Ternary HNO3âH2SO4âH2O Mixtures: A Simplified Approach for the

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Ternary HNO-HSO-HO mixtures: a simplified approach for the calculation of the equilibrium composition Danilo Russo, Raffaele Marotta, Mario Commodo, Roberto Andreozzi, and Ilaria Di Somma Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04193 • Publication Date (Web): 17 Jan 2018 Downloaded from http://pubs.acs.org on January 17, 2018

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Industrial & Engineering Chemistry Research

Ternary HNO3-H2SO4-H2O mixtures: a simplified approach for the calculation of the equilibrium composition Danilo Russoa†, Raffaele Marottaa, Mario Commodob, Roberto Andreozzia, Ilaria Di Sommab a Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale. Università di Napoli “Federico II”, p.le V. Tecchio, 80 -80125- Napoli, Italy b

Istituto di Ricerche sulla Combustione (CNR), p.le V. Tecchio, 80 -80125- Napoli, Italy

†

Corresponding author. Tel.: +39 081 7682253; fax: +39 081 5936936. E-mail address: [email protected] (D. Russo).

Keywords: nitric acid; nitration; sulfuric acid; Raman spectroscopy; dissociation; nitronium. Abstract Concentrated ternary mixture of nitric acid, sulfuric acid and water are often used in the chemical industry for a wide range of applications. Among these, nitrations of organic substrates are the most common. Nevertheless, there is still a poor understanding of speciation of the acids in the mixtures and different simplified or semi-empirical approaches have been found in the literature to model nitration kinetics by mixed acids. Most of the found investigations are relevant in restricted ranges of experimental conditions, resulting in a fragmentary vision. In this work, most of the approaches found in the literature were reviewed in order to define their limits of validity and new empirical equations for the estimation of nitronium ion concentration are proposed. Moreover, on the basis of original experimental data, a simplified model is proposed to calculate the dissociation of acids at varying experimental conditions and the main assumptions reported in the literature were verified. Adopted simplifying assumptions were verified at sulfuric acid concentration higher than 2.1 mol·L1

, and nitric acid concentration ranging from 2.0 to 11 mol·L-1.

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1. Introduction Concentrated mixtures of nitric and sulfuric acids, namely mixed acid, are widely employed in fine and bulk chemicals production.1-7 Even though several attempt and studies focused on the adoption of new nitrating agents,8-11 mixed acids are still the most used reaction media in nitration processes.6 Thus, there is a need to better characterize the behavior of the system in order to predict the equilibrium concentration of the undissociated acids and the ionic species deriving from their dissociation. Moreover, oxidation reactions often take place in mixed acids, and a deeper understanding of the equilibrium concentrations of HNO3 and H+ is thus necessary for an adequate kinetic modeling.12,13 Furthermore, most nitration/oxidation processes of organics in mixed acids are carried out in liquid-liquid heterogeneous phase14-16 so that the equilibrium composition of the acid mixture is important to model the contribution of each ionic and neutral species to the solubility of the organics in the acidic aqueous mixture. Finally, an interest has been shown in speciation of nitric acid in sulfuric acid in several atmospheric reaction studies.17,18 Several attempts have been made in order to measure and describe the concentration of these species at varying acidic conditions.19-23 It has been shown that, depending on the initial concentration of mineral acids and water, the principal species in equilibrium in concentrated mixtures are HNO3, NO3-, NO2+, H2SO4, HSO4- and H+. Sulfate ion SO42- is also present in high diluted acidic mixtures, but its concentration is generally negligible for highly acidic media, which are normally used in the abovementioned industrial applications. At the best of the Authors’ knowledge, the most extended available experimental data on nitronium ion (NO2+) concentrations, measured by Raman spectroscopy, can be found in Albright et al. (1996)19 and Edwards et al. (1994).24 Albright proposed a modeling of the system based on the following equilibria (R.1 - R.3)

+ ↔ + +

(R.1)

↔ +

(R.2) 2 ACS Paragon Plus Environment

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↔ +

(R.3)

