Alkylation Of Anion Research Articles

Coordination Sites for Sodium and Potassium Ions in Nucleophilic Adeninate Contact ion-Pairs: A Molecular-Wide and Electron Density-Based (MOWED) Perspective.

The adeninate anion (Ade−) is a useful nucleophile used in the synthesis of many prodrugs (including those for HIV AIDS treatment). It exists as a contact ion-pair (CIP) with Na+ and K+ (M+) but the site of coordination is not obvious from spectroscopic data. Herein, a molecular-wide and electron density-based (MOWED) computational approach implemented in the implicit solvation model showed a strong preference for bidentate ion coordination at the N3 and N9 atoms. The N3N9-CIP has (i) the strongest inter-ionic interaction, by −30 kcal mol−1, with a significant (10–15%) covalent contribution, (ii) the most stabilized bonding framework for Ade−, and (iii) displays the largest ion-induced polarization of Ade−, rendering the N3 and N9 the most negative and, hence, most nucleophilic atoms. Alkylation of the adeninate anion at these two positions can therefore be readily explained when the metal coordinated complex is considered as the nucleophile. The addition of explicit DMSO solvent molecules did not change the trend in most nucleophilic N-atoms of Ade− for the in-plane M-Ade complexes in M-Ade-(DMSO)4 molecular systems. MOWED-based studies of the strength and nature of interactions between DMSO solvent molecules and counter ions and Ade− revealed an interesting and unexpected chemistry of intermolecular chemical bonding.

New Biobased Sulfonated Anionic Surfactants Based on the Esterification of Furoic Acid and Fatty Alcohols: A Green Solution for the Replacement of Oil Derivative Surfactants with Superior Proprieties.

The surfactant market represents a key sector of the chemical industry and encompasses many diverse applications. Their sustainability in terms of feedstock used, synthetic procedure, biodegradability, and formulation are crucial parameters to assessing the environmental impact of the surfactant. The anionic surfactant linear alkyl benzene sulfonates have proven successful to date because of their high performance, low cost, and extensive studies within formulations to optimize performance, allowing usage in a large variety of applications, especially in cleaning. Due to their advantageous properties and extensive research and development, their substitution with a biobased surfactant such as sodium dodecyl sulfate has struggled to succeed. Furan surfactants have been reported as valuable candidates for the implementation of green alternatives to traditional anionic sulfonated surfactants with a perfect trade-off between performances and green credentials. However, their implementation suffers of scalability and high cost in producing the final product due to feedstock availability and low yields of the final product. Herein, we report a new class of furan surfactants, sulfonated alkyl furoates, which are derived from the esterification of furoic acid and fatty alcohols, followed by a sulfonation step. Compared to traditional surfactants, they showed more favorable behavior in basic proprieties (such as critical micelle concentration, ecotoxicity, hard water resistance, surface tension water/oil), which gives a good prospective for the introduction of a new biobased chemical with superior performances.

Quantification of the interactions in halide-anion-based imidazolium ionic liquids

Non-covalent interactions between constituent ions of ionic liquids (ILs) define their distinctive physicochemical properties and are critical for understanding their micro and bulk structures as well as designing new task-specific ILs. Therefore, the quantification of these interactions can improve our understanding of this unique class of materials. A set of 20 halide-anion-based imidazolium ILs (Cnmim X, X = Cl, Br, I, and BF4; n = 2, 4, 6, 8, and 10) was selected for this study. The variation of the anion (hydrogen-bond-acceptor property and size), presence of water, and the alkyl chain length of the imidazolium ring have all been considered as parameters when attempting to address mainly the following two fundamental questions: How does the strength of hydrogen bonding in these selected Coulomb systems change? How much do dispersion forces play a role in the net attractive interaction energy despite being weak? To this end, dispersion-corrected density functional theory (DFT) computations were executed to acquire the optimized structures of all the considered ILs, followed by an ensemble of NCI and QATIM analyses to explore the strength of non-covalent interactions. Further, quantum mechanical energy decomposition analysis (QM-EDA) based on symmetry-adapted-perturbation-theory (SAPT) has been employed to dissect the total interaction energy into its components. An assessment of QM-EDA demonstrates that the electrostatic interaction dominates the intermolecular attraction, although induction and dispersion components also play a substantial role. The dispersion energies are amplified when water is present, as well as when anion size and alkyl chain length increase. We quantified the non-covalent interactions between ion pairs using NCI-RDG and Bader's QTAIM analyses. Strong hydrogen bonding with a partial covalent character was observed between monoatomic anions and C2-proton of the imidazolium ring, but for the multiatomic anion (BF4−) and interaction between imidazolium ring alkyl groups and anions, a weak electrostatic hydrogen bonding was found. The hydrogen bonding strength decreases with increasing anion size; it is strongest in the C2mim Cl ion pair. NBO analysis gives a clear indication of nX→σC−H*(X=Cl,Br,I,andF) type intermolecular interaction with highest stabilization energy (En→σ*(2)). A clear correlation between E(2) and hydrogen bond lengths were observed. Overall, the current study illuminates the intricate network of covalent-like and non-covalent interactions in selected imidazolium ILs based on halide anions.

