5 micro M GSH increased from 8.3 +/- 1.4% to 39.6 +/- 1.6% with increased molar excess of PAO from 2 to 20, respectively. The GSH consumption was considerably enhanced in a changed solvent system consisting of 25% acetonitrile and 75% 10 mM ammonium formate, pH 5.0 (v:v) up to 80% of the original peptide amount at an only threefold molar arsenic excess.

Acid/base and hydrogen bonding effects on the proton-coupled electron transfer of quinones and hydroquinones in acetonitrile: Mechanistic investigation by voltammetry, 1H NMR and computation

This report seeks to address the role of hydrogen bonding with Brønsted acids and bases in proton-coupled electron transfer (PCET) as it pertains to concerted or stepwise pathways of quinone (Q) and hydroquinone (QH 2) electrochemistry. This study was performed using a series of techniques that included cyclic voltammetry (CV), digital simulations, computational chemistry and 1H NMR. Hydrogen bonding was inferred by a decrease in diffusion coefficient ( D) values measured using a pulsed gradient echo- (PGE-) 1H NMR technique. Changes of 40.8% and 37.9% in D values were only noted after the addition of two equivalents of acetate to 1,4-hydroquinone (1,4-QH 2) and catechol (1,2-QH 2), respectively. In contrast, the D values for the addition of selected amines (pyridine, N,N-diisopropylethylamine and triethylamine) changed only 3.2% on average. Quantum mechanical calculations were conducted to determine the p K a of all quinoid species to serve as a starting point for the determination of equilibrium constants in voltammetric simulations. Simulations indicate that 1,4-benzoquinone undergoes stepwise electron–proton transfer upon addition of acetic acid, N-ethyldiisopropylammonium perchlorate and pyridinium nitrate and were simulated without the presence of hydrogen bonds. The QH 2 compounds show stepwise proton–electron transfers after addition of the both the conjugate amines and acetate.

Formation and Stability of Gaseous WS2Cl2, WS2Br2 and WS2I2 – A Combined Experimental and Theoretical Study

AbstractGaseous WS2Cl2 and WS2Br2 are formed by the reaction of solid WS2 with chlorine resp. bromine at temperatures of about 1000 K. This could be shown by mass spectrometric measurements. The heats of formation and entropies of WS2Cl2 and WS2Br2 have been determined by means of mass spectrometry (MS) and quantum chemical calculations (QC). WS2I2 could not be detected by experimental methods. This is in line with the quantum chemically determined equilibrium constant of the formation reaction. The following values are given:, ΔfH0298(WS2Cl2) = –230.8 kJ·mol–1 (MS), ΔfH0298(WS2Cl2) = –235.0 kJ·mol–1 (QC),, S0298(WS2Cl2) = 370.7 J·K–1·mol–1 (QC) and, cp0T(WS2Cl2) = 103.78 + 7.07 × 10–3 T – 0.93 × 105 T–2 – 3.25 × 10–6 T2 (298.15 K < T < 1000 K) (QC). ΔfH0298(WS2Br2) = –141.9 kJ·mol–1 (MS), ΔfH0298(WS2Br2) = –131.5 kJ·mol–1 (QC),, S0298(WS2Br2) = 393.9 J·K–1·mol–1 (QC) and, cp0T(WS2Br2) = 104.84 + 5.32 × 10–3 T – 0.75 × 105 T–2 – 2.45 × 10–6 T2 (298.15 K < T < 1000 K) (QC). ΔfH0298(WS2I2) = –18.0 kJ·mol–1 (QC), S0298(WS2I2) = 409.9 J·K–1·mol–1 (QC) and, cp0T(WS2I2) = 105.17 + 4.77 × 10–3 T – 0.67 × 105 T–2 – 2.19 × 10–6 T2 (298.15 K < T < 1000 K) (QC). These molecules have the expected C2v‐symmetry.

Determination of the Hydrolysis Constants and Solubility Product of Chromium(III) from Reduction of Dichromate Solutions by ICP-OES and UV–Visible Spectroscopy