However, the proposed mathematical model is based on the hypothesis of ideal mixtures without taking into account the contribution of the activity coefficients. Although the experimental nitronium concentrations were predicted with some accuracy, the model is inaccurate at low nitric acid concentrations (< 5% mol) and fails for nitric acid concentrations lower than 0.5% mol.19 In addition, the calculated concentrations of the other species are not supported by any experimental measurements. In fact, most of the kinetic experimental investigations on nitration reactions have been carried out under those less acidic conditions for safety reasons.13,25-31 Moreover, in some industrial processes the thermal power generated by the exothermic reactions is controlled by working under less acidic conditions. The problem of the calculation of low concentrations of nitronium ion (less than 40 mmol·L-1) in mixed acid was addressed following different approaches,20,27,32,33 since it is impossible to quantify them by Raman analyses.34 Some authors modeled the equilibrium composition of the systems adopting the ASPEN software,23,35-37 but at the best of the Authors’ knowledge, none of the parameters necessary to calculate the nitronium ion activity coefficient according to the most used models (Pitzers, eNRTL, etc.) have been estimated yet. Moreover, these models are often fairly complex and difficult to implement in a more general kinetic model. Very similar issues need to be addressed when modeling nitric acid dissociation in the presence of sulfuric acid and viceversa. Very little or none information is available about nitrate and bisulfate experimental concentrations in ternary systems whereas extensive data have been published for the HNO3-H2O and H2SO4-H2O binary systems.38-42 Two simplified semi-empirical approaches have been adopted to model the NO2+ concentration and the activity coefficients for the acids dissociation equilibria relations, respectively: the HR27,32 and the MC functions.20,33,43 A description of the most adopted approaches, together with their limitations is presented in this paper. Moreover, some new nitronium ion concentrations data, obtained through an indirect experimental method in the low concentration range ([NO2+] less than about 10 mmol·L-1), are presented and compared with the results obtained by using the semi-empirical approaches proposed 3 ACS Paragon Plus Environment


in the literature. Finally, a significant number of ternary mixtures were submitted to Raman analysis in order to quantify the dissociation degree of nitric acid and sulfuric acid. The previous information was taken into account in a simplified model capable to predict the equilibrium concentrations of the species at room temperature (20 °C).

2. Materials & Methods 2.1. Materials All the reagents (nitric acid fuming ≥99%, sulfuric acid ≥99.999%, sodium nitrate ≥99.0 %, benzaldehyde ≥99.0%, 2-nitrobenzaldehyde ≥98.0%, 3-nitrobenzaldehyde ≥99.0%, acetonitrile for HPLC, methanol for HPLC, phosphoric acid 85%, urea 98%) were purchased from Sigma-Aldrich and used as received. Bi-distilled water was used for all the experimental runs. 2.2. Procedures Proper amounts of sulfuric acid, nitric acid and water were prepared and cooled down to 5°C. The acids were then added drop-wise to the water under continuous stirring and cooling at 5°C in a jacketed batch glass reactor (V = 30 mL) thermostated by means of a Julabo F32 refrigerated/heated circulator. Successively, the obtained mixture was heated to 20°C and submitted to Raman analysis. Raman spectra were acquired using a Raman microscope (Horiba XploRA) equipped with a 20X objective (Olympus UPlanFL). The laser source was a frequency doubled Nd:YAG laser ( λ= 532 nm, 12 mW maximum laser power at the sample). The calibration of the system was performed against the Stokes Raman signal of pure silicon at 520 cm−1. A 100 µm pinhole was used for confocal photons collection. Spectra were obtained with a laser beam power of 100%, and an accumulation-exposure time of 3 cycles of 10 s each. Benzaldehyde nitration was chosen as a reference reaction in order to estimate nitronium ion low concentrations. For each isothermal kinetic run, a ternary mixture of nitric acid, sulfuric acid and 4 ACS Paragon Plus Environment

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water was prepared as previously described and thermostated at 20°C. A proper amount of benzaldehyde was added to the mixture. Low benzaldehyde concentrations (from 45 mM to 120 mM) were chosen in order to obtain a homogeneous system and limit the generated thermal power. Samples (V = 100 µL) were collected at different reaction times and rapidly quenched by dilution (1:100) with a solution of urea in acetonitrile (4 g·L-1). The samples were rapidly analyzed by HPLC. All the experimental runs were carried out in triplicate. HPLC analysis was carried out with an Agilent 1100 HPLC equipped with a UV-DAD detector, and a Synergi 4µm polar RP/80A (Phenomenex). The mobile phase (1 mL·min-1) was constituted of 80% v/v eluent A and 20% v/v eluent B; eluent A was 5% v/v methanol, 0.4% v/v phosphoric acid in water; eluent B was reagent grade acetonitrile.

3. Results In order to achieve a complete simplified characterization of the stationary concentrations of the main ionic species in mixed acid, two different experimental campaign were carried out. In a first investigation, the problem of the determination and prediction of nitronium ion concentration was examined to propose new empirical correlations and verify the previous published results (paragraph 3.1). Secondly, Raman analysis were carried out to evaluate the dissociation of nitric and sulfuric acid to nitrate and bisulfate, respectively (paragraph 3.2). Finally, the results were integrated in a comprehensive simplified model (paragraph 3.3). 3.1. Nitronium ion concentrations All the investigated mixtures reported in the literature19 together with some of the experimental conditions adopted in this work and previous investigations13,29 are shown in Fig. 1. The red circles represent the mixtures investigated by Albright et al. (1996)19 in which the nitronium ion concentration is measurable by Raman spectroscopy. Under the conditions represented by the green 5 ACS Paragon Plus Environment


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triangles, a slow nitration of benzaldehyde was reported29 in accordance with the concentration of nitronium ion lower than the limit of detection by Raman spectroscopy.34 The orange squares are representative of high diluted nitrating mixtures under which no nitration or very slow nitration of organic substrates occurs.13 Fig. 1 In the following we will refer to acid solutions represented by red circles, green triangle and orange squares, as highly concentrated, concentrated and diluted mixtures, respectively, considering their application in nitrations. The experimental nitronium ion concentrations measured by Albright et al. (1996)19 and Edwards et al. (1994)24 are shown in Fig. 2. At a fixed molar percentage of HNO3 (N%), the molar concentration (mol·L-1) of NO2+ vs the molar percentage of H2SO4 (S%) follows a sigmoidal profile. Fig. 2 Therefore, in this work we propose the following semi-empirical function (eq.1) to predict the continuous lines reported in Fig. 2

=

1 + ∙ exp (− ∙ %)

(eq.1)

where a, b and c are three adjustable parameters, depending on nitric acid molar percentage N%, [NO2+] is nitronium ion molar concentration, and S% sulfuric acid molar percentage. All the parameters were optimized, by means of the Matlab Software, in order to minimize the mean square deviation from experimental data. The estimated values of the parameters a, b and c were plotted against the nitric acid molar percentage (N%) (Fig. 3). They were interpolated using the following polynomial expressions (eq.2 - eq.4) Fig. 3


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( ·

!

) = −2.409 ∙ 10' (%) + 6.392 ∙ 10* (%) − 6.942 ∙ 10 (%)

(eq.2)

+ 2.823 ∙ 10! (%) = 16426

(eq.3)

= 1.891 ∙ 10!, (%)- − 3.934 ∙ 10. (%)* + 3.169 ∙ 10- (%) − 1.226

(eq.4)

∙ 10 (%) + 2.395 ∙ 10 (%) − 2.085 ∙ 10 (%) + 2.2686 ∙ 10!

Eq.1. can predict with high accuracy nitronium ions concentrations [NO2+] higher than 40mM for N% > 10%. However, for lower concentrations of nitronium ion (green triangles and orange squares reported in Fig. 1) the results are inaccurate, since the predicted values are higher than the limit of quantification, but the experimental Raman spectra did not show any evidence of nitronium ion peaks. The previously reported nitronium ion concentration modeling,19 not taking into account the non-ideality of the system, fails in calculating very low nitronium ions concentrations, too. However, most nitration kinetic models reported in the literature are based on experimental data obtained with mixtures (namely standard mixed acid) of N% and S% about 15.6% and 30% respectively, which corresponds to a weight percentage composition of 20% wt. HNO3, 60% wt. H2SO4, and 20% wt. H2O.13,25-30 Under these conditions, even though nitration processes still occur, no nitronium ion quantification is possible by Raman analysis34 since the nitronium ion concentration is present at levels lower than the limits of detection and quantification and the eq.s 14 are not accurate. To overcome this problem, a semi-empirical function has been proposed, namely HR function.27,32 According to this theory following the equilibrium (R.4)

∙ + ↔ + + 2

(R.4)

it is possible to evaluate [NO2+] by eq.5

012 3−

8=; : =?:@A =; : ∆ ∆ 7 012 3 7 = 89:;< 8=9:> =; ?:@ 56 5


(eq.5)


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where the activities are expressed in mol·L-1, together with the molar concentrations of the species in square brackets. In the neighbourhood of the standard mixed acid composition, i.e. 20% wt. HNO3, 60% wt. H2SO4, and 20% wt. H2O, 89:;< can be considered constant and incorporated in the constant entropic term of the equilibrium constant, whereas 8=; : and 8=9:> can be calculated in accordance with Khudhairy et al. (1989).44 The dimensionless HR function can be defined as follows (eq.6)

−B = C

=;?:@ =?:@A =; :

(eq.6)

and it can be related (in the neighbourhood of the standard mixed acid) to the molar analytical concentration of nitric and sulfuric acids and the absolute temperature27 using eq.7

−B = (0.52 + 0.56 ) 30.33 +

49.0 7 6

(eq.7)

Nitronium ion concentration can be thus predicted as

= 012 3−

∆ ∆ ∗ 8=9:> = 7 012 3 7 10 E 56 5 8=; :

(eq.8)

Where ∆ and ∆ ∗ were recalculated with respect to those previously published27 taking into account the 8 dependence on the temperature and their values are 50.94 kJ·mol-1 and 39.63 J·mol1

·K-1, respectively. It is worth stressing that, in eq.8, the superscript asterisk to the entropic term

∆ ∗ was added because of the inclusion of the 89:;< in this term, as previously explained. However no experimental measurements are present in the literature to validate eq.8. In order to demonstrate the validity and the limitations of eq. 8, the concentration of nitronium ion was estimated using an indirect experimental approach based on the nitration of an organic substrate, namely benzaldehyde. According to the general reaction mechanism of nitration, under the adopted conditions, the nitration reaction rate of an aromatic substrate FG is

G = HIJK FG

eq. 9


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where HIJK is the intrinsic kinetic constant of the reaction between nitronium ion and the aromatic substrate, and and FG are molar concentrations. Considering two experimental runs carried out at the same temperature but in different nitrating mixtures, the initial reaction rate for L = 0 can be derived from the initial slope of the concentration profile vs. the time. It can be expressed as

G!, = HIJK !, FG !,

eq. 10

G, = HIJK , FG ,

eq. 11

where the subscripts 1 and 2 refer to two different experimental runs. From equations 10 and 11, the following expression can be derived

, =

G, FG !, !, G!, FG ,

eq. 12

that makes it possible to calculate the concentration of nitronium ion in an unknown mixture 2, once the !, concentration is known. Equation 12 can be adopted to estimate nitronium ion steadystate concentrations in all the possible ternary mixtures, once the initial reaction rate is measured. The method was validated verifying equation 12 for three different nitrating mixture for which experimental data are available in the literature.19 Three nitration experiments were run at 20 °C with experimental nitronium ion concentration of 0.149, 0.055, and 0.04 mol·L-1. The concentration of nitronium ion for each run was estimated by eq. 12 considering as reference, one at time, the other two runs and the estimated values were always close to the experimental ones (maximum 7% error). Once validated, the method was further used to estimate nitronium ion concentration in mixtures with an unknown concentration of NO2+, in the neighbourhood of the standard mixed acids for all the mixtures reported in Table 1. The comparison between the experimental indirect measurements and the calculations of the HR function are reported in Fig.4b, together with the comparison with the overestimated concentrations calculated using the model by Albright et al. (1996)19, and the eq.s 1-4 proposed in this work (Fig. 4a), that are both inaccurate for low nitronium ion concentration



estimation, in concentrated and diluted mixtures. The calculated and experimental nitronium ion concentrations have been arbitrarily plotted vs. the molar concentration of nitric acid. [HNO3]0 (mol·L-1)

[H2SO4]0 (mol·L-1)

2.41 3.04 3.87 4.93 5.25 4.70 5.03 5.21 4.55 5.26 5.61 4.07 3.31 5.93 4.85 4.86 5.29

9.49 9.40 9.16 10.03 9.35 9.86 9.23 8.80 9.25 8.96 9.41 9.22 9.08 8.45 9.35 9.37 9.14

Table 1. Initial concentrations of nitric and sulfuric acids adopted to estimate nitronium ion concentration in the neighbourhood of the standard mixed acid (4.8 mol·L-1 HNO3; 9.3 mol·L1 H2SO4). Fig. 4 The results reported in Figure 4 show that the adoption of the HR function in the neighbourhood of the standard mixed acids composition gives good results in nitronium ion concentrations prediction. For higher concentrations the HR function is inadequate and the above-mentioned sigmoidal function (eq.1) can be adopted for a better estimation. In the following, the proposed sigmoidal model and the HR function were used to predict nitronium ion concentrations depending on the initial nitric and sulfuric acid concentrations.

3.2. Raman estimation of HNO3, NO3-, HSO4-, H2SO4, and H+ concentrations


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In order to estimate nitric and sulfuric acids dissociation degree in aqueous ternary mixtures, 31 ternary mixtures with HNO3, H2SO4 and H2O analytical concentrations varying between 1.14 – 10.93 mol·L-1, 1.75 – 15.9 mol·L-1 and 5.69 – 44.7 mol·L-1, respectively, were submitted to Raman analysis. Bisulfate ion concentration was estimated through the intensity of the peak at ̴ 426 cm-1. This peak is due to the ν2 band of HSO4-.14,46 The intensity was calibrated using some aqueous sulfuric acid mixtures with [H2SO4]0 lower than 11 mol·L-1, for which the dissociation degree of sulfuric acid to bisulfate ions was known.14,40,42 Once bisulfate ion concentrations were calculated, nitrate ion concentrations were estimated using a deconvolution procedure at ̴ 1048 cm-1. Binary H2SO4-H2O mixtures with unitary dissociation degree, and aqueous sodium nitrate and sodium sulfate were adopted for the calibration procedure. Undissociated acids concentrations were calculated as the difference between the initial concentrations and the measured concentrations of the species deriving from their dissociation. Sulfate ion concentration was ruled out since it can be considered negligible for relatively highly acidic media, such as those considered in the present study. In fact, as a general result of the literature survey, the dissociation of a strong acid is inhibited in the presence of a stronger acid, that is the case of bisulfate ion in the presence of undissociated nitric acid.20,47 Moreover the sharp band at 980 cm-1, which is ascribed to sulfate ion, 48

was absent or not significant in the investigated acidity range. It is worth noting that this

simplifying assumption, is not necessarily verified for more diluted media, whose speciation is not under consideration in the present study. Preliminary sulfate ion estimations, carried out at 980 cm1

, confirmed that sulfuric acid dissociation degree to sulfate was lower than 3.5% for sulfuric acid

concentration lower than 5.0 mol·L-1 in the presence of comparable concentrations of nitric acid, except for a couple of diluted sample (mixtures 18 and 25 in Table 2), in which it was ~5%. For these reasons, sulfate ion concentration was neglected in the following. Therefore, this simplifying assumption was verified at sulfuric acid concentration higher than 2.1 mol·L-1, and nitric acid concentration ranging from 2.0 to 11 mol·L-1.



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In previous investigations20,28,43 the Authors assumed that, in a ternary mixture, sulfuric acid dissociation to bisulfate is not affected in the presence of nitric acid, since the former (reported pKa ranging from -3 to -949-52) is a much stronger acid than the latter, pKa = -1.4.53 This assumption was verified in the literature for very low nitric acid concentrations47 ranging from 10-4-10-2 mol·L-1 and was assumed to be true also for higher nitric acid concentrations20,28 without any further experimental direct evidence. In this work, some preliminary Raman spectra were collected to verify this hypothesis. In Fig. 5. the Raman spectra between 325 cm-1 and 520 cm-1 of three mixtures of aqueous sulfuric acid at different concentrations are compared to the Raman spectra of ternary mixture with the same sulfuric acid concentrations. The results clearly show that sulfuric acid dissociation is unaffected in the presence of nitric acid, even for nitric acid molar concentrations comparable with [H2SO4].

Fig. 5.

The experimental results for the sulfuric acid and nitric acid dissociation degree are summarized in Table 2, while the concentrations of nitronium ion, where detectable by Raman technique, are calculated by means of the previously proposed semi-empirical eq.1 and eq.8.

Mixture MNOP Q MR SOT Q MR O Q MR SOT MSO T 1 2.77 12.45 12.45 0.95 11.50 2 8.72 7.56 12.79 0.06 7.50 3 6.02 10.84 7.23 0.84 10.00 4 1.14 15.94 5.69 1.46 14.49 5 4.53 13.59 4.53 1.47 12.12 6 6.96 11.60 4.64 0.91 10.69 7 9.51 9.51 4.76 0.06 9.45 8 10.93 6.83 9.56 0.16 6.67 9 2.41 9.49 23.28 0.09 9.40 10 4.93 10.03 14.52 0.28 9.75 11 5.81 9.52 13.72 0.48 9.04 12 5.03 9.23 16.84 0.23 9.00 13 5.61 9.41 14.61 1.53 8.94 14 6.17 9.54 13.06 0.56 8.98 12 ACS Paragon Plus Environment

MNOP 2.52 8.19 5.92 0.00 1.20 3.98 7.13 10.21 2.14 4.52 5.37 4.65 5.18 5.74

NO P 0.10 0.53 0.10 0.00 0.42 0.42 0.12 0.51 0.27 0.41 0.44 0.38 0.43 0.44

NO

R 0.15 0.00 0.00 1.14 2.91 2.56 2.27 0.21 0.01 0.01 0.02 0.00 0.02 0.03

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15 2.92 2.78 42.11 0.36 2.42 1.61 1.31 0.00 16 6.59 6.76 20.34 0.12 6.64 6.23 0.36 0.00 17 3.18 8.80 22.74 0.15 8.64 2.86 0.31 0.00 18 0.92 1.75 50.39 0.26 1.49 0.56 0.37 0.00 19 3.25 6.27 30.47 0.29 5.98 2.79 0.46 0.00 20 1.93 10.39 21.11 0.00 10.39 1.60 0.32 0.00 21 2.64 7.04 29.49 0.15 6.89 2.27 0.37 0.00 22 2.63 7.86 9.26 0.11 7.75 1.94 0.69 0.02 23 10.02 6.42 13.35 0.59 5.84 9.66 0.36 0.02 24 9.28 5.94 16.30 0.90 5.68 8.98 0.29 0.01 25 2.00 2.11 44.70 0.06 2.05 1.11 0.89 0.00 26 3.00 5.00 33.85 0.11 4.89 2.30 0.70 0.00 27 4.61 1.30 41.36 0.02 1.28 2.50 2.10 0.00 28 4.64 1.92 39.58 0.00 1.92 2.73 1.92 0.00 29 4.73 3.28 35.69 0.01 3.27 3.34 1.39 0.00 30 3.13 1.94 43.01 0.23 1.71 1.49 1.64 0.00 31 6.24 3.22 32.31 0.04 3.19 4.92 1.32 0.00 Table 2. Experimental equilibrium molar concentrations by Raman analysis. Mean experimental error: 9%.

As presented in Table 2, for H2SO4 concentrations up to ̴ 11 mol·L-1 the sulfuric acid dissociation degree is always higher than 90% with a mean value of about 95%. This is in accordance with literature data about binary H2SO4-H2O mixture14,40,42 for which the dissociation is almost complete under the same experimental conditions. Nitric acid dissociation degree is almost always lower than 10% for highly acidic mixtures whereas the ionisation degree went up to 52% in less acidic mixture (mixture 30 in Table 2). The reported general considerations are in accordance with the previously published observations.20,43

3.3. Equilibrium simplified model On the basis of the previous investigations and the data presented in this work, a simplified model can be adopted to predict the equilibrium species concentrations in mixed acid. The following reactions were considered for nitric and sulfuric acid dissociation:



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→ +

R.2

↔ +

R.3

Incongruous information is reported for sulfuric acid pKa from -3 to -9.49-52 This is probably due to (i) the difficulties in calculating such a high value for the dissociation constant that can vary in a wide range for small errors in the equilibrium concentrations determination; (ii) the difficulties in evaluating with high accuracy the activity coefficient variation of ionic and neutral species in a strongly non-ideal solution for the full range of concentrations. In fact, several efforts have been made to find correlations to evaluate the activity coefficients variation in a wide range of concentrations. The reported thermodynamic models23,35-37 are often very complicated and the identification of the model parameters is still an important subject of study. Therefore, different simplified approaches have been proposed.20,28,43 However, for all practical purposes, at sulfuric acid concentrations up to about 11 mol·L-1 a complete dissociation can be assumed without a significant error, since the experimental error in the determination of the equilibrium concentrations is higher than the error of the model determination. For the nitric acid dissociation in the presence of sulfuric acid the following equilibrium relation can be considered13,43

V9 = 10JW XY 55.56 ∙ =; :

(eq.13)

where V9 is expressed in mol·L-1, such as the activity of water =; : and the molar concentration of the species in square brackets. In eq. 13 the molar concentration of pure water (55.56 mol·L-1) was taken into account together with the activity of water =; : to be in accordance with the pKa definition for acids in aqueous solutions. In fact, the Ka value is defined for highly diluted ideal solutions for which the activity of water is coincident with its molar concentration and is included in the equilibrium constant.13 According to Sampoli et al., (1985)43 the ratio between the activity coefficients can be related to a function of the sulfuric acid concentration, namely Mc function, as follows (eq.14)


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89:>A 8= < 8=9:>

= 10JXY

(eq.14)

where n is a dimensionless constant. The dimensionless MC function can be calculated using a polynomial expression desumed from data reported by Marziano et al. (1981)54

Z[ = −2.0359 ∙ 10 ∙ , + 8.2033 ∙ 10 ∙ , − 1.2824 ∙ 10!

(eq.15)

∙ , + 5.6384 ∙ 10 ∙ , − 2.3932 ∙ 10! On the basis of the previous hypothesis, a simplified model is proposed to predict the equilibrium species concentrations.. The model is based on the following mass balances, together with eq.13

≈ 0

(eq.16)

≈ ,

(eq.17)

, = + +

(eq.18)

+ = +

(eq.19)

In all the above-mentioned equations, the molar concentration of the i-th species is indicated in square brackets. In the presented model, nitronium ion concentration was estimated from the sigmoidal model (eq. 1) or the B function model (eq. 8), depending on the initial conditions. The set of equations (eq.s 13-19) was solved in order to find the values of KN and n minimizing the mean square deviation between experimental and calculated data for the set including 31 mixtures analyzed and reported in Table 2. The best estimated values were of KN = 25 ± 0.87 mol·L-1 and n = 0.37 ± 0.03. It is worth noting that the KN estimated value corresponds to pKN = -1.4, previously reported in the literature.53 In Fig. 6. the results of the experimental (symbols) and calculated (continuous lines) concentrations of the species in all the considered mixtures are shown. Once optimized, the two estimated thermodynamic parameters KN and n were used to numerically solve the system of equations 13-19, without any further adjustment, for each analyzed mixture. As a result, the experimental data presented in Table 2 (symbols), together with their error bars, and the results of the numerical calculations (vertices of the continuous lines) were reported in Fig. 6. As shown, the model is capable to predict the experimental equilibrium concentrations in a wide range 15 ACS Paragon Plus Environment


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of initial concentrations for highly acidic media. An example of the speciation calculation results, together with the correspondent experimental results, is shown in Table 3.

MNOP Q

MR SOT Q

MNOP

NO P

6.24

3.22

4.92

1.32

NO

R

M

not

exp.

4.51 detectable

/

calc.

/

4.85

1.38

3.0·10-7

4.61

Table 3. Example of calculated and experimental molar concentration.

Fig. 6.

Conclusions The dissociation and speciation of nitric and sulfuric acids in concentrated ternary mixture was investigated. The assumption of the independence of sulfuric acid dissociation on the presence of nitric acid was verified in a wide range of concentrations and a simplified model was proposed to predict nitric acid dissociation degree in concentrated mixture. Nitric acid dissociation was found to be affected by sulfuric acid concentration. Specifically, sulfuric acid is capable of partially inhibiting the dissociation of nitric acid to nitrate ion. Therefore a simplified model was proposed to predict nitric acid dissociation at sulfuric acid concentration higher than 2.1 mol·L-1, and nitric acid concentration ranging from 2.0 to 11 mol·L-1. In concentrated and diluted mixtures, nitronium ion concentration was found to be too low to be detected by Raman spectroscopy but still capable of nitrating organic substrates. For this reason, the main approaches found in the literature for the estimation of low concentrations of nitronium ion were experimentally verified by indirect experimental measurements. The acidity function theory was found to be accurate in the neighbourhood of standard mixed acid composition (20% wt. HNO3, 60% wt. H2SO4, and 20% wt. H2O). However, it failed in reproducing experimental data for highly concentrated mixtures for which an empirical correlation was proposed. 16 ACS Paragon Plus Environment

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Acknowledgement The Authors are grateful to Dr. Patrizia Minutolo for his precious support for Raman analysis. References [1] Urbanski, T. Chemistry and technology of explosives; Pergamon Press, PWN-Polish Scientific Publishers: Warszawa, Vol.1, 1964. [2] Wang, Y.; Tam, W.; Stevenson, S.H.; Clement, R.A.; Calabrese, J. New organic non-linear optical materials of stilbene and diphenylacetylene derivatives. Chem. Phys. Lett. 1988, 148, 136. [3] Chen, C.Y.; Wu, C.W.; Duh, Y.S.; Yu, S.W. An experimental study of worst case scenarios of nitric acid decomposition in a toluene nitration process. Process. Saf. Environ. 1998, 76, 211. [4] Kockmann, N.; Roberge, D.M. Harsh reaction conditions in continuous-flow microreactors for the pharmaceutical production. Chem. Eng. Technol. 2009, 32, 1682. [5] Kulkarni, A.A.; Kalyani, V.S.; Joshi, R.A.; Joshi, R.R. Continuous flow nitration of benzaldehyde. Org. Process Res. Dev. 2009, 13, 999. [6] Kulkarni A.A. Continuous flow nitration in miniaturized devices. Beilstein J. Org. Chem. 2014, 10, 405. [7] Quadros, P.A.; Oliveira, M.C.; Baptista, C.M.S.G. Continuous adiabatic industriale benzene nitration with mixed acid at a pilot plane scale. Chem. Eng. J. 2005, 108(1-2), 1. [8] Sreedhar, I.; Singh, M.; Raghavan, K.V. Scientific advances in sulphuric acid free toluene nitration. Catal. Sci. Technol. 2013, 3, 2499. [9] Zarchi, M.A.K.; Rahmani, F. An efficient method for nitration of aromatic compounds over solid acid and polymer-supported sodium nitrite. J. Appl. Polym. Sci. 2011, 121(1), 582. [10] Yadav, U.; Mande, H.; Ghalsasi, P. Nitration of phenols using Cu(NO3)2: green chemistry laboratory experiment. J. Chem. Educ. 2012, 89(2), 268. [11] Lu, C.X. Study progress on green nitration. Chinese Journal of Explosives and Propellants 34(1) (2001) 1-8. 17 ACS Paragon Plus Environment


[12] Gattrell, M.; Louie, B. Adiabatic nitration for mononitrotoluene (MNT) production. ACS Symposium Series 1155, Chapter 3, 2013. [13] Di Somma, I.; Russo, D.; Andreozzi, R.; Marotta, R.; Guido, S. Kinetic modeling of benzyl alcohol oxidation in aqueous misture of nitric and sulfuric acids. Chem. Eng. J. 2017, 308, 738. [14] Quadros, P.A.; Reis, M.S.; Baptista, C.M.S.G. Different modeling approaches for a heterogeneous liquid-liquid reaction process. Ind. Eng. Chem. Res. 2005, 44, 9414. [15] Maestri, F.; Copelli, S.; Rota, R. Simple procedure for optimal scale-up of fine chemical processes. II. Nitration of 4-chlorobenzotrifluoride. Ind. Eng. Chem. Res. 2009, 48(3), 1316. [16] Yu, Z.; Lv, Y.; Yu, C.; Su, W. A high-output selective and heterogeneous nitration of pdifluorobenzene. Org. Process Res. Dev. 2013. [17] Burley, J.D.; Johnston, H.S. Ionic mechanisms for heterogeneous stratospheric reactions and ultraviolet photoabsorption cross sections for NO2+, HNO3, and NO3- in sulfuric acid. Geophys. Res. Lett. 1992, 19(13), 1359. [18] Bianco, R.; Wang, S.; Hynes, J.T. Chapter 18 - Theoretical studies of the dissociation of sulfuric acid and nitric acid at model aqueous surfaces. Adv. Quantum Chem. 2008, 55, 387. [19] Albright, L.F.; Sood, M.K.; Eckert, R.E. Modeling nitronium ion concentrations in HNO3H2SO4-H2O mixtures. ACS Symposium Series; American Chemical Society: Washington, DC, 1996. [20] Zaldivar, J.M.; Molga, E.; Alos, M.A.; Hernandez, H.; Westerterp, K.R. Aromatic nitrations by mixed acid. Slow liquid-liquid reaction regime. Chem. Eng. Process. 1995, 34, 543. [21] Minogue, N.; Riordan, E.; Sodeau, J.R. Raman spectroscopy as a probe of low-temperature ionic speciation in nitric acid and sulfuric acid stratospheric mimic systems. J. Phys. Chem. A 2003, 107, 4436. [22] Chen, C.-C.; Wang, M.; Yu, Y. Modeling mixed-solvent electrolyte systems. Chem. Eng. Prog. 2016, 112(2).


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[23] Wang, M.; Kaur, H.; Chen, C.C. Thermodynamic modeling of HNO3-H2SO4-H2O ternary system with symmetric electrolyte NRTL model. AIChE J. 2017, 63(7), 3110. [24] Edwards, H,G.M.; Fawcett, V. Quantitative Raman spectroscopic studies of nitronium ion concentrations in mixture of sulphuric and nitric acids. J. Mol. Struct. 1994, 326, 131. [25] Chen, L.; Zhou, Y.; Chen, W.; Yang, T.; Xu, S.; Rao, G. Tcf and MTSR of toluene nitration in mixed acid. Chem. Eng. Trans. 2016, 48, 601. [26] Di Somma, I.; Marotta, R.; Andreozzi, R.; Caprio, V. Increasing the yield of 2nitrobenzaldehyde during benzaldehyde nitration by mixed acid: chemical and safety investigation. Chem. Eng. Trans. 2014, 36, 181. [27] Di Somma, I.; Marotta, R.; Andreozzi, R.; Caprio, V. Kinetic and safety characterization of the nitration process of methyl benzoate in mixed acid. Org. Process Res. Dev. 2012, 16(12), 2001. [28] Li, L.; Yao, C.; Jiao, F.; Han, M.; Chen, G. Experimental and kinetic study of the nitration of 2-ethylhexanol in capillary microreactors. Chem. Eng. Process.: Process Intensification 2017, 117, 179. [29] Russo, D.; Onotri, L.; Marotta, R.; Andreozzi, R.; Di Somma, I. Benzaldehyde nitration by mixed acid under homogeneous condition: a kinetic modeling. Chem. Eng. J. 2017, 307, 1076. [30] Russo, D.; Di Somma, I.; Marotta, R.; Tomaiuolo, G.; Andreozzi, R.; Guido, S.; Lapkin, A.A. Intensification of