Characterization of cholinium-carboxylate-based aqueous biphasic systems

In the past years, large efforts have been placed in the development of novel separation techniques with improved resolution, simplicity, speed and easy to scale-up. Among these, ionic-liquid-based (IL-based) aqueous biphasic systems (ABS) have been broadly proposed for the separation of high-value compounds, allowing improved extraction performance and purification. More recently, significant efforts have been arranged on the synthesis and use of novel ILs with both an acceptable environmental footprint and enhanced biocompatibility. In this sense, this work aims to characterize ABS composed of cholinium carboxylate ILs ([Ch][CnO2], with n = 2 to 7), K3PO4 and water. The respective ternary phase diagrams, including binodal curves, tie-lines and tie-line lengths, were determined at (298 ± 1) K and at atmospheric pressure. The ability to form ABS (or of the IL to be salted-out) increases with the increase of the alkyl chain length of the IL anion, up to [Ch][C5O2]; nevertheless, for longer anion alkyl chain lengths ([Ch][C6O2] and [Ch][C7O2]) the ILs self-aggregation leads to a decrease of the ILs ability to form ABS. The liquid−liquid equilibrium data experimentally determined were modeled using the local composition activity coefficient model NRTL (Non-Random Two Liquid). Finally, the partition behavior of three alkaloids (nicotine, caffeine and theobromine), used here as hydrophobicity probes, was evaluated. In all studied systems, alkaloids preferentially migrate to the IL-rich phase, with partition coefficients (K) ranging between 2.23 and complete extraction, in a single-step. Furthermore, the set of ILs investigated allowed identifying an odd-even effect in the alkaloids partitioning derived from the IL anion alkyl chain length. These results support the salting-out effect exerted by K3PO4 and favorable dispersive interactions established between the IL-rich phase-forming components and the alkaloids.

A DFT examination of the role of proximal boron functionalities in the S-alkylation of sulfenic acid anions.

Sulfenic acid anions represent an emerging nucleophile for the preparation of sulfoxides. Their S-functionalization chemistry can often be influenced by a nearby group that interacts with the component atoms of the sulfenate through non-bonding interactions. This study uses DFT methods to assess the importance of proximal boron-containing functional groups to direct S-alkylation chemistry of selected sulfenate anions. Several structural variations were modelled at the B3LYP/6-311++G(d,p) level, with the boron species positioned 3 to 5 carbons away from the alkylation site. Transition state free energies of S-alkylation transition states were located with and without sulfenate oxygen precomplexing to the nearby boron atom. The outcomes suggest that an ortho-substituted boronate ester on benzyl bromide can direct and accelerate an alkylation reaction principally due to a reduction of the entropic barrier. It was also determined that an intermolecular precomplex imparts too much stabilization to the sulfenate, thereby reducing its reactivity. The modelling suggests a possible aryl migration of the boronate/sulfenate complex is not competitive with S-alkylation.

