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J IRAN CHEM SOC (2016) 13:279–287DOI 10.1007/s13738-015-0735-4

ORIGINAL PAPER

Does bromine atom‑free radical (Br·) undergo a chemical reaction before dimerization to dibromine (Br2)? An electrochemical investigation

Muhammad Tariq1,2 · M. Mohammad2 · I. A. Tahiri3 · A. Dar2

Received: 3 March 2015 / Accepted: 11 September 2015 / Published online: 21 September 2015 © Iranian Chemical Society 2015

Introduction

Our interest in bromine atom-free radical (Br·), its genera-tion and reactions, arose from the previous studies from this laboratory on iodine atom-free radical as “friendly free radical” [1]. In various works [1–3] not only the hypotheses of Vetter [4, 5] was confirmed, but also the work of Popov and Geske [s] was extended to more reactions—reactions of I· with some component compounds of DNA and pro-tein [1–3]. The reaction of I· with leukemic cells was also explored [8]. After such studies on I·, going to Br· was the obvious next choice.

In fact there is nothing entirely new about the production of halogen atom-free radicals and their chemistry [9–12]. But mostly, these atom-free radicals have been obtained through photo-chemical reaction or radiolysis process. These are “hot atoms”. The reaction of these atom-free radicals is studied through fast reaction techniques [13, 14]. For example, Zewail worked on such I· atom-free radi-cal [13] and Merényi and Lind reported work on such Br· atom-free radical [14]. They have reported some reactions of such I· and Br· atom-free radicals.

The main problem in studying the chemistry of these atom-free radicals is their dimerization reaction and the subsequent reactions of the dimer molecules:

For I· atom free radical, dimerization rate constant has been reported as high [O] 109 M−1 s−1 [14]. But electrochemi-cally generated iodine atoms are quite inactive towards dimerization [1, 6–8]. If the same is true for Br· atom—slow dimerization of electrochemically generated Br· atom

2 X·→ X2, X

·= I· orBr· atomfreeradical

X2 + Y ⇋ Z; Y is a reactant and Z is a product.

Abstract The important question, does bromine atom free radical, Br·, undergo a chemical reaction with a sub-strate before it dimerizes to dibromine Br2, is investigated through electrochemical oxidation of bromide ion Br−. Cyclic voltammetry and spectrophotometry were used as electro-oxidation and monitoring devices. Simulation of cyclic voltammogram was used to obtain information about the mechanism of electro-oxidation process as well as reac-tion with substrates. It is shown that the primary electro-oxidation product (PEOP) of Br−, Br· (bromine atom-free radical), reacts with chemicals like chloroform, glycine, cytosine, etc. It can also dimerize, for example in acetoni-trile. Reactions of PEOP Br· with substrate chloroform, acetone, DNA components adenine, cytosine, thymine and amino acid glycine were studied and their kinetics are reported here.

Keywords Bromine atom-free radical Br· · Dimerization · Cyclic voltammetry · DNA components simulation of CV

* Muhammad Tariq tariq_ftj@yahoo.com

* M. Mohammad mahboob.md@hotmail.com

1 National Center of Excellence in Physical Chemistry, University of Peshawar, Peshawar 25120, Pakistan

2 Reactive Intermediates-Free Radical Chemistry Group, HEJ Research Institute of Chemistry, International Center for Chemical and Biological Sciences, University of Karachi, Karachi 75270, Pakistan

3 Chemistry Department Federal Urdu University of Science and Technology, Karachi 75270, Pakistan

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free radical—then the door of the Br· atom-free radical chemistry opens which may very well be different from photochemically or radiolytically generated (hot) Br· atom-free radical chemistry.

Bromine atom-free radical, claimed to be reactive in nature, may react with a substrate or may combine with another bromine atom-free radical to form the dimer, dibro-mine (Br2), and subsequently react with the substrate as shown in Eqs. (1–4):

or

In most studies reported so far, it has been suggested that when a bromine atom-free radical (Br·) is generated, it dimerizes to Br2 [15, 16] and then Br2 reacts with any other substrate [16, 17]. However, we did report the electrochem-ical production and reactivity of Br· [2].