The determination of equilibrium constants is difficult when several chemical species are simultaneously present in solution. In this investigation, optical emission spectroscopic determinations of chromium(III) concentration in a 10−4 mol⋅dm−3 solution, prepared from K2Cr2O7 reduced in HNO3 or HCl media, were used to construct the pCr(aq)–pC H diagram. This diagram was used to calculate the pC H borderline of precipitation, to estimate the solubility product $(\log_{10}K_{\mathrm{sp,Cr(OH)}_{3}}^{*})$ , and the hydrolysis constants $(\log_{10}\beta_{\mathrm{Cr,H}}^{*},\log_{10}\beta_{\mathrm{Cr,2H}}^{*}$ , and $\log_{10}\beta_{\mathrm{Cr,3H}}^{*})$ of Cr(III). The hydrolysis constants were also calculated using the SQUAD and SUPERQUAD software, along with the average ligand number method. UV-Vis absorption data and associated variables were used in SQUAD, SUPERQUAD, and the average ligand calculations. Results are: 9.00±0.04 for the pC H at the onset of precipitation, 12.40 for $\log_{10}K_{\mathrm{sp,Cr(OH)}_{3}}^{*}$ , −3.52±0.02 for $\log_{10}\beta_{\mathrm{Cr,H}}^{*}$ , −9.30±0.87 for $\log_{10}\beta_{\mathrm{Cr,2H}}^{*}$ and −17.18±0.16 for $\log_{10}\beta_{\mathrm{Cr,3H}}^{*}$ , respectively. All methods produced essentially the same values for the hydrolysis constants of Cr(III).

Host-guest complexation studied by fluorescence correlation spectroscopy: adamantane-cyclodextrin inclusion.

The host-guest complexation between an Alexa 488 labelled adamantane derivative and β-cyclodextrin is studied by Fluorescence Correlation Spectroscopy (FCS). A 1:1 complex stoichiometry and a high association equilibrium constant of K = 5.2 × 104 M−1 are obtained in aqueous solution at 25 °C and pH = 6. The necessary experimental conditions are discussed. FCS proves to be an excellent method for the determination of stoichiometry and association equilibrium constant of this type of complexes, where both host and guest are nonfluorescent and which are therefore not easily amenable to standard fluorescence spectroscopic methods.

Influence of current and temperature on discharge characteristics of electrochemical nickel−cadmium system

The paper elaborates determination of characteristic values in the discharging process of non-hermetic nickel-cadmium galvanic battery with nominal voltage Un = 60 V and nominal capacity qn = C5 = 190 Ah and its dependence from current and temperature. Study has been performed with the set of experimental metering of voltages, electromotive force, current from discharge time range and electromotive force in steady state regime before and after battery charging. Electromotive force characteristics are obtained by using the Nernst?s equation, while the least square method was used to determine the average values of internal electrical resistivity, power losses and efficiency level. These results were used in the approximate exponential functions to determine the range dependence of the efficiency level from the internal electrical resistance of discharge current in reliance from the temperature range. Obtained results show that, in accordance to the given voltage variation of 10% Un, this type of battery holds maximal full load current of one hour capacity at the temperature of 25?C and maximal full load current of two hours capacity at the temperature of ?30?C. The methodology used in the case study covers determination of the electromotive force in time range based on the metered results of values during complete battery fullness and emptiness with prior determination of equilibrium constants of galvanic battery reaction through method suggested by the author of this paper. Further process, using the electromotive force values obtained through the aforementioned process, the metered current, and approximate polynomial function of the nominal discharge voltage characteristic determines range of battery internal electric resistance from time, followed by the selection of discharge cases with average values for: voltage, electromotive force, internal electrical resistance, available and utilized power, power losses, and battery efficiency level. An overview of the obtained characteristics for analyzed battery and their comparison with the producers prescribed values and standards led to gaining of the valuable data that show how and in what measure do current and temperature influence the discharge characteristic of non-hermetic nickel-cadmium batteries with an especial observation of internal electrical resistance and battery efficiency level. Obtained results show that electrochemical power sources may provide electric energy with prescribed quality and quantity, with high level of work reliability, as well as with all other positive technical and economic effects within the given current-temperature range.

Computational Calculation of Equilibrium Constants: Addition to Carbonyl Compounds

Hydration reactions are relevant for understanding many organic mechanisms. Since the experimental determination of hydration and hemiacetalization equilibrium constants is fairly complex, computational calculations now offer a useful alternative to experimental measurements. In this work, carbonyl hydration and hemiacetalization constants were calculated from the free energy differences between compounds in solution, using absolute and relative approaches. The following conclusions can be drawn: (i) The use of a relative approach in the calculation of hydration and hemiacetalization constants allows compensation of systematic errors in the solvation energies. (ii) On average, the methodology proposed here can predict hydration constants within +/- 0.5 log K(hyd) units for aldehydes. (iii) Hydration constants can be calculated for ketones and carboxylic acid derivatives within less than +/- 1.0 log K(hyd), on average, at the CBS-Q level of theory. (iv) The proposed methodology can predict hemiacetal formation constants accurately at the MP2 6-31++G(d,p) level using a common reference. If group references are used, the results obtained using the much cheaper DFT-B3LYP 6-31++G(d,p) level are almost as accurate. (v) In general, the best results are obtained if a common reference for all compounds is used. The use of group references improves the results at the lower levels of theory, but at higher levels, this becomes unnecessary.