Constructing hollow carbon sphere liquid with permanent porosity via electrostatic modification of polyionic liquids for CO2 gas adsorption

• HCS and polyionic liquid through cation-π electrostatic interaction to construct HCS-based PLs. • The permanent porosity of HCS in PLs was confirmed by the higher CO 2 adsorption capacity of PLs than PILs-PEGS. • Changes in particle size and the outer layer can achieve CO 2 adsorption and viscosity control. • Electrostatic surface modification strategy can be used to prepare rich PLs based on other porous materials. Porous liquids (PLs) are a type of porous materials that combine the porosity of solids and fluidity of liquids, which has attracted widespread attention. In this paper, we report a new TypeⅠhollow carbon sphere-based porous liquids, which are constituted of hollow carbon sphere (HCS) as the porous host, polymeric ionic liquid (PILs) as the corona and poly(ethylene glycol) 4-nonylphenyl 3-sulfopropyl ether potassium salt (PEGS) as the canopy. The viscosity of PLs is 8900 mPa·s at 50 ℃ (like syrup), which has good fluidity. Under 3 MPa pressure conditions, the best CO 2 adsorption capacity of 450-P[VHIm]Br-PEGS and 450-P[VBBI]Cl-PEGS are 2.06 and 1.90 mmol/g at 25 °C, respectively, higher than PILs-PEGS. Under the same conditions, the CO 2 adsorption capacity of PLs is 10.5 times higher than that of N 2 . Therefore, HCS-based PLs have the potential for CO 2 /N 2 selective gas separation. Not only PILs and the anionic alkyl chain of the outer layer widen the liquid range of PLs, but also is suitable for preparing PLs with other cavity units.

Direct 1,2‐Dicarbonylation of Alkenes towards 1,4‐Diketones via Photocatalysis

Abstract1,4‐Dicarbonyl compounds are intriguing motifs and versatile precursors in numerous pharmaceutical molecules and bioactive natural compounds. Direct incorporation of two carbonyl groups into a double bond at both ends is straightforward, but also challenging. Represented herein is the first example of 1,2‐dicarbonylation of alkenes by photocatalysis. Key to success is that N(n‐Bu)4+ not only associates with the alkyl anion to avoid protonation, but also activates the α‐keto acid to undergo electrophilic addition. The α‐keto acid is employed both for acyl generation and electrophilic addition. By tuning the reductive and electrophilic ability of the acyl precursor, unsymmetric 1,4‐dicarbonylation is achieved for the first time. This metal‐free, redox‐neutral and regioselective 1,2‐dicarbonylation of alkenes is executed by a photocatalyst for versatile substrates under extremely mild conditions and shows great potential in biomolecular and drug molecular derivatization.

Direct 1,2-Dicarbonylation of Alkenes towards 1,4-Diketones via Photocatalysis.

1,4-Dicarbonyl compounds are intriguing motifs and versatile precursors in numerous pharmaceutical molecules and bioactive natural compounds. Direct incorporation of two carbonyl groups into a double bond at both ends is straightforward, but also challenging. Represented herein is the first example of 1,2-dicarbonylation of alkenes by photocatalysis. Key to success is that N(n-Bu)4+ not only associates with the alkyl anion to avoid protonation, but also activates the α-keto acid to undergo electrophilic addition. The α-keto acid is employed both for acyl generation and electrophilic addition. By tuning the reductive and electrophilic ability of the acyl precursor, unsymmetric 1,4-dicarbonylation is achieved for the first time. This metal-free, redox-neutral and regioselective 1,2-dicarbonylation of alkenes is executed by a photocatalyst for versatile substrates under extremely mild conditions and shows great potential in biomolecular and drug molecular derivatization.

Simultaneous adsorption of anionic alkyl sulfate surfactants onto alpha alumina particles: Experimental consideration and modeling

Simultaneous adsorption of four anionic alkyl sulfate (AS) surfactants, including sodium octyl sulfate, sodium decyl sulfate, sodium dodecyl sulfate and sodium tetradecyl sulfate named as C8, C10, C12 and C14, onto alpha alumina (α-Al2O3) particles were systematically investigated. Concentrations of all mixtures of anionic AS surfactants in aqueous solution were quantified by capillary electrophoresis coupled with contactless conductivity detection (CE-C4D). Adsorption isotherms of the four anionic AS surfactant homologs increased with either the decrease of pH from 6.0 to 4.0 due to enhancement of electrostatic attractions between the positively charged α-Al2O3 surface and the anionic AS surfactants or the increase of carbon chain length due to enhanced hydrophobic interactions. At different salt concentrations, a common intersection point (CIP) obtained for adsorption isotherms demonstrated that the contributions of electrostatic and hydrophobic interactions were reversed. The ionic strength effect on anionic AS surfactant adsorption isotherms onto α-Al2O3 particles was thoroughly studied. Simultaneous adsorption of the four AS surfactants onto the α-Al2O3was controlled by both electrostatic and hydrophobic interactions that were in accordance with Langmuir and two-step models.