Here we present the results of our investigations: (1) electro-oxidation of Br− in aqueous and some non-aqueous media and characterizing the preliminary electro-oxidation product (PEOP) as Br· atom-free radical (2) reactions of Br· with some biologically important compounds, such as cytosine, cytidine, thymine, uracil, uridine, adenine and glycine. Cyclic voltammetry, controlled potential electroly-sis and spectrophotometry [18] were used to generate Br· and monitor its reaction with various substrates, mentioned above. For, characterization purpose reactions of these sub-strates with dibromine were also studied. Simulations of cyclic voltammograms were carried out for exploring the mechanism of reactions.

Experimental

Instruments

Cyclic voltammetry experiments were performed using Analytical Electrochemical Work Station, Model AEW2-10 mA (Sycoppel Scientific Ltd) controlled by IBM com-patible computer with software E.C. Prog V3. Saturated calomel electrode was used as reference electrode while Pt (BASi) and graphite (PAR) electrodes were used as work-ing and counter electrodes, respectively. The bulk elec-trolysis was performed using Ministat Precision Potentio-stat, rating 25 volts, 1 Ampere (Sycoppel Scientific Ltd). For bulk electrolysis a platinum wire (as quasi-reference) was used, while a gold foil (area ≈ 4 cm × 1 cm) and a

(1)Br− ⇋ Br· + e

(2)Br· + substrate →[

product]

(3)Br· + Br· → Br2

(4)Br2 + substrate →[

product]

platinum foil (area ≈ 2.5 cm × 2.5 cm) were used as coun-ter and working electrodes, respectively. The UV–visible spectra were recorded on GENESYS 10 µv spectrophotom-eter (Thermo, USA).

Chemicals

Glycine (99.7 % Merck), Potassium bromide (99.5 % Merck), cytosine (Ultra pure grade Amresco), uracil (98 % Merck), adenine (>99 % Fluka), uridine (99 % Sigma), cytidine (≥99 % Sigma-Aldrich), potassium perchlorate (99 % Panreac), tetrabutylamminum perchlorate (TBAP) (>98.0 TCI-GR) and bromine (dibromine Br2; 99.5 % Aldrich) were used without further purification. Acetoni-trile, methanol and chloroform (HPLC grade Fisher Scien-tific), 1, 2-dimethoxyethane, acetone (99 % Wako), all were used without further purification dried over 4A molecular sieve [1].

General procedure

A 5-mM KBr solution was prepared in distilled water. 0.1 M KClO4 was used as supporting electrolyte. 1, 5 and 50 solution of substrate was used as needed; generally, 5 mM solutions were used for bromine atom-free radical reaction studies. All cyclic voltammetric measurements were carried out in 3-electrode configuration with instru-mental IR compensation. The scan rate was 0.05 V s−1.

For in situ electrolysis combined with spectrophotom-etry work, a custom-made “spectro-electrochemical” cell [18] was used. First, a cyclic voltammogram was taken with platinum as quasi-reference electrode (QRE). This cyclic voltammograms was used for adjusting the potential at which electrolysis was to be carried out. Slightly higher (more positive) potential than peak potential was main-tained through potentiostat, and in situ spectrum of prod-uct formed during electrolysis was recorded. Simulation of cyclic voltammograms was carried out using bioanalytical system: Digisim 3.05 program.

Results and discussion

Cyclic voltammetric studies of Br− in protic media, water and methanol

Cyclic voltammograms (CV) of Br− in water (5 mM aque-ous solution, 0.1 M KClO4 supporting electrolyte) and in methanol (5 mM LiBr, 0.1 M TBAP supporting elec-trolyte) on platinum electrode are given in Figs. 1a and 2, respectively. In water the CV shows an anodic peak [(Ep)a = 979 mV vs. SCE] and a corresponding cathodic

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peak [(Ep)c = 834 mV vs. SCE]. The C.V. could be inter-preted through processes given in Eqs. (1) or (1, 3, 5).

Followed by dimerization

kf1 = k1(Dimer)

And then followed by

This mechanism is simple, can simulate the experimental C.V. and also explain the production of dibromine which has also been reported by Compton for the oxidation of Br− [16, 17]. The above process, Eq. (5) occurring, with the same E1/2 as for process Eq. (1).

The simulated CV with the ECE Eqs. (1, 3, 5) mecha-nism is given in Fig. 1b; the various parameters are col-lected in Table 1 (kinetic parameters) and the electrochemi-cal parameters in the caption of Fig. 1b. Interestingly, the experimental CV can also be simulated by assuming simple EC mechanism Eqs. (1, 3) (Fig 1c). For parameters used in various simulations see Table 1 (chemical parameters) and captions of respective figures (electrochemical parameters). CV of Br− in methanol is not much different from that in water.