A three-compartment model for micropollutants sorption in sludge: Methodological approach and insights

In sludge resulting from wastewater treatment, organic micropollutants sorb to particles and to dissolved/colloidal matter (DCM). Both interactions may influence their physical and biological fate throughout the wastewater treatment processes. To our knowledge, sludge has never been considered as a three-compartment matrix, in which micropollutants coexist in three states: freely dissolved, sorbed-to-particles and sorbed-to-DCM. A methodology is proposed to concomitantly determine equilibrium constants of sorption to particles (K part) and to DCM (K DCM). Polycyclic Aromatic Hydrocarbons (PAHs) were chosen as model compounds for the experiments. The logarithm of estimated equilibrium constants ranged from 3.1 to 4.3 and their usual correlation to PAH hydrophobicity was verified. Moreover, PAH affinities for particles and for DCM could be compared. Affinity for particles was found to be stronger, probably due to their physical and chemical characteristics. This work provided a useful tool to assess the freely dissolved, sorbed-to-particles and sorbed-to-DCM concentrations of contaminants, which are necessary to accurately predict their fate. Besides, guidelines to investigate the link between sorption and the fundamental concept of bioavailability were proposed.

1H NMR investigation of self-association of vanillin in aqueous solution

A self-association of vanillin have been studied by 1H NMR spectroscopy using the analysis of proton chemical shifts changes in aqueous solution as a function of concentration. The experimental results have been analysed using indefinite non-cooperative and cooperative models of molecular self-association, enabling the determination of equilibrium constants, parameters of cooperativity and the limiting values of vanillin proton chemical shifts in the complex. It was found that the dimer formation creates energetically favourable conditions for subsequent molecular association.

Introduction of non-natural amino acid residues into the substrate-specific P 1 position of trypsin inhibitor SFTI-1 yields potent chymotrypsin and cathepsin G inhibitors

A series of trypsin inhibitor SFTI-1compounds modified in substrate-specific P 1 position was synthesized by the solid-phase method. Lys5 present in the wild inhibitor was replaced by Phe derivatives substituted in para position of the phenyl ring, l-pyridylalanine and N-4 -nitrobenzylgycine. Their inhibitory activities with bovine α-chymotrypsin and cathepsin G were estimated by determination of association equilibrium constants ( K a). All analogues inhibited bovine α-chymotrypsin. The highest inihbitory activity displayed peptides with the fluorine, nitro and methyl substituents. They were 13–15-fold more active than [Phe 5]SFTI-1 used as a reference. They are the most potent chymotrypsin inhibitors of this size. Substitution of Lys5 by Phe did not change the cathepsin G inhibitory activity. Introduction of Phe( p-F), Phe( p-NH 2) and Phe( p-CH 3) in this position retained the affinity towards this proteinase, whereas Phe( p-guanidine) gave an inhibitor more than twice as active, which appeared to be stable in human serum. On the other hand, a peptomeric analogue with N-4-nitrobenzylglycine failed to inhibit cathepsin G. Despite the fact the introduced amino acids were non-coded, the peptide bonds formed by them were hydrolyzed by chymotrypsin. We postulate that additional interaction of para-substitutents with the enzyme are responsible for the enhanced inhibitory activity of the analogues.

A review of chloride assisted copper sulfide leaching by oxygenated sulfuric acid and mechanistic considerations

The beneficial effect of chloride on sulfide leaching in sulfuric acid has been widely reported over the last 3–4 decades but the reasons have not been resolved. A review of recent literature shows that sulfide leaching is complex due to alternative reaction paths, competitive reactions and interim compounds formed on solid surfaces or in solutions. This study focuses on analysis of rate data for covellite leaching by oxygenated sulfuric acid in the presence of sodium chloride and comparison with the leaching data of chalcocite. The published results for initial copper leaching from covellite are analysed on the basis of a shrinking particle kinetic model to determine the apparent rate constants and reaction orders with respect to the concentrations of chloride, dissolved oxygen, and hydrogen ions. The first stage leaching of chalcocite to an intermediate CuS appears to be controlled by the mass transport of oxygen to the sulfide surface. A comparison has been made between the second stage leaching of chalcocite and the initial leaching of pure covellite to produce elemental sulfur by considering the effect of temperature on dissolved oxygen concentration and apparent rate constants. The Arrhenius plots gave comparable values for activation energy for covellite (101 kJ mol − 1 ) and second stage leaching of chalcocite (96 kJ mol − 1 ). A linear correlation of stability constants was used to determine equilibrium constants for the formation of CuS 2 and Cu(OH)(Cl). The peak potentials of voltammograms of covellite are in reasonable agreement with the predicted potentials based on thermodynamics of a range of solid phases including CuS, CuS 2, Cu(OH)Cl, and Cu 2Cl(OH) 3. These observations are used to propose a reaction mechanism via mixed-ligand complex species.