Nanostructure, electrochemistry and potential-dependent lubricity of the catanionic surface-active ionic liquid [P6,6,6,14] [AOT

HypothesisA catanionic surface-active ionic liquid (SAIL) trihexyltetradecylphosphonium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfonate ([P6,6,6,14] [AOT]) is nanostructured in the bulk and at the interface. The interfacial nanostructure and lubricity may be changed by applying a potential. ExperimentsThe bulk structure and viscosity have been investigated using small angle X-ray scattering (SAXS) and rheometry. The interfacial structure and lubricity as a function of potential have been investigated using atomic force microscopy (AFM). The electrochemistry has been investigated using cyclic voltammetry. Findings[P6,6,6,14] [AOT] shows sponge-like bulk nanostructure with distinct interdigitation of cation–anion alkyl chains. Shear-thinning occurs at 293 K and below, but becomes less obvious on heating up to 313 K. Voltammetric analysis reveals that the electrochemical window of [P6,6,6,14] [AOT] on a gold micro disk electrode exceeds the potential range of the AFM experiments and that negligible redox activity occurs in this range. The interfacial layered structure of [P6,6,6,14] [AOT] is weaker than conventional ILs and SAILs, whereas lubricity is better, confirming the inverse correlation between the near-surface structure and lubricity. The adhesive forces of [P6,6,6,14] [AOT] are lower at −1.0 V than at open circuit potential and +1.0 V, likely due to reduced electrostatic interactions caused by shielding of charge centres via long alkyl chains.

Ionic liquid-air interface probed by sum frequency generation spectroscopy and molecular dynamics simulation: influence of alkyl chain length and anion volume

ABSTRACT Understand the structure of the ILs/air interface on a molecular level is significant. In this work, the liquid-air interface of a class of ILs containing 1-alkyl-3-methylimidazolium cations ([Cnmim]+, n = 4, 6 and 8) was investigated by a sum-frequency generation vibrational spectroscopy experiment. The length of the alkyl chain of cations and anion type (tetrafluoroborate ([BF4]−), thiocyanate ([SCN]−), dicyanamide ([DCA]−), hexafluorophosphate ([PF6]−)) were varied to determine their intrinsic effects to the micro-structure on the interface. Meanwhile, combining with the experiment, the orientation angle and surface density for cations and anions of ILs at the air interface was analyzed by molecular dynamics simulation. It is found that the butyl side chain of cations protrudes out into the air as well as the orientation angle between the side chain and interface is 30°–50°. Meanwhile, the anion volume of ILs has almost no influence on the butyl side chain and the methyl on the side chains tend almost planar to the interface with the increased chain length. This research is highly significant for the theoretical and quantitative understanding of the interface chemistry of imidazole-based ILs.

Nanobioremediation: A sustainable approach towards the degradation of sodium dodecyl sulfate in the environment and simulated conditions.

Nanotechnology has gained huge importance in the field of environmental clean-up today. Due to their remarkable and unique properties, it has shown potential application for the remediation of several pesticides and textile dyes. Recently it has shown positive results for the remediation of sodium dodecyl sulfate (SDS). One of the highly exploited surfactants in detergent preparation is anionic surfactants. The SDS selected for the present study is an example of anionic linear alkyl sulfate. It is utilized extensively in industrial washing, which results in the high effluent level of this contaminant and ubiquitously toxic to the environment. The present review is based on the research depicting the adverse effects of SDS in general and possible strategies to minimizing its effects by bacterial degradation which are capable of exploiting the SDS as an only source of carbon. Moreover, it has also highlighted that how nanotechnology can play a role in the remediation of such recalcitrant pesticides.

Insights into the Formations of Host-Guest Complexes Based on the Benzimidazolium Based Ionic Liquids-β-Cyclodextrin Systems.