Cyclic voltammetric studies of Br− in aprotic media

CV in acetonitrile (MeCN) and dimethoxy ethane (DME)

In both MeCN and DME the C.Vs of Br− look a little quasi-reversible, Figs. 3 and 4. These CVs could arise from the processes as given in Eq. (1) or as in Eqs. (1, 3, 5) or as Eqs. (1, 3, 5, 6).

Simulated CV with the mechanism ECCE Eqs. (1, 3, 5, 6) is also presented in Fig. 3 for MeCN (Fig. 5).

(5)Br− ⇋ Br· + e

(6)Br· + Br·k(Dimer)

⇆ Br2Keq.1 = kf1/kb1

(7)Br2 + e ⇋ Br−2

(6)Br2 + Br− ⇋ Br−3

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I / μ

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I / μ

A

Fig. 1 C.V of 5mMBr− (0.1 M KClO4); a on platinum micro disk electrode (closed square), b simulated C.V. with mechanism ECE (closed square), c simulated C.V. with mechanism EC (closed square); solvent, H2O. Simulation parameters for ECE mecha-nism b concentration of Br− = 1–5 mM, E1

0 (V) = 0.908 = E20 (V);

α1/λ (eV) = 0.5 = α2/λ (eV); ksh1 (cm/s) = 0.005 = ksh2 (cm/s), Do (cm2/s) = 1 × 10−5; For EC mechanism c concentration of Br− = 1–5 mM, E0 (V) = 1.028, α/λ (eV) = 0.5, ksh (cm/s) = 0.055, Do (cm2/s) = 1 × 10−5; chemical parameters from Table 1

▸

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C.V. in acetone and chloroform

The CV of Br− in acetone is depicted in Fig. 6. From the figure—the absence of cathodic peak—it can be deduced that the PEOP, Br·, is undergoing reaction with solvent ace-tone. The reaction of Br· with chloroform has been reported earlier [3]. Also, its simulated CV is given in Fig. 7. The mechanism was assumed to involve Br· atom-free radical (Eqs. 1, 2).

The pseudo-first order rate constant, kps, was estimated from the anodic/cathodic current ratio [19–21] and sweep rate: kps, > 0.5 s−1. It can be, here, deduced that it is not

the dimer product of Br. atom-free radical—the dibromine Br2—which reacted with chloroform (or acetone): it is well known that Br2 is rather stable in chloroform and used as solvent for dibromine by some workers [22, 23] and only reacts slowly with acetone to form iodoform.

In situ electrolysis-spectrophotometric studies of Br− and spectrophotometric studies on Br2.

In situ electrolysis‑spectra studies of Br−

In situ electrolysis-optical-spectrophotometric studies on Br− and spectrophotometric studies on Br2 have lent the support to the existence of Br· as PEOP and its instability in solvents water, acetonitrile, acetone and trichloromethane (chloroform) [3]. Some details of these studies are given below.

In water and methanol

The optical spectra obtained on the controlled potential electrolysis of Br− in water and methanol, on platinum electrode and in the spectroelectrochemical cell are given in Figs. 8, 9. The spectra of the electro-oxidation product(s) are the same as that of dibromine in the two solvents! The same result has been obtained in aprotic solvent acetonitrile and dimethoxyethane (see below).

In acetonitrile and 1, 2‑dimethoxy ethane

The optical spectra of electro-oxidation product of Br− in acetonitrile (on Pt-electrode) is given in Fig. 10 The spec-trum of dibromine in the same solvent is included in the same figure (Fig. 10). It is easy to conclude that the PEOP,

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Fig. 2 C.V of 5 mM Br− [0.1 M tetrabutylammonium per chlorate (TBAP)]; on platinum micro disk electrode (closed square), solvent, CH3OH

Table 1 Fitted CV Parameter in DigiSim Digital® Simulation program

a Value to fit in DigiSim programb As per simulationc From Eq. (7)d Values for simulation purposee See text

