1 Introduction

Peroxosulfur salts (PS) like peroxydisulfate (PDS) and peroxymonosulfate (PMS) are among the family of the most versatile oxidants in aqueous solution [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The peroxydisulfate ion (S2O82−), and the peroxomonosulfate ion (SO52−) are oxyanions. Both PDS and PMS are powerful oxidizing agents with reduction potentials (PDS with E° = 2.01 V, and PMS with E° = 1.84 V) higher than H2O2 (E° = 1.76 V) [2]. Important salts comprising peroxydisulfate (PDS) anion include sodium persulfate (Na2S2O8), potassium persulfate (K2S2O8), and ammonium persulfate ((NH4)2S2O8). These salts are colourless, water-soluble solids, which are available easily at a low cost and affordable to any laboratory as bench top chemicals. These salts are highly stable at ambient temperatures with ease of storage and transport [2]. The use of persulfate has recently been the focus of attention for an alternative oxidant in the chemical oxidation of contaminants [5,6,7,8,9]. Review articles published by House [1], Wilmarth and Haim [2] furnish excellent bibliography and summary of the results pertain to the kinetic studies and their plausible mechanisms prior to 1961. On the otherhand, Potassium peroxymonosulfate (potassium monopersulfate, Caroat, Oxone or PMS) is well known for the oxidation of boron-, nitrogen-, phosphorus-, and sulfur-containing compounds [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. In highly acidic solutions the standard electrode potential for this compound is + 2.51 V with a half reaction generating the hydrogen sulfate (pH = 0), which makes it as effective oxidizing agent [23].

$${\text{HSO}}_{ 5}^{ - } + 2 {\text{H}}^{ + } + 2 {\text{e}}^{ - } \to {\text{HSO}}_{ 4}^{ - } + {\text{H}}_{ 2} {\text{O}}$$

Nitration of aromatic and heteroaromatic compounds has received a surging impact because nitroarenes are widely used as important intermediates and precursors during the synthesis of organic and organometallic compounds, pharmaceuticals, explosives, dyes, polymers, pesticides, plastics, drugs and medicines [25,26,27,28]. The classical mixed acid or acid mixture (mixture of two strong acids, sulfuric and nitric acid) method of nitration is still used in industries, which is a notoriously polluting process because it generates large quantities of hazardous waste acid streams. But in the past several decades, several alternative synthetic protocols were used to prevent such acid waste [25,26,27,28]. In this part of the work the authors have taken up the kinetics and mechanism of PDS and PMS triggered nitration of aromatic compounds with a hope that the findings will contribute to the greenery of nitration reactions because the reagents such as PDS, sodium nitrite, and bisulphate used herein are green chemicals and the excess outlets are minimum under kinetic conditions (Scheme 1).

Scheme 1
scheme 1

Peroxysulfates/NaNO2 mediated nitration of aromatic compounds in aqueous bisulfate medium

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2 Experimental details

2.1 General

Reagent grade chemicals procured from Avra, Loba, Merck, SD fine chemicals, which are used as suchwithout further purification. Distilled water purified over acid dichromate and alkaline permanganate is used for preparation of solutions. HPLC grade acetonitrile is used to prepare stock solutions of phenolic compounds. Systronics Model 144 spectrophotometer was used to follow the increase in absorbance of the nitro product (OD or Absorbance(A)) at 400 nm.

2.2 Kinetic method of following the reaction

The reactant solutions were kept stirred in a water thermostat at desired temperature, and, samples were pipetted out into a cuvette at different time intervals, and the coloured product analysed spectrophotometrically. Systronics Model 144 spectrophotometer was used to follow the increase in absorbance of the compound (OD or A) at 405 nm. Absorbance values were in agreement with each other with an accuracy of ± 3 percentage error. The kinetic runs were conducted under pseudo order conditions [Phenol] and [NaNO2] ≫ [catalyst]([PDS] or [PMS]) in aqueous KHSO4 solutions. We have used graphical method of approach to determine order of reaction using the following first order and second order rate Eqs. (1 and 2) appropriately depending on reaction conditions.