Inclusion complexation is one of the best strategies for developing a controlled release of a toxic drug without unexpected side effects from the very beginning of the administration to the target site. In this study, three benzimidazolium based ionic liquids (ILs) having bromide anion and cation bearing long alkyl chains, hexyl- ([C6CFBim]Br), octyl- ([C8CFBim]Br), and decyl- ([C10CFBim]Br) were designed and synthesized as antibacterial drugs. Inclusion complexes (ICs) of studied ILs have been prepared by the combination of β-cyclodextrin (β-CD), considering these conjugations should enhance the benignity of ILs and make them potential candidates for the controlled drug release. Characterizations and structural analysis of studied ICs have been performed by 1H NMR, 2D-ROESY NMR, FT-IR, HRMS, TGA, DSC, surface tension, ionic conductivity, dynamic light scattering (DLS), and isothermal titration calorimetry (ITC). Further, the morphology of the ICs has been analyzed by SEM and TEM. Furthermore, neat ILs and ICs have been treated against Escherichia coli and Bacillus subtilis to investigate their antibacterial activity, which confirms the prevention of bacterium growth and the shrinkage of the bacterial cell wall. The findings of this work provide the proof of concept that studied benzimidazolium based ILs-β-CD host-guest complexes should act as a potential candidate in controlled drug delivery and other biomedical applications.

Synthesis of novel oligomeric anionic alkyl glycosides using laccase/TEMPO oxidation and cyclodextrin glucanotransferase (CGTase)-catalyzed transglycosylation.

Modification of alkyl glycosides, to alter their properties and widen the scope of potential applications, is of considerable interest. Here, we report the synthesis of new anionic alkyl glycosides with long carbohydrate chains, using two different approaches: laccase/2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) oxidation of a long-carbohydrate-chain alkyl glycosideand cyclodextrin glucanotransferase (CGTase)-catalyzed elongation of anionic alkyl glycosides. The laccase/TEMPO oxidation of dodecyl β- d-maltooctaoside proceeded efficiently with the formation of aldehyde and acid products. However, depolymerization occurred to a large extent, limiting the product yield and purity. On the other hand, CGTase-catalyzed coupling/disproportionation reactions with α-cyclodextrin and dodecyl β- d-maltoside diuronic acid (DDM-2COOH) or octyl β- d-glucuronic acid (OG-COOH) as substrates gave high conversions, especially when the CGTase Toruzyme was used. It was found that pH had a strong influence on both the enzyme activity and the acceptor specificity. With non-ionic substrates (dodecyl β- d-maltoside and octyl β- d-glucoside), Toruzyme exhibited high catalytic activity at pH 5-6, but for the acidic substrates (DDM-2COOH and OG-COOH) the activity was highest at pH 4. This is most likely due to the enzyme favoring the protonated forms of DDM-2COOH and OG-COOH, which exist at lower pH (pKa about 3).

The Pd-catalysed asymmetric allylic alkylation reactions of sulfamidate imines.

The Pd-catalysed asymmetric allylic alkylation (Pd-AAA) of prochiral enamide anions derived from 5H-oxathiazole 2,2-dioxides has been developed. Various 4,5-disubstituted and 4-substituted cyclic sulfamidate imines have participated in the transformation with a range of allyl carbonates—as well as 2-vinyl oxirane, 2-vinyl-N-tosylaziridine, and 2-vinyl-1,1-cyclopropane dicarboxylate—to furnish the desired C-allylated products in moderate to high yields, with high regioselectivites and generally high enantioselectivities. Conversion between N- and C-allyl products was observed, with the N-allylated products converting to the C-allylated products over time. The resulting high-value allylated heterocyclic products all bear a tetrasubstituted stereogenic centre and can be reduced to an allylated chiral sulfamidate or an amino alcohol.

Revealing the Origin of the Specificity of Calcium and Sodium Cations Binding to Adsorption Monolayers of Two Anionic Surfactants.