Comparative study on uni-univalent and uni-bivalent ion-exchange reaction on Doulite A-116

Determination of ion-exchange equilibrium constant (K) for Cl−/I− and Cl−/C2O42− system was studied at different temperatures from 25 to 45°C and by varying concentration of iodide and oxalate ion solution. For both uni-univalent and uni-bivalent exchange systems, using 0.5 g of ion-exchange resin DUOLITE A-116 (in chloride form), the value of K increases with rise in temperature i.e., from 13.0 at 25°C to 19.05 at 45°C for Cl−/I− system and 33.0 at 25°C to 63.0 at 45°C for Cl−/C2O42− system indicating the endothermic ion-exchange reaction. The difference in K values at the same temperature for the two was related to the ionic charge of exchangeable ions in the solution.

Redox-Regulated Ethylene Binding to a Rhenium-Thiolate Complex

The influence of oxidation state on the reversibility of carbon-sulfur bond forming reactions between ethylene and [Re(DPPBT)(3)](n+) (n = 0, +1, +2; DPPBT = 2-diphenylphosphinobenzenethiolate) has been investigated. For the neutral complex [Re(DPPBT)(3)], no reaction with ethylene is spectroscopically detectable consistent with the determined equilibrium constant, K(1), of (1.9 +/- 0.4) x 10(-11) M(-1). Oxidation by one electron to [Re(DPPBT)(3)](+) yields a stable complex that rapidly and reversibly binds ethylene with electrochemically determined constants of k(f) = (1.2 +/- 0.2) x 10(-1) M(-1) s(-1), k(r) = (3.0 +/- 0.4) x 10(-2) s(-1), and K(2) = 4.0 +/- 0.8 M(-1). C-S bond formation/cleavage can be regulated by ethylene concentration, and the system is stable to multiple cycles of nitrogen/ethylene purges. Further oxidation to the dication in the presence of ethylene by chemical or electrochemical methods stabilizes the C-S bond, K(3) = (2.5 +/- 0.9) x 10(9) M(-1), and the dithioether product has been characterized by X-ray crystallography. The large differences in K as a function of charge permit the controlled binding and release of ethylene as a function of applied potential.

Experimental determination of equilibrium constant for the complexing reaction of nitric oxide with hexamminecobalt(II) in aqueous solution

Ammonia solution can be used to scrub NO from the flue gases by adding soluble cobalt(II) salts into the aqueous ammonia solutions. The hexamminecobalt(II), Co(NH 3) 6 2+, formed by ammonia binding with Co 2+ is the active constituent of eliminating NO from the flue gas streams. The hexamminecobalt(II) can combine with NO to form a complex. For the development of this process, the data of the equilibrium constants for the coordination between NO and Co(NH 3) 6 2+over a range of temperature is very important. Therefore, a series of experiments were performed in a bubble column to investigate the chemical equilibrium. The equilibrium constant was determined in the temperature range of 30.0–80.0 °C under atmospheric pressure at pH 9.14. All experimental data fit the following equation well: K p = ( 1.9051 ± 0.124 ) × 10 − 6 exp 5359.25 ± 280.13 T ( ba r − 1 ) where the enthalpy and entropy are Δ H° = −(44.559 ± 2.329) kJ mol −1 and Δ S° = −(109.50 ± 7.126) J K −1 mol −1, respectively.

Spectrophotometric Determination of the Ionization Constants of Aqueous Nitrophenols at Temperatures up to 225 °C

The UV-visible spectra of aqueous o-, m-, and p-nitrophenol were measured as a function of pH at temperatures from 50 to 225 °C at a pressure of 7 MPa. These were used to determine equilibrium constants for the acid ionization reaction of each isomer. The new results were combined with literature data on the ionization of nitrophenols and used for parameter optimization in the thermodynamic model of Marshall and Franck (J. Phys. Chem. Ref. Data 10:295–304, [1981]), to describe the dependence of ionization properties on temperature and pressure. The model yields predictions of the ionization constants for o-, m-, and p-nitrophenol, log 10Ka, to at least 250 °C and 20 MPa with an estimated uncertainty in log 10Ka of less than ±0.06.