International Journal of Computational and Theoretical Chemistry
Volume 3, Issue 2, March 2015, Pages: 6-18

Computational Study of the Mechanism of the Oxidation of Hydrazine / Hydrazinium Ion by Iodine in the Gas Phase

Gideon Adamu Shallangwa*, Adamu Uzairu, Victor Olatunji Ajibola, Hamza Abba

Department of Chemistry, Ahmadu Bello University, Zaria, Kaduna State, Nigeria

Email address:

(G. A. Shallangwa)

To cite this article:

Gideon Adamu Shallangwa, Adamu Uzairu, Victor Olatunji Ajibola, Hamza Abba. Computational Study of the Mechanism of the Oxidation of Hydrazine / Hydrazinium Ion by Iodine in the Gas Phase. International Journal of Computational and Theoretical Chemistry. Vol. 3, No. 2, 2015, pp. 6-18. doi: 10.11648/j.ijctc.20150302.11


Abstract: The reaction mechanisms of the oxidation of hydrazine / hydrazinium ion by iodine have been studied using 6311+G** basis set of the density functional theory (DFT) method at the B3LYP level of computation. The study shows that the oxidation reactions can proceed via four independent routes or pathways that can be separately monitored. Two of the proposed pathways involved a two-step reaction mechanism each, in which two transition states were produced while each of the other two routes involved three-step reaction mechanism in which three activated complexes were produced. The results obtained were based on the analyses of the computational energetics of the optimized reactants, intermediates, transition states and products of the reaction of iodine with hydrazine / hydrazinium ion. The study showed that all the four proposed routes were possible by comparing the enthalpies of reactions of the four proposed pathways as well as the activation barriers of the respective rate determining steps which were found to be reasonably acceptable. Rate laws, which were consistent with the written mechanisms, were also derived for each of the proposed mechanisms.

Keywords: DFT Calculations, Reaction Mechanisms, Rate Laws, Iodine, Hydrazine, Transition States


1. Introduction

Iodine is an essential micronutrient for mammals including humans and, in fact, appears to be the heaviest required element in a diet [1,2,3]. Iodine compounds are useful in medicine and lack of iodine in the diet, is a cause of goitre. Iodine is absolutely necessary for a healthy thyroid as well as ovaries, breasts and prostate. Iodine deficiency, though easily treated, continues to be a problem for approximately a fifth of the world population [4,5]. Goitre, or enlargement of the thyroid, has been recognized for many years as symptom of iodine deficiency. These pathological conditions are normally grouped under the common name of iodine deficiency disorders (IDD) [6]. Iodine deficiency is, in fact, the largest preventable cause of mental retardation worldwide [3]. In severe cases, it can result in cretinism, a form of mental retardation. Mshelia et al, [7] reported in their studies that volatization from oceans and precipitation of ocean water is the origin of most iodine content of diet and is considered critical to compensate for metabolic losses. Goitre surveys so far are limited to clinical symptoms, urinary iodine output and, to some extent, plasma thyroid hormone levels.

Iodine is used to prevent iodine deficiency and its consequences, including goiter. It is also used for treating a skin disease caused by a fungus (cutaneous sporotrichosis); treating fibrocystic breast disease; preventing breast cancer, eye disease, diabetes, and heart disease and stroke; and as an expectorant [8,9,10,11]. Iodine is applied to the skin to kill germs, prevent soreness inside the mouth (mucositis) caused by chemotherapy, and treat diabetic ulcers [12,13]. It is also reported that iodine has very specific protective effects against several common poisons like fluoride and bromide and, to a lesser extent, helps eliminate lead and mercury from the body [14]. These are just a few of the reasons why the study of iodine is quite interesting.

It is also well known that hydrazine and its derivatives play important role in biological activity studies. A number of hydrazide-hydrazone are claimed to possess interesting antibacterial, antifungal [14], anticonvulsant [16], anti-inflammatory [17], antimalarial [17] and antituberculosis activities [18]. It is also well known that iodine quantitatively oxidizes substances containing the -NH-NH group. This reaction is the basis of one of the standard analytical procedures to titrate hydrazine and related substances, in particular isonicotinoyl-hydrazide which is widely used in the pharmaceutical industry because of its bacteriostatic properties against Mycobacterium tuberculosis [3,7,19,20,21,22].