The studied anionic surfactants linear alkyl benzene sulfonate (LAS) and sodium lauryl ether sulfate (SLES) are widely used key ingredients in many home and personal care products. These two surfactants are known to react very differently with multivalent counterions, including Ca2+. This is explained by a stronger interaction of the calcium cation with the LAS molecules, compared to SLES. The molecular origin of this difference in the interactions remains unclear. In the current study, we conduct classical atomistic molecular dynamics simulations to compare the ion interactions with the adsorption layers of these two surfactants, formed at the vacuum-water interface. Trajectories of 150 ns are generated to characterize the adsorption layer structure and the binding of Na+ and Ca2+ ions. We found that both surfactants behave similarly in the presence of Na+ ions. However, when Ca2+ is added, Na+ ions are completely displaced from the surface with adsorbed LAS molecules, while this displacement occurs only partially for SLES. The simulations show that the preference of Ca2+ to the LAS molecules is due to a strong specific attraction with the sulfonate head-group, besides the electrostatic one. This specific attraction involves significant reduction of the hydration shells of the interacting calcium cation and sulfonate group, which couple directly and form surface clusters of LAS molecules, coordinated around the adsorbed Ca2+ ions. In contrast, SLES molecules do not exhibit such specific interaction because the hydration shell around the sulfate anion is more stable, due to the extra oxygen atom in the sulfate group, thus precluding substantial dehydration and direct coupling with any of the cations studied.

Transition-Metal-Free Cross-Coupling by Using Tertiary Benzylic Organoboronates.

The transition-metal-free cross-coupling of alkyl or aryl electrophiles by using tertiary benzylic organoboronates is reported. This reaction involves the generation of tertiary alkyl anions from organoboronates in the presence of an alkoxide base and then their substitution reactions. This protocol allows the simple and efficient construction of quaternary carbon centers.

Ion Dissociation in Ionic Liquids and Ionic Liquid Solutions

The extent to which cations and anions in ionic liquids (ILs) and ionic liquid solutions are dissociated is of both fundamental scientific interest and practical importance because ion dissociation has been shown to impact viscosity, density, surface tension, volatility, solubility, chemical reactivity, and many other important chemical and physical properties. When mixed with solvents, ionic liquids provide the unique opportunity to investigate ion dissociation from infinite dilution in the solvent to a completely solvent-free state, even at ambient conditions. The most common way to estimate ion dissociation in ILs and IL solutions is by comparing the molar conductivity determined from ionic conductivity measurements such as electrochemical impedance spectroscopy (EIS) (which measure the movement of only the charged, i.e., dissociated, ions) with the molar conductivity calculated from ion diffusivities measured by pulse field gradient nuclear magnetic resonance spectroscopy (PFG-NMR, which gives movement of all of the ions). Because the NMR measurements are time-consuming, the number of ILs and IL solutions investigated by this method is relatively limited. We have shown that use of the Stokes-Einstein equation with estimates of the effective ion Stokes radii allows ion dissociation to be calculated from easily measured density, viscosity, and ionic conductivity data (ρ, η, λ), which is readily available in the literature for a much larger number of pure ILs and IL solutions. Therefore, in this review, we present values of ion dissociation for ILs and IL solutions (aqueous and nonaqueous) determined by both the traditional molar conductivity/PFG-NMR method and the ρ, η, λ method. We explore the effect of cation and anion alkyl chain length, structure, and interaction motifs of the cation and anion, temperature, and the strength of the solvent in IL solutions.

Transition‐Metal‐Free Cross‐Coupling by Using Tertiary Benzylic Organoboronates

AbstractThe transition‐metal‐free cross‐coupling of alkyl or aryl electrophiles by using tertiary benzylic organoboronates is reported. This reaction involves the generation of tertiary alkyl anions from organoboronates in the presence of an alkoxide base and then their substitution reactions. This protocol allows the simple and efficient construction of quaternary carbon centers.

Sulfonium closo-hydridodecaborate anions as active components of a potentiometric membrane sensor for lidocaine hydrochloride

A method for the preparation of sulfonium derivatives of the closo-hydridodecaborate anion [B10H9SR2]− with exo-polyhedral alkyl groups (R = i-Pr, n-Pr, n-Bu, n-C8H17, n-C12H25, n-C18H37) has been developed. A procedure for the preparation of mono-S-substituted derivatives of the closo-hydridodecaborate anion by the interaction between the [B10H9SH]2− anion and secondary alkyl halides has been developed. This paper presents the results of studies on the use of the sulfonium derivative of the closo-hydridodecaborate anion [B10H9S(C18H37)2]− as the active component of a hybrid polymer membrane designed to create a potentiometric lidocaine-selective sensor. The optimal composition of the proposed membrane composition has been found. The electroanalytical characteristics of the manufactured potentiometric sensor have been determined; the detection limit of lidocaine has been found to be 3.5 • 10−8 M.