$${ \ln }\left[ {\left( {{\text{A}}_{\infty } - {\text{A}}_{0} } \right)/ \, \left( {{\text{A}}_{\infty } - {\text{A}}_{\text{t}} } \right)} \right] = {\text{k}}^{{\prime }} {\text{t}}$$
(1)
$$\frac{1}{{\left( {{\mathbf{A}}_{\infty } - {\mathbf{A}}_{{\mathbf{t}}} } \right)}} = {\mathbf{kt}} + \frac{1}{{\left( {{\mathbf{A}}_{\infty } - {\mathbf{A}}_{0} } \right)}}$$
(2)

In the above expressions, if (x) is the product obtained during the course of reaction, and (a) the initial concentration of reactant, (a–x) represents unreacted concentration of reactant at given instant of time (t). If At is the absorbance of nitrate species produced during the course of reaction at a given time, A∞ is the absorbance at infinite time (at the end of the reaction) and A0, the absorbance (if any) before the on-take of reaction, then (A∞ − A0) and (A∞ − At) are proportional to (a) and (a – x) respectively. The pseudo first-order logarithmic plots [ln (A∞ − A0)/(A∞ − At)] versus time were linear passing through origin indicating first order kinetics in [Peroxysulfate] ([PDS] and [PMS]), as shown in Figs. 1, 2, 3, 4, 5 and 6. The observed first-order rate constants, k′, were evaluated from the slopes of these plots. The plot of (k′) versus [Substrate]) was linear, passing through the origin (under otherwise similar conditions) showing first order dependence on [Substrate] (Figs. 7, 8). The plot of (1/(A∞ − At) versus time under pseudo second order conditions [NaNO2] ≫ [Catalyst] = [Phenol], [KHSO4] (where A0, At, and A∞ are the absorbance at any given time t and at the end of the reaction respectively). Representative second order plots are given in Figs. 9, 10, 11, 12 and 13 respectively.

Fig. 1
figure 1

First order plot of phenol. 103[Phenol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 313 K

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Fig. 2
figure 2

First order plot of P-Cresol. 103[P-Cresol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 3
figure 3

First order plot of P-Chloro phenol. 103[P-Chloro phenol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 4
figure 4

First order plot of phenol. 103[Phenol] = 5.0 mol/dm3; 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 0.010 mol/dm3; MeCN(% V/V) = 5.0; temperature = 303 K

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Fig. 5
figure 5

First order plot of P-Cresol. 103[P-Cresol] = 5.0 mol/dm3; 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 0.010 mol/dm3; MeCN(% V/V) = 5.0; temperature = 308 K

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Fig. 6
figure 6

First order plot of P-chloro Phenol. 103[P-chloro Phenol] = 5.0 mol/dm3; 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 0.010 mol/dm3; MeCN(% V/V) = 5.0; temperature = 303 K

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Fig. 7
figure 7

Plots of (k′) versus [Sub] in PDS/NaNO2 mediated nitration reactions of Phenols. 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 0.010 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K; a Phenol, b p-Cresol, c p-Bromophenol

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Fig. 8
figure 8

Plots of (k′) versus [Sub] in PMS/NaNO2 mediated nitration reactions of Phenols. 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 0.010 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K; a Phenol, b p-Cresol , c p-Bromophenol

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Fig. 9
figure 9

Second order plot of phenol. 104[Phenol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 10
figure 10

Second order plot of P-Cresol. 104[P-Cresol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 11
figure 11

Second order plot for P-chloro Phenol. 104[P-chloro Phenol] = 5.0 mol/dm3; 104[PDS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 12
figure 12

Second order plot of phenol. 104[Phenol] = 5.0 mol/dm3; 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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Fig. 13
figure 13

Second order plot of P-Cresol. 104[P-Cresol] = 5.0 mol/dm3; 104[PMS] = 5.0 mol/dm3; 103[NaNO2] = 5.0 mol/dm3; 103[KHSO4] = 5.0 mol/dm3; MeCN(% V/V) = 5.0; temperature = 298 K