S. no Reaction/substrate Mechanism Ka (M−1) kib,c (M−1 s−1)

1 Electro-oxidation of Br− (water) (a) ECE(b) EC

1000107

5 × 109, b

5 × 109,b

2 Electro-oxidation of Br− (MeCN) (a) ECCE(b) EC

Keq1 = 1020

Keq2 = 7 × 105kf1 = 1014,d

kf2 = 1014,d

kdimer = 103,

3 Reaction of Br· with(a) Cytidine(b) Adenine(c) Thymine(d) Glycine

EC′CEC′CEC′CEC′C

Keq1 = 1500Keq.2 = 1 × 108

Keq1 = 10Keq2 = 5000Keq1 = 500Keq2 = 1 × 108

Keq1 = 10Keq2 = 1 × 104

kf1 = 1500e

kf2 = 1 × 104

kf1 = 10kf2 = 1 × 106

kf1 = 300kf2 = 1 × 107

kf1 = 50kf2 = 1 × 107

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Br·, does not react with the solvent acetonitrile but dimer-izes to dibromine. The same result is obtained for DME (as solvent). The same conclusion had been drawn from the earlier CV studies (mentioned above).

In chloroform

The optical spectra of the electro-oxidation product of Br− in chloroform is given in Fig. 11. The optical spectra of dibromine in the same solvent is also included in the same figure (Fig. 11). Comparing the two figures one can easily

conclude that no dibromine is formed in this solvent from the electro-oxidation of Br− and the optical spectra for the electro-oxidation product of bromide should be that of the reaction product of Br· with chloroform. It may be recalled that the same conclusion—reaction of the PEOP, Br·, with chloroform—had also been deduced from CV studies.

Spectrophotometric studies of Br2

To help ascertain if the electro-oxidation product of bro-mide, in various solvents, was dibromine or something else,

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b

b

a

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I / μ

A

Fig. 3 a C.V of 5 mM Br− [0.1 M Tetrabutylammonium per chlo-rate (TBAP)]; on platinum micro disk electrode. Solvent, CH3CN (acetonitrile). b Simulated C.V. with mechanism ECCE c similar condition as mentioned in a only switching potential was adjusted as 0.85 V. Simulation Parameters for mechanism b concentra-tion of Br− = 5 mM, E1

0 (V) = 0.79, = E20 (V); α1/λ (eV) = 0.4,

α2/λ (eV) = 0.36; ksh1 (cm/s) = 0.05, ksh2 (cm/s) = 0.008, Do (cm2/s) = 1 × 10−5, chemical parameters from Table 1

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Fig. 4 C.V of 5 mM Br− [0.1 M lithium per chlorate (LiClO4)]; on platinum micro disk electrode. Solvent, 1, 2-DME (1, 2-dimethox-yethane)

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Ep

(V)

lnC*(mol/L)

Fig. 5 Ep vs lnC graph (see Eq. 5)

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Fig. 6 C.V. of Br− in acetone

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optical spectra of dibromine were also recorded in all the solvents used: water, MeOH, MeCN and acetone (dibro-mine reacts with acetone slowly). Some of these spectra are included in Fig. 12. Optical spectra of dibromine in ace-tonitrile and chloroform are given in Figs. 10, 11.

It is thus concluded from these spectrophotometric and bulk electrolysis-optical spectra studies that PEOP (Br·) reacts with water acetone and chloroform during bulk elec-trolysis but in acetonitrile and dimethoxy ethane it dimer-izes to dibromine, Eqs. (1, 3).

(5)Br2 + e ⇋ Br−2

In chloroform and acetone

(S = substrate = acetone, chloroform)

Kinetics studies

It can be inferred from the above studies that, of all spe-cies produced in the electro-oxidation process of Br−, it is

(7)Br−2 + ROH ⇋ Product(s) (R = H, CH3)

(2)Br· + ROH ⇋ Product

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Fig. 7 C.V of Br− [0.1 M tetra-n-butylammonium per chlorate (TBAP)]; on platinum micro disk electrode (a), with full simulation (b) and with simulation up to first peak (c). Solvent, CHCl3 (chloro-form)

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Fig. 8 a UV spectra of electrolyzed Product of 5 mM Br− on plati-num electrode (open square), b 3 mM dibromine (closed triangle), c 3 mM Tribromide ion [circle (open circle) on bold blue line] and d 5 mM KBr (+). Solvent; H2O, electrolysis carried out in two com-partment (UV–Vis–) spectroelectro-chemical cell. A platinum (Pt) foil was used as working electrode for bulk electrolysis of Br−