The study of the mechanisms of oxidation of substrates by iodine has been the subject of several studies, but among which no complete agreement is found [1,7,20,23,24,25,26]. The mechanisms of the oxidation of substances by iodine is not only as varied as the number of authors who have published such works, but also as the number of internationally recognized peer reviewed journals in which such work were published [2,7,20,21,22,23,24,25,26,27,28,29]. A further investigation seemed desirable [30,31].

The present paper desired to report the results of computational studies on the mechanism of the oxidation of hydrazine / hydrazinium ion by iodine. The computational analyses of the structures using DFT (B3LYP) are reported. Computational chemistry methods can be used to explore the theoretical chemistry behind reactive systems, to compare the relative chemical reactivity of different systems, and, by extension, to predict the reactivity of new systems. Transition states for reaction of hydrazine / hydrazinium ion with iodine were determined and equilibrium states of reactants, intermediates and products were searched by computational means. In theoretical studies, using ab initio or density functional theory (DFT) methods, adequate choices of a theoretical method and a basis set are very important in obtaining reliable results. Theoretical studies on compounds containing iodine, a 5th period halogen element, are less abundant compared to those containing F, Cl or Br which are 2nd, 3rd and 4th period elements, respectively [1,23]. Heavy elements like iodine have a large number of core electrons which are in general less important for the chemical reactivity and bonding modes. However, it needs a large number of basis sets or functions to describe the corresponding orbitals. This makes computations with heavy elements like iodine very time consuming and expensive [32,33,34]. However, compounds containing iodine atom play very interesting and important roles in many chemical reactions, especially in the life sciences. Despite the challenges therefore, this makes the study of iodine quite interesting, especially when using the more exact method of DFT.

2. Materials and Methods

2.1. Materials

The Spartan ‘14 v1.1.0 density functional theory (DFT) method was used on Microsoft window XP professional version 2002 SP3 computer system, with Intel(R) Pentium(R) Dual CPU,E2200@2.20 GHz 219GHz, 3.24GB of RAM. All equations were written using Design Science MathType 6.9 program. All graphs were drawn using Microsoft Excel 2010, while the structures in Schemes 2-5, were produced using ChemBio Office 2008 software.

2.2. Geometry Optimization of Reactants, Intermediates, Transition States and Products

All the electronic structure calculations reported in this work were performed using the Spartan ‘14 v1.1.0 program packages. The geometries included in the reaction of hydrazine / hydrazinium ion with iodine were fully optimized using density functional theory (DFT) method [35,36,37]. To check the influence of basis set, PM3 of semi empirical method and 6-311+G** basis set of DFT at the B3LYP levels of computation were employed to optimize the geometries of the reactants, intermediates, transition states and products. There were marked differences between the semi empirical method and the DFT method. It thus indicated that the geometrical parameters were sensitive to the sizes of the basis sets or computational levels. The starting geometries for all of the DFT calculations were at first optimized in the Spartan ‘14 v1.1.0 Global calculations environment work space at the PM3 level, and then followed by the DFT B3LYP calculations at 6311+G** basis set level. The optimized geometries of the reactants, intermediates, transition states and products were confirmed in terms of vibrational analysis [35,38]. The transition state for each step was located and confirmed by animating the vibration corresponding to the reaction coordinate by selecting the imaginary frequency at the top of the list of frequencies on the IR tab. No arbitrary assumptions were imposed on finding the most likely geometries for the transition state in each case.

3. Results Section

3.1. Published Mechanism

The outline of the published mechanism of the oxidation of hydrazine / hydrazinium ion with iodine as given by past workers [6] is shown in scheme1below.

(1)

(2)

(3)

(4)

(5)

Scheme 1. The reaction mechanism as proposed by Mshelia et al [7].

Mshelia et al [6] gave the stoichiometry of their reaction as (6) below.

(6)

The mechanism as proposed in Scheme 1 by Mshelia et al [7] was not consistent with their stated stoichiometric equation. Whereas the number of all atoms on the reactants side and those on the products side were balanced, the number of positive charges on the products was twice that on the reactants side. However, it was noted that their stoichiometry was consistent with their other data. It, therefore, showed the problem was with the mechanism they proposed. It is the desire of this work to find out if mechanisms that are consistent with the stoichiometry or, better still, mechanisms that are more favourable energetically than the one proposed by Mshelia et al [7] could be formulated in current study. Four mechanisms were proposed and presented in schemes 2 - 5 as routes I, II, III and IV, respectively.

3.2. Geometry Optimization of Intermediates and Transition States; and Validity of the Generally Accepted Mechanism

Geometry optimization of the reactants, intermediates, transition states and products in the hydrazine / hydrazinium ion reaction with iodine was executed. The geometry optimizations of all these species were successfully completed and the heat of formation (ΔHo) at standard condition of 1 atmosphere and 298.15K were evaluated and presented together with other thermodynamic parameters in Table 1 for route I, Table 2 for route II, Table 3 for route III and Table 4 for route IV. The activation parameters for all the routes proposed were given in Tables 5 and 6.

Table 1. Heat of formation at standard condition of 1 atmosphere and 298.15K of reacting species for route I for hydrazine / hydrazinium ion – iodine system.

S/N Reacting Specie Heat of formation together with other thermodynamic parameters at 1 Atm and 298.15K for route I
ΔHo (kJ/mol) ΔGo (kJ/mol) ΔSo (kJ/mol.K)
1 I2 -36,334,465.70 -36,334,542.14 260.55
2 H2O -200,678.03 -200,732.28 188.64
3 H3O+ -201,317.55 -201,375.65 194.90
4 Hyd+ -294,265.02 -294,343.59 263.55
5 Hyd -293,512.76 -293,585.77 244.93
6 HI -18,168,774.40 -18,168,835.99 206.59
7 Int. -290,042.75 -290,100.30 364.75
8 N2 -287,570.90 -287,627.96 191.57
9 TSF -494,142.06 -494,634.72  
10 TS1 -36,527,976.45 -36,528,075.41 331.95
11 TS2 -36,618,245.67 -36,625,511.49  
12 R1 -494,943.05    
13 P1 -494,830.31    
14 R2 -36,627,978.46    
15 P2 -36,627,591.55    
16 R3 -36,624,508.45    
17 P3 -72,962,668.50    
18 Ea1 800.99    
19 Ea2 100,002.01    
20 Ea3 6,262.78    

Where I2 was iodine molecule, H2O was water molecule, Hyd+ was hydrazinium ion, Hyd was hydrazine, HI was hydrogen iodide molecule, HOI was hypoiodous acid, Int was intermediate (diazine), TS1was transition state for step 1, N2 was nitrogen molecule, R1 and R2 were all the reactants for step 1 and step 2, P1 and P2 were all the products for step 1 and step 2, Ea1 and Ea2 were the activation energies for steps 1 and 2.

Table 2. Heat of formation at standard condition of 1 atmosphere and 298.15K of reacting species for route 2 for hydrazine / hydrazinium ion –iodine system.

S/N Reacting Specie Heat of formation together with other thermodynamic parameters at 1 Atm and 298.15K for route 2
ΔHo (kJ/mol) ΔGo (kJ/mol) ΔSo (kJ/mol.K)
1 I2 -36,334,465.70 -36,334,542.14 260.55
2 H2O -200,678.03 -200,732.28 188.64
3 H3O+ -201,317.55 -201,375.65 194.90
4 Hyd+ -294,265.02 -294,343.59 263.55
5 Hyd -293,512.76 -293,585.77 244.93
6 HI -18,168,774.40 -18,168,835.99 206.59
7 N2 -287,570.90 -287,627.96 191.57
8 TSF -494,142.06 -494,634.72  
9 TSB -72,948,708.06 -72,963,181.09  
10 R1 -494,943.05    
11 P1 -494,830.31    
12 RB -72,962,444.16    
13 PB -72,962,668.50    
14 Ea1 800.99    
15 EaB 13,736.10    

Where I2 was iodine molecule, H2O was water molecule, Hyd+ was hydrazinium ion, Hyd was hydrazine, HI was hydrogen iodide molecule, HOI was hypoiodous acid, Int was intermediate (diazine), TS1was transition state for step 1, N2 was nitrogen molecule, R1 and R2 were all the reactants for step 1 and step 2, P1 and P2 were all the products for step 1 and step 2, Ea1 and Ea2 were the activation energies for steps 1 and 2.

Table 3. Heat of formation at standard condition of 1 atmosphere and 298.15K of reacting species for route 3 for hydrazine / hydrazinium ion – iodine system.

S/N Reacting Specie Heat of formation together with other thermodynamic parameters at 1 Atm and 298.15K for route 3
ΔHo (kJ/mol) ΔGo (kJ/mol) ΔSo (kJ/mol.K)
1 I2 -36,334,465.70 -36,334,542.14 260.55
2 H2O -200,678.03 -200,732.28 188.64
3 H3O+ -201,317.55 -201,375.65 194.90
4 Hyd+ -294,265.02 -294,343.59 263.55
5 Hyd -293,512.76 -293,585.77 244.93
6 HI -18,168,774.40 -18,168,835.99 206.59
7 N2 -287,570.90 -287,627.96 191.57
7 TSF -494,142.06 -494,634.72  
8 TS1 -36,527,976.45 -36,528,075.41 331.95
9 TSC -72,948,830.75 -72,963,303.79 451.51
10 R1 -494,943.05    
11 P1 -494,830.31    
12 RC -72,962,444.16    
13 PC -72,962,668.50    
14 Ea1 800.99    
15 EaC 13,613.41    

Where I2 was iodine molecule, H2O was water molecule, Hyd+ was hydrazinium ion, Hyd was hydrazine, HI was hydrogen iodide molecule, HOI was hypoiodous acid, Int was intermediate (diazine), TS1 was transition state for step 1, N2 was nitrogen molecule, R1 and R2 were all the reactants for step 1 and step 2, P1 and P2 were all the products for step 1 and step 2, Ea1 and Ea2 were the activation energies for steps 1 and 2.

Table 4. Heat of formation at standard condition of 1 atmosphere and 298.15K of reacting species for route 4 for hydrazine / hydrazinium ion – iodine system.

S/N Reacting Specie Heat of Formation together with other activation parameters at 1 Atm and 298.15K for route 4
ΔHo (kJ/mol) ΔGo (kJ/mol) ΔSo (kJ/mol.K)
1 I2 -36,334,465.70 -36,334,542.14 260.55
2 H2O -200,678.03 -200,732.28 188.64
3 H3O+ -201,317.55 -201,375.65 194.90
4 HOI -18,366,219.67 -18,366,295.58 254.58
5 Hyd+ -294,265.02 -294,343.59 263.55
6 Hyd -293,512.76 -293,585.77 244.93
7 HI -18,168,774.40 -18,168,835.99 206.59
8 N2 -287,570.90 -287,627.96 191.57
9 TSF -494,142.06 -494,634.72  
10 TSD -36,534,957.18 -36,535,052.36 319.24
11 TSE -37,019,091.68 -37,056,036.73  
12 R1 -494,943.05    
13 P1 -494,830.31    
14 RD -36,535,143.73    
15 PD -36,534,994.07    
16 RE -37,025,952.10    
17 PE -37,026,475.76    
18 Ea1 800.99    
19 EaD 186.55    
20 EaC 6,860.42    

Where I2 was iodine molecule, H2O was water molecule, Hyd+ was hydrazinium ion, Hyd was hydrazine, HI was hydrogen iodide molecule, HOI was hypoiodous acid, Int was intermediate (diazine), TS1 was transition state for step 1, N2 was nitrogen molecule, R1 and R2 were all the reactants for step 1 and step 2, P1 and P2 were all the products for step 1 and step 2, Ea1 and Ea2 were the activation energies for steps 1 and 2.

Table 5. Heat of formation and other activation parameters at standard condition of 1 atmosphere and 298.15K of reacting species for routes I and II for hydrazine / hydrazinium ion – iodine reaction system.

Route Reacting Species Heat of formation together with other activation parameters at 1 Atm and 298.15K for routes 1 and 2
ΔrHo (kJ/mol) Δ‡G (kJ/mol) Δ‡S (kJ/mol.K) Δ‡Ea (kJ/mol)
Route I R1 -494,943.05      
  P1 -494,830.31      
  TS1 -36,527,976.45      
  Step I   2.76 x104 -1.75 x103 8.01 x102
  R2 -36,627,978.46      
  P2 -36,627,591.55      
  TS2 -36,618,245.67      
  Step II   -2.70 x104 -1.73 x105 1.00 x105
  R3 -36,624,508.45      
  P3 -72,962,668.50      
  TS3 (TSF) -494,142.06      
  Step III   -1.52 x107 -3.66 x107 6.26 x103
Route II R1 -494,943.05      
  P1 -494,830.31      
  (TS1) TSF -494,142.06      
  Step I   2.76 x104 -1.75 x103 8.01 x102
  RB -72,962,444.16      
  PB -72,962,668.50      
  TSB -72,948,708.06      
  Step II   5.91 x104 -2.45 x105 1.37 x104

Table 6. Heat of formation and other activation parameters at standard condition of 1 atmosphere and 298.15K of reacting species for routes III and IV for hydrazine / hydrazinium ion – iodine reaction System.

Route Reacting species Heat of formation together with other activation parameters at 1 Atm and 298.15K for routes 3 and 4
ΔrHo (kJ/mol) Δ‡G (kJ/mol) Δ‡S (kJ/mol.K) Δ‡Ea (kJ/mol)
Route III R1 -494,943.05      
  P1 -494,830.31      
  (TS1) TSF -494,142.06      
  Step I   2.76 x104 -1.75 x103 8.01 x102
  RC -72,962,444.16      
  PC -72,962,668.50      
  TSC -72,948,830.75      
  Step II   7.37 x104 -1.23 x105 1.37 x104
           
Route IV R1 -494,943.05      
  P1 -494,830.31      
  (TS1) TSF -494,142.06      
  Step I   2.76 x104 -1.75 x103 8.01 x102
  RD -36,535,143.73      
  PD -36,534,994.07      
  TSD -36,534,957.18      
  Step II   1.57 x109 -5.40 x106 1.87 x102
  RE -37,025,952.10      
  PE -37,026,475.76      
  TSE -37,019,091.68      
  Step II   8.01 x104 -1.24 x106 6.86 x103

In all the four routes proposed, the first step always started with the hydrolysis of the hydrazinium ion or abstraction of hydrogen ion by water to yield hydrazine. In fact, the abstraction of hydrogen ion or the hydrolysis of hydrazinium ion by water to yield hydrazine has been reported by several authors [39,40,41].

All the transition states in the schemes proposed in this work were found to be true transition states or activated complexes. They all have higher energies compared to other species in their respective elementary steps as can be seen in Tables 1 – 6. They all occupied saddle points on scaled potential energy surface diagrams as drawn in Figures 1 – 4. The trueness of the transition states were also confirmed by animating the vibration corresponding to the reaction coordinate by selecting the imaginary frequency at the top of the list of frequencies on the IR tab.

Figure 1. Energy profile of the oxidation of hydrazine / hydrazinium ion by iodine according to the route I proposed mechanism.

Where R1, TS1 and P1 were reactants, transition state and products, respectively, for the first step; while R2A and R3A were reactants, TS2A and TS3A were transition states, in second and third steps, respectively. P2 and P3 were the products of the reaction in steps 2 and 3, respectively.

Figure 2. Energy profile of the oxidation of hydrazine / hydrazinium ion by iodine according to the route II proposed mechanisms.

Where R1, TS1 and P1 were reactants, transition state and products, respectively, for the first step; while R3A were reactants and TS3A was transition state, in second step. P3A were the products of the reaction the step.

Figure 3. Energy profile of the oxidation of hydrazine / hydrazinium ion by iodine according to the route III proposed mechanisms.

Where R1, TS1 and P1 were reactants, transition state and products, respectively, for the first step; while R3A were reactants and TS3A was transition state, in second step. P3A were the products of the reaction the step.

Figure 4. Energy profile of the oxidation of hydrazine / hydrazinium ion by iodine according to the route IV proposed mechanism.

Where R1, TS1 and P1 were reactants, transition state and products, respectively, for the first step; while R2D and R3E were reactants, TSD and TSE were transition states, in second and third steps, respectively. P2D and P3E were the products of the reaction in steps 2 and 3, respectively.

3.3. Proposal of a More Plausible Mechanism for the Reaction

Based on the discussion of the DFT calculations of the various optimized reacting species, the four reaction routes or mechanisms shown in Schemes 2 - 5 are more plausible than the mechanism version published by Mshelia et al [6].

3.3.1. Route I

Scheme 2. The first proposed mechanism for the hydrazine / hydrazinium ion reaction with iodine.

In this scheme (equations 7-9), water molecule reacted with the hydrazinium ion to yield hydrazine and hydroxonium ion via the transition state TS1. The hydrazine molecule formed in the first step then reacted with an iodine molecule via transition state TS2 to give a diazine molecule and two molecules of HI. Finally, the diazine molecule reacted with another iodine molecule via transition state TS3 to give a nitrogen molecule plus two molecules of HI.

3.3.2. Route II

Scheme 3. The second proposed mechanism for the hydrazine / hydrazinium ion reaction with iodine.

In this scheme (equations 10 and 11), water molecule reacted with the hydrazinium ion to yield hydrazine and hydroxonium ion via the transition state TS1. The hydrazine formed is then attacked concurrently by two molecules of iodine via the transition state TSB to yield the products of nitrogen molecule plus four molecules of HI.

3.3.3. Route III

Scheme 4. The second proposed mechanism for the hydrazine / hydrazinium ion reaction with iodine.

This was another two-step pathway scheme (equations 12 and 13) just like the previous one. The only difference was that each of the two molecules of iodine attacked and abstracted two hydrogen atoms attached to the same nitrogen atoms of the hydrazine molecule. In the previous route, each iodine molecule attacked and abstracted two hydrogen atoms attached to different nitrogen atoms of the hydrazine molecule.

3.3.4. Route IV

Scheme 5. The second proposed mechanism for the hydrazine / hydrazinium ion reaction with iodine.

This scheme (equations 14 - 16), a three-step process, started, as usual, with water molecule reacting with the hydrazinium ion to yield hydrazine and hydroxonium ion via the transition state TS1 in the first step. In the second step, two molecules of iodine reacted with two molecules water via the transition state TSD to yield two molecules of hypoiodous acid plus two molecules of HI. In the final step, two molecules of hypoiodous acid intermediate attacked and abstracted two hydrogen atoms attached to different nitrogen atoms of the hydrazine molecule via transition state TSD to give back the two water molecules, used as catalyst in step two, plus the products of nitrogen molecule and two molecules of HI.

The stoichiometries of the four proposed mechanisms are the same, and are consistent with each of the proposed scheme. In the scheme published by Mshelia et al [7] their stoichiometry was not consistent with their proposed mechanism, in relation to the net charges carried by reacting species. The stoichiometric equation of all the proposed mechanisms is as given below in equation (17).

(17)

Route I of the four mechanisms proposed had three saddle points, TSF, TS1 and TS2 as can be seen in Table 1 and Figure 1. Evidently, step 2 was the rate determining step with an activation barrier, Ea2, of 100,002.01kJ/mol. Routes II and III were both two-step mechanisms. Step 2 for both schemes were the rate determining steps with respective activation energies, EaB and EaC, of 13,736.10kJ/mol and 13,613.41 kJ/mol respectively. The forth route proposed, a water molecule catalyzed mechanism scheme, had three elementary steps with the third step being the rate determining step. The rate determining step had an activation barrier, EaE, of 6,860.4 kJ/mol. In comparing the rate determining steps of the four proposed schemes, the fourth route had the least activation barrier of 6,860.42 kJ/mol, followed by the third with activation energy of 13,613.41 kJ/mol, then the second route with activation energy of 13,736.10 kJ/mol, and lastly, the first route with highest activation barrier of 100,002.01 kJ/mol. Evidently, the fourth scheme proposed would be the most favorable mechanism energetically, and the reaction, in every likelihood, would follow the path of least energy [42].

3.4. Enthalpy of Reaction and Rate Constant Calculations [42, 43, 44, 45]

The enthalpies of reaction were calculated by using the Spartan software package to calculate heats of formation at standard temperature of 298.15K and pressure of 1 atmosphere. The calculations were done by taking the appropriate sums and differences as given in equation (18).

(18)

The computed enthalpy of reaction at standard conditions was 357.96kJ/mol for each of the four proposed pathways. This is because they all have the same stoichiometry. The computed enthalpy of reaction also showed the reactions were endothermic. The potential energy surface diagrams (Figures 1 – 4) also confirmed this. ΔGoand ΔSo were also computed by using the Spartan software package, but for some species where there was no convergence, these parameters were calculated by using the Eyring [44] equation (19).

(19)

The rate constant calculations were computed according to (20).

(20)

Where k (298.15K) = reaction rate at temperature (298.15K), kB= Boltzmann constant (1.380662 X 10-23 J/K), T = temperature (298.15K), h = Planck’s constant (6.626176 x 10-34Js), Co = concentration (taken to be 1), Δ‡Go = Gibbs free energy of activation (kJ/mol),R = gas constant (8.31441 J/mol. K).

The first step for all the four proposed schemes is the same. The rate constants, k1, for this step was calculated to be 68.02 x 103 dm3mol-1sec-1. However, k2 was calculated as 1.84 x 10-5 dm3mol-1sec-1 for route I. k2for routes II, III, and IV were calculated as 22.29 x 109 dm3mol-1 sec-1, 8.02 x 1012 dm3mol-1 sec-1 and 5.68 x 1012 dm3mol-1 sec-1, respectively. The fourth scheme proposed, which incidentally, is the most preferred mechanism, energetically, had the third step as the rate determining step. The rate constant, k3, for this scheme was calculated as 108.48 x 1012 dm3mol-1sec-1. Again, in comparing the rate constants for the rate determining steps for the four proposed pathways, it showed that even kinetically, the fourth scheme was the most favoured yet, as it was reported that the larger the value of the rate constant, the faster the reaction [46].

The overall rate constant, k, for each of the proposed pathways were also calculated after the rate laws were derived. The overall rate constant, k = 1.00 x 10-4 dm3mol-1 sec-1for route I, k = 1.21 x 1013 dm3mol-1 sec-1for route II, k = 4.36 x 1013 dm3mol-1 sec-1for route III and, k = 4.19 x 1031 dm3mol-1 sec-1for route IV

3.5. Rate Laws for the Four Proposed Pathways

Four different mechanisms were proposed for the hydrazine / hydrazinium ion – iodine reaction system, tagged route I to route IV (schemes 2 – 5). The rate laws for the various mechanisms are as derived below.

3.5.1. Route I

Route I is a three - steps reaction mechanism as given in scheme 2.

The second step is the slowest and this is the rate determining step. Therefore, rate,

At the steady state, rate of formation of [N2H2] = rate of consumption of [N2H2].

Therefore,

Therefore, k = 1.00 x 10-4 dm3mol-1 sec-1.

3.5.2. Route II

Route II is a two-step reaction mechanism as given in scheme 3.

The second step is the slowest and this is the rate determining step. Therefore, the rate,

At the steady state, equilibrium is set up and, therefore,

Therefore, k = 1.21 x 1013 dm3mol-1 sec-1for route II.

3.5.3. Route III

Route III is another two-step reaction mechanism as given in scheme 4. The rate law is exactly the same as that of route II. That is,

The second step is the slowest and, therefore, the rate- determining, with the rate,

At the steady state, equilibrium is set up and, therefore,

Therefore, k = 4.36 x 1013 dm3mol-1 sec-1for route III

3.5.4. Route IV

Route IV is a three-step reaction mechanism as given in scheme 5.

The third step is the slowest and this is the rate determining step. Therefore,

At the steady state, equilibrium is set up and, therefore,

and

 

k-2 is approx. zero

Therefore, k = 4.19 x 1031 dm3mol-1 sec-1for route IV.

4. Conclusion

The mechanism of the reaction of hydrazine / hydrazinium ion with iodine was studied using 6311+G** basis set of DFT at the B3LYP level of computation method. The results of this study were compared with previously published work on the reaction of hydrazine / hydrazinium ion with iodine. This work proposed four different reaction mechanisms for the reaction of hydrazine / hydrazinium ion with iodine. The study was also able to demonstrate that the reaction can follow any of the four routes proposed because the activation energies for the rate determining steps in all pathways were comparable. Rate laws for the four proposed mechanisms were also derived, and each of the derived rate laws was consistent with mechanisms proposed. Rate constants for the various reactions were also calculated.


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