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2.3 General procedure for synthesis of nitroarenes under kinetic conditions

We have taken up the synthesis of nitroarenes under kinetic conditions used in the present study to identify and confirm the reaction products. Reaction mixture prepared under kinetic conditions in a clean two necked round bottom flask and constantly stirred the mixture under reflux conditions. Progress of the reaction was monitored chromatographically with TLC. After completion, the reaction mixture was treated with NaHCO3 solution to attain neutral condions. The organic layer was separated, dried over Na2SO4, and evaporated under vacuum. The crude product was purified by column chromatography using ethyl acetate – hexane as eluent to get pure product. The synthesized compounds were characterized by 1H NMR and mass spectroscopic methods (Table 1).

Table 1 Peroxydisulphate (PDS) and peroxymonosulphate (PMS) as catalysts for nitration of Phenols
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2.4 Test for the detection of free radicals

Freshly prepared acrylamide or deareated acrylonitrile were added to the reaction mixture containing potassium peroxydisulfate (PDS) and/or peroxymonosulfate (PMS) under nitrogen atmosphere in situ in order to detect the formation of free radical intermediates during the course of reaction, olefinic monomers to detect whether free radical intermediates are formed in situ during the course of reaction. Peroxysulfates such as potassium peroxydisulfate (PDS) and/or peroxymonosulfate (PMS) did not initiate/induce polymerization of added olefinic monomers even after 24 h under reflux conditions. This observation indicated the absence of free radical intermediates during the course of present reaction.

2.5 Effect of variation of [additives]

In order to have a closer look into the mechanism and the rate law, effect of variation of different additives like [KHSO4] (0.005–0.050 mol/dm3), [NaNO2] (0.001–0.010 mol/dm3), and [peroxysulfate] (0.001–0.002 mol/dm3) were studied under otherwise similar conditions (Table 2). None of these additives had any significant effect on the the rate of nitration. These observations put together probably point out that peroxy sulphates (PDS and/or PMS) are stoichiometric reagents, which in situ generate nitronium ion species when they react with nitrite (NO2−) in the presence of mild acid (obtained from the dissociation of (HSO4−) bisulphate anion). Further, the constancy in the k′-values with the increase in [PS] confirms that order with respect to [PS] is unity.

Table 2 Effect of variation of [Additives] on pseudo first order rate constants (k′) in PDS, PMS (PS)/NaNO2 mediated nitration reactions of phenol
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3 Results and discussion

3.1 Reactive species and mechanism of nitration in PDS/NaNO2 mediated nitration of aromatic compounds

Persulfate is known to exist mainly as PDS anion (S2O82−) in aqueous solution. However, in the present study, nitration of aromatic compounds is conducted in presence of NaNO2 by taking [NaNO2] ≫ [PDS] in aqueous bisulphate (HSO4−) medium. Nitrite picks up a proton, released from the dissociation of HSO4− to form (HNO2), which could be oxidised PDS anion (S2O82−) to generate active nitronium ion (NO2+), as repoted by Edwards and coworkers [8]. Nitronium ion thus formed, reacts with aromatic compounds (R-C6H4-X) in a slow step undergo electrophilic nitration to afford the nitro aromatic compounds, according to the following reaction steps:

$${\text{HSO}}_{ 4}^{ - } \overset {{\text{K}}_{\text{d}} } \rightleftharpoons {\text{H}}^{ + }+ {\text{SO}}_{ 4}^{ 2- }$$
(3)
$${\text{NO}}_{ 2}^{ - } + {\text{H}}^{ + } \overset {{\text{K}}_{1} } \rightleftharpoons {\text{HNO}}_{ 2}$$
(4)
$${\text{HNO}}_{ 2} + {\text{ S}}_{ 2} {\text{O}}_{ 8}^{ - 2} \overset {{\text{K}}_{2} } \rightleftharpoons {\text{NO}}_{ 2}^{ + } + {\text{H}}^{ + } + {\text{ 2SO}}_{ 4}^{ 2- }$$
(5)
$${\text{NO}}_{ 2}^{ + } + {\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}\xrightarrow{{\text{Slow}}\left( {{\text{k}}_{ 1} } \right)} {\text{R-C}}_{ 6} {\text{H}}_{ 3}{\text{-X-}}\left( {{\text{NO}}_{ 2} } \right) + {\text{ H}}^{ + }$$
(6)

Rate-law for the above sequence of mechanistic steps could be derived as given in the following steps using equilibria (3–5) and step (4).

$${\text{Rate}} = - {\text{d}}[{\text{R-C}}_{ 6} {\text{H}}_{ 4} {\text{-X}}\left]/ {{\text{dt}} = {\text{k}}_{ 1} } \right[{\text{NO}}_{ 2}^{ + } ]\left[ {{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}} \right]$$
(7)

From step (3)

$$\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {\text{K}}_{ 2} \left[ {{\text{HNO}}_{ 2} } \right]\left[{\text{S}}_{ 2} {\text{O}}_{ 8}^{ 2- } \right] /\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]^{ 2}$$
(8)

But from step (4) in situ produced [HNO2] could be evaluated as,

$$\left[ {{\text{HNO}}_{ 2} } \right] \, = {\text{ K}}_{ 1} [{\text{NO}}_{ 2}^{ - } ][{\text{H}}^{ + } ]$$
(9)

Substituting for [HNO2] from Eq. (9) into Eq. (8), [NO2+] could be obtained as,

$$\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {\text{K}}_{ 1}\, {\text{K}}_{ 2} \left[ {{\text{S}}_{ 2} {\text{O}}_{ 8}^{ 2- } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]]\left[ {{\text{H}}^{ + } } \right] \, /\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]^{ 2}$$
(10)

From step (3), [H+] can be obtained from the dissociation step of (HSO4−) as,

$$\left[ {{\text{H}}^{ + } } \right] = \left( {{{{\text{K}}_{\text{d}} [{\text{HSO}}_{ 4}^{ - } } \mathord{\left/ {\vphantom {{{\text{K}}_{\text{d}} [{\text{HSO}}_{ 4}^{ - } } {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}} \right. \kern-0pt} {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}} \right)$$
(11)

Substitution of [H+] from Eq. (11) into Eq. (10), [NO2+] could be again reduced to,

$$\left[{{\text{NO}}_{ 2}^{ + } } \right] = {{\text{K}}_{\rm d}} {\text{K}}_{ 1}\,{\text{K}}_{ 2} \left[ {\text{PDS}} \right]\left[ {{\text{HSO}}_{ 4}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]/ \left[ {{\text{SO}}_{ 4}^{ - 2} } \right]^{ 3} \quad \left( {{\text{where}}\;{\text{PDS}} = {\text{S}}_{ 2} {\text{O}}_{ 8}^{ 2- } } \right)$$
(12)

Now, substitution of active species [NO2+] from Eq. (12) into Eq. (7), final rate law comes out as,

$${\text{Rate}} = - {\text{d}}\left[ {{\text{R - C}}_{6} {\text{H}}_{4} {\text{ - X}}} \right]/{\text{dt}} = \mathop {{\text{kK}}_{{\text{d}}} {\text{K}}_{1} {\mkern 1mu} {\text{K}}_{2} \left[ {{\text{PDS}}} \right]\left[ {{\text{HSO}}_{4}^{ - } } \right]\left[ {{\text{NO}}_{2}^{ - } } \right]\left[ {{\text{R - C}}_{6} {\text{H}}_{4} {\text{ - X}}} \right]}\limits_{{[{\text{SO}}_{4}^{{2 - }} ]^{3} }}$$
(13)

Above rate equation is in consonance with the observed kinetic results viz., first order in [Substrate] (i.e., R–C6H4–X), and [PDS]. Since [NO2−] is taken in large excess over [PDS], and [KHSO4], it implies that order in [active NO2+ species] is also one. Bisulphate term ([HSO4−]) appeared in the numerator of rate law is negated by ([SO −24 ]3) term in the denominator, thus accounting for the observed negligible (HSO4−) effect on rate of the reaction. Thus, at constant (HSO4−) concentration, and known excess of [NO2−] the rate law reduces to,

$${{\text{Rate}}} = {{ -{\text{d}}\left[ {{\text{R-C}}_{6} {\text{H}}_{ 4}{\text{-X}}} \right]}/ {{\text{dt}} = {\text{ k}}\left[ {{\text{NO}}_{ 2}^{ + } } \right]\left[ {{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}} \right]}}\quad \left( {{\text{where}}\;\left[ {{\text{NO}}_{ 2}^{ + } } \right] = \left( {{\text{K}}_{\rm d}} {\text{K}}_{ 1}\, {\text{K}}_{ 2} \left[ {\text{PDS}} \right]\left[ {{\text{HSO}}_{ 4}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]/ \left[ {{\text{SO}}_{ 4}^{ 2- } } \right]^{3} \right)} \right)$$
(14)

On the basis of the foregoing discussion, the sequential mechanistic steps for the nitration of aromatic compounds of this study can be summarized as shown in Scheme 2.

Scheme 2
scheme 2

PDS/NaNO2 mediated mechanism of Nitration of aromatic compounds

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3.2 Reactive species and mechanism of nitration in PMS/NaNO2 mediated nitration of aromatic compounds

Potassium Permonosulfate is a salt of Caro’s acid (H2SO5), which is known to mainly exist as PMS (HSO5−). Present investigation (the nitration reactions) is taken up in aqueous bisulphate (HSO4−) solutions, under the conditions [NaNO2] ≫ [PMS], [HSO4−]; [HSO4−] > [PMS]. Bisulphate (HSO4−) behaves like a monoprotic acid and gives a proton (H+) according to the equilibrium (1) as mentioned in the previous section. In aqueous HSO4− medium Nitrite ion (NO ‒2 ) may protonate to form HNO2. The PMS (HSO52−) may oxidize HNO2 and generate active nitronium ion (NO2+) species in situ, which inturn reacts with aromatic compounds (R-C6H4-X) in a slow step, which undergo electrophilic nitration and afford the nitro aromatic compounds, as shown in the following reaction steps, given in the following steps

$${\text{HSO}}_{ 4}^{ - } \overset {{\text{K}}_{\text{d}} } \rightleftharpoons {\text{H}}^{ + }+ {\text{SO}}_{ 4}^{ 2- }$$
(3)
$${\text{NO}}_{ 2}^{ - } + {\text{H}}^{ + } \overset {{\text{K}}_{1} } \rightleftharpoons {\text{HNO}}_{ 2}$$
(4)
$${\text{HSO}}_{ 5}^{ - } + {\text{ HNO}}_{ 2} \overset {{\text{K}}_{4} } \rightleftharpoons {\text{NO}}_{ 2}^{ + } + {\text{ SO}}_{ 4}^{ 2- } + {\text{ H}}_{ 2} {\text{O}}$$
(15)
$${\text{NO}}_{2}^{ + } + {\text{ R-C}}_{6} {\text{H}}_{4} - {\text{X}}\mathop{\longrightarrow}\limits^{{{\text{Slow}}\left( {{\text{k}}_{1} } \right)}}{\text{R-C}}_{6} {\text{H}}_{3}{\text{-X}} - \left( {{\text{NO}}_{2} } \right){\mkern 1mu} + {\text{ H}}^{ + }$$
(16)

Rate-law for these mechanistic steps could be derived using equilibria (3, 4 and 1) and step (1).

$${\text{Rate}} = {{ - {\text{d}}\left[ {{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}} \right]} \mathord{\left/ {\vphantom {{ - {\text{d}}\left[ {{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}} \right]} {\text{dt}}}} \right. \kern-0pt} {\text{dt}}}\left] { = {\text{k}}_{ 1} } \right[{\text{NO}}_{ 2}^{ + } ]\left[ {{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}} \right]$$
(17)

From step (1)

$$\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {{{\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{HNO}}_{ 2} } \right]} \mathord{\left/ {\vphantom {{{\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{HNO}}_{ 2} } \right]} {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}} \right. \kern-0pt} {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}$$
(18)

But from step (4) in situ produced [HNO2] could be evaluated as,

$$\left[ {{\text{HNO}}_{ 2} } \right] = {\text{K}}_{ 1} \left[ {{\text{H}}^{ + } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]$$
(19)

Substituting for [HNO2] from Eq. (19) into Eq. (18), [NO2+] could be given as,

$$\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {{{\text{K}}_{ 1}\, {\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]\left[ {{\text{H}}^{ + } } \right]} \mathord{\left/ {\vphantom {{{\text{K}}_{ 1}\, {\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]\left[ {{\text{H}}^{ + } } \right]} {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}} \right. \kern-0pt} {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]}}$$
(20)

Upon substitution of [H+] from Eq. (11) into Eq. (18) and further simplification, the active species [NO2+] could be written as,

$$\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {{\text{K}}_{\rm d}} {\text{K}}_{ 1} {\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right]\left[ {{\text{HSO}}_{ 4}^{ - } } \right]/ {\left[ {{\text{SO}}_{ 4}^{ 2- } } \right]^{2} }$$
(21)

Subtitution of active species [NO2+] from Eq. (21) into Eq. (19), final rate law comes out as,

$${\text{Rate}} = - {\text{d}}[{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}]/{\text{dt}} = \left( {{\text{kK}}_{\rm d}} {\text{K}}_{ 1}\, {\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right] {\left[ {{\text{HSO}}_{ 4}^{ - } } \right]} \left[{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}} \right]\right)/ \, [{\text{SO}}_{ 4}^{ 2- } ]^{ 2}$$

Above rate equation is keeping in with the observed kinetic results viz., first order in [Substrate] (i.e., R-C6H4-X), and [PMS]t. Since [NO2−]t ≫ [PMS]t, and [KHSO4], it is understood that order in [active NO2+ species] is also one. Bisulphate term ([HSO4−]) appeared in the numerator of the rate law is negated by (SO42−) term in the denominator, suggesting the observed negligible (HSO4−) effect on rate of the reaction. Thus, at constant (HSO4−) concentration, and known excess that rate law reduces to,

$${\text{Rate}} = - {\text{d}}\left[{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}}\right]/ {\text{dt }} = {\text{ k}}\left[ {{\text{NO}}_{ 2}^{ + } } \right] \, \left[{\text{R-C}}_{ 6} {\text{H}}_{ 4}{\text{-X}} \right]\quad \left( {{\text{where}},\;\left[ {{\text{NO}}_{ 2}^{ + } } \right] = {\text{K}}_{\rm d}} {\text{K}}_{ 1}\, {\text{K}}_{ 4} \left[ {{\text{HSO}}_{ 5}^{ - } } \right]\left[ {{\text{NO}}_{ 2}^{ - } } \right] {\left[ {{\text{HSO}}_{ 4}^{ - } } \right] \, / \, } \left[{\text{SO}}_{ 4}^{ 2- }\right]^{ 2} \right)$$

On the basis of the foregoing discussion, the sequential mechanistic steps for the nitration of aromatic compounds of this study can be summarized as shown in Scheme 3.

Scheme 3
scheme 3

PMS/NaNO2 mediated mechanism of nitration of aromatic compounds

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3.3 Temerature effect on the rate of nitration

The PDS and PMS catalysed nitration of different phenols reactions have been studied in different aqueous acetonitrile medium at four to five temperatures in twenty centigrade degree range (300–325°K). The free energy of activation (∆G#) at a given temperature is calculated using Eyring’s theory of reaction rates [29, 30] using the following steps:

$$\Delta {\text{G}}^{\# } = {\text{ RT}}\,\ln \left( {{\text{RT}}/{\text{Nhk}}} \right)$$

Substituting for R, N, and h (in SI units), ∆G# could be simplified accordingly as,

$$\Delta {\text{G}}^{\# } = { 8}. 3 1 4\times {\text{T}}\left[ { 2 3. 7 6 4 1 { } + { \ln }\left( {{\text{T}}/{\text{k}}} \right)} \right]$$

Substituting the value of a temperature (T) in Kelvin degrees and second order rate constant (k), ∆G# could be obtained. We have also evaluated enthalpy and entropies of activation (∆H# and ∆S#) from the slope and intercept values of the Gibbs-Helmholtz plot ∆G# versus temperature (T), according to the following relationship:

$$\Delta {\text{G}}^{\# } =\Delta {\text{H}}^{\# } - {\text{ T}}\Delta {\text{S}}^{\# }$$

Few representative Gibbs–Helmholtz plots for PDS and PMS catalytic nitration reactions are given in Figs. 14, 15, 16, 17, 18 and 19. Activation parameters thus evaluated are compiled in Table 3.

Fig. 14
figure 14

Gibbs-Helmholtz plot (∆G# vs temperature) for PDS/NaNO2 mediated nitration of phenol

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Fig. 15
figure 15

Gibbs-Helmholtz plot (∆G# vs temperature) for PDS/NaNO2 mediated nitration of p-Cresol

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Fig. 16
figure 16

Gibbs-Helmholtz plot (∆G# vs temperature) for PDS/NaNO2 mediated nitration of P-chloro phenol

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Fig. 17
figure 17

Gibbs-Helmholtz plot (∆G# vs temperature) for PMS/NaNO2 mediated nitration of phenol

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Fig. 18
figure 18

Gibbs-Helmholtz plot (∆G# vs temperature) for PMS/NaNO2 mediated nitration of P-Cresol

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Fig. 19
figure 19

Gibbs-Helmholtz plot (∆G# vs temperature) for PMS/NaNO2 mediated nitration of P-chloro phenol

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Table 3 Second order rate constants and activation parameters for PS/NaNO2 and PMS/NaNO2 reactions (PS = PDS or PMS)
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3.4 Quantitative structure and reactivity study

A perusal of the kinetic revealed that the introduction of electron donating or withdrawing groups (EDG and EWG) into the aromatic ring generally altered the rate of nitration with a decreasing trend: m–Me > P–MeO > –H > P–Me > m–OH > ≈ P–Br ≈ P–OH > P–Cl. The ortho substituted phenols indicated a sequence: o–OH > o–Me > –H. Efforts were made correlate the rate data into Hammett’s quantitative structure and reactivity relationship [31,32,33] using the following equation:

$${ \log }\left( {\text{k}} \right) \, = { \log }\left( {{\text{k}}_{0} } \right) \, \pm \sigma \rho$$

According to Hammett, log(k) versus (σ, the Hammett’s substituent constant) a straight line with either a positive or negative slope (ρ; Hammett’s Rho) should be obtained. But, the Hammett’s plots of log(k) versus σ indicated poor linear relationship with very low correlation coefficient (R2) and scattered points. The obtained deviations may be explained due to the mesomeric para interaction energy (ΔΔGp) parameters, and exalted sigma (σ̅ or σeff) values, as suggested by Brown, Okamoto, van Bekkum, Webster and others [34, 35].

4 Conclusions

In summary, the author has developed peroxydisulfate (PDS) and peroxymonosulfate (PMS) as efficient green reagents for the nitration of aromatic compounds (Phenols) using NaNO2/KHSO4. The reaction followed second order kinetics with first order dependence on [PeroxySulfate] (i.e. [PDS] or [PMS]) and [Phenol], when NaNO2 concentration is taken far excess over all other reagents. The observed kinetic data is sensitive to the structural variation of phenol. Reaction rates accelerated with the introduction of electron donating groups and retarded with electron withdrawing groups: m–Me > P–MeO > –H > P–Me > m–OH > ≈ P–Br ≈ P–OH > P–Cl. On the other hand, ortho substituted phenols indicated a sequence: o–OH > o–Me > –H. But the data did not fit well into the Hammett’s quantitative linear free energy relationship. Deviations could be probably due to mesomeric para interaction energy (ΔΔGp) parameters arising from the exalted sigma (\({\bar{\upsigma }}\) or σeff) values, and Yukawa–Tsuno parameter (r).