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Fig. 9 a UV spectra of electrolyzed Product of 5 mM Br− on plati-num (open square), b dibromine (closed triangle), c tribromide ion circle (open circle) on solid line; (closed circle) on dash line repre-sent Br−3 formation, d 5 mM LiBr (+). Solvent, CH3OH, electrolysis carried out in two compartment (UV–Vis–) spectroelectro-chemical cell. A Gold (Au) and platinum (Pt) foil was used as working elec-trode for bulk electrolysis of Br−

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Fig. 10 a UV spectra of electrolyzed product of 1 mM LiBr [circle on a line (open circle)], b 0.005 mM dibromine (closed triangle), c 1 mM LiBr [square on dotted line (closed square)]. Solvent, CH3CN (acetonitrile), electrolysis was carried out in two compartment (UV–Vis–) spectroelectrochemical cell. platinum (Pt) foil was used as working electrode for bulk electrolysis of Br−

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PEOP, Br·, which is most reactive and probably reacts with the surrounding substrate molecules present in large excess.

Since the primary interest has been to explore the reac-tivity of I· and Br· as friendly free radicals, we embarked upon studying the reaction of I· [1–3] and Br·, [1–3] with the DNA component compounds and an amino acid. In general, all these reactions were studied through cyclic vol-tammetry, in aqueous media (or methanol) and on platinum electrode.

Reactions of Br. with DNA components

Reactions of Br· with some DNA components (cytosine, adenine, thymine) and related compounds (cytidine, uracyl,

uridine) are presented here. Reaction with guanine could not be studied because of solubility problem.

Reaction with cytosine and cytidine

Reaction of Br· with cytosine in water has been reported elsewhere [3]. The conclusion drawn about the reaction

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Absorbance

nm/wavelength

Fig. 11 a UV spectra of electrolyzed product of saturated solution (~1 mM) bromide ion (closed square), b dibromine (closed triangle), c saturated solution (~1 mM) of LiBr (+). Solvent, CHCl3 (chloro-form), Electrolysis was carried out in two compartment (UV–Vis–) spectroelectrochemical cell. Platinum (Pt) foil was used as working electrode for bulk electrolysis of Br−

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Fig. 12 UV-Spectra of dibromine in a H2O (closed square), b CH3CN (closed triangle), (c) CH3OH [circle (open circle) on solid line)

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Fig. 13 C.V representing reaction of electro-oxidation product of Br− with cytosine on platinum (Pt) electrode; a C. V of 5 mM Br− (solid line), b C.V of 5 mM Br− in the presence of 5 mM cytosine (closed square), c simulated C.V (closed triangle). Solvent: CH3OH (methanol); EC′C mechanism; simulation parameters concentration, [Br−] = 0.005 M = [cytosine]; E0 (V) = 0.789; α1/λ (eV) = 0.5; ksh (cm/s) = 0.0015, Do (cm2/s) = 1 × 10−5, chemical parameters from Table 1

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Fig. 14 C.V. of Br− in the absence and presence of thymine and the simulated one, a experimental C.V of 5 mM Br− (bold line), b Exper-imental C.V of 5 mM Br− in the presence of 5 mM thymine [circles (open circle) c Simulated C.V (closed triangle]; solvent, CH3OH (methanol). Concentration, [Br−] = 0.005 M; [thymine] = 0.005 M E0 (V) = 0.798; α1/λ (eV) = 0.5; ksh (cm/s) = 0.0015, Do (cm2/s) = 1 × 10−5, chemical parameters from Table 1

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was that they undergo a sort of EC mechanism reaction and that the reaction is quite fast. The mechanism of the reac-tion was proposed as [3]

Reaction of cytosine with Br· in methanol is quite differ-ent as reflected in the CV of Br− in the presence of cyto-sine (Fig. 13) The considerable rise in the anodic peak current, disappearance of corresponding cathodic peak without cathodic shift in the anodic peak potential, sug-gests involvement of catalytic process [18]. This is sup-ported by the simulation of the CV—a EC′C process, Fig. 13.

Reaction of cytidine with Br· (and Br2), in methanol, is more or less the same as of cytosine.

Reaction with thymine

The experimental cyclic voltammogram of Br− in the absence and presence of thymine (in methanol) and the simulated one, all are given in Fig. 14. The CV is explained through EC′C mechanism.

Br− ⇋ Br· + e

(8)Cyt+ Br· ⇄K

kbY(a product)

Yslow−→ Z, (another product)

Reaction with uracil and uridine

The reaction of electro-oxidation product of Br− (Br·) with uracil (Fig. 15) and uridine follows the same path of cyto-sine described above.

Reaction with Glycine

The reaction of glycine with PEOP (Br·), in water, has been reported in our earlier work [3]. Nevertheless, the C.V.s of Br− in the absence and presence of glycine along with the simulated CV are depicted in Fig. 16. The in situ electroly-sis and spectrophotometric studies on Br−, in the presence of glycine, confirmed the catalytic mechanism of the reac-tion. At the same time, spectrophotometric study of reac-tion between Br2 and glycine as well as the simulation (of C.V.) strongly suggests the simple EC′C mechanism: the mechanism thus proposed is

Gly = glycine; Y being an intermediate,

The mechanism does not involve electro-generated Br2, Eqs. (3, 4).

(1)Br− = Br· + e

(2)Br− + Gly ⇋ Y + Br−

(2a)Y + Br− ⇋ Z (product)

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Fig. 15 C.V representing reaction of electro-oxidation product of Br− with Uracil on platinum (Pt) electrode; a C.V of 5 mM Br− (solid line), b C.V of 5 mM Br− in the presence of 25 mM Uracil (closed square), c C.V of 5 mM Br− in the presence of 50 mM gly-cine (closed triangle). Solvent, H2O

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Fig. 16 C.V. representing reaction of electro-oxidation product of Br− with glycine and simulation of the cyclic voltammogram through mechanism (EC′C); a experimental C.V of 5 mM Br− (bold line), b experimental C.V of 5 mM Br− in the presence of 50 mM Glycine [circles (open circle) c simulated C.V (closed triangle); sol-vent. H2O, electrode: Pt.]. Concentration, [Br−] = 0.007 M; [thy-mine] = 0.05 M E0 (V) = 0.91; α1/λ (eV) = 0.5; ksh (cm/s) = 0.005, Do (cm2/s) = 1 × 10−5, chemical parameters from Table 1

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The reaction of glycine with Br2, however, is

No attempt was made to identify the product(s).

Conclusions

It is established that the electro-oxidation of Br− in protic as well as aprotic solvents gives the PEOP as Br· atom-free radical which undergoes various type of reactions, depend-ing upon the environment. These possible reactions are listed as follows:

In water and methanol (neat, containing no other reac-tant) [EC (Eqs. 1, 3) or ECE (Eqs. 1, 3, 5); in MeCN and DME (neat, no other reactant]: EC (Eqs. 1, 3); in acetone and chloroform (neat, no other reactant): EC (Eqs. 1, 2).

Kinetics studies: simulation of CVs of Br− in the pres-ence of various reactants gave the following kinetic results:

Cytosine: EC in water, EC′C in methanol; adenine: ECC′ in methanol; thymine: EC′C in methanol; glycine: EC′C in water.

Schemes

MechanismEC

ECE

ECCE

EC′C

(4)Br2 + Gly ⇋ I (an intermediate)

(4a)I → Z′ (a different product than Z, 2a)

Br− ⇋ Br· + e E0, ksh, α

2Br· ⇋ Br2 Keq.1 = kf1/ kb1

Br− ⇋ Br− + e E01; ksh1, α1

2Br· ⇋ Br2 Keq.1 = kf1/ kb1

Br2 + e ⇋ Br−2 E02; ksh2, α2

Br− ⇋ Br− + e E01; ksh1, α1

2Br· ⇋ Br2 Keq.1 = kf1/ kb1

Br2 + Br− ⇋ Br−3 Keq.2 = kf2/ kb2

Br2 + e ⇋ Br−2 E02; ksh2, α2

A = B + e ksh, α

where, sayA = Br−, B = Br·, C = cytosine (say),D = [Cytosine]+·, H = [cytosine-Br] + H+

Acknowledgments Financial support for this research was provided by Higher Education Commission, Pakistan, under Foreign Faculty Program.

Compliance with ethical standards

Conflict of interest None.

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B + C = D + A Keq1 = kf1/kb1

B+D=H Keq2 = kf2/kb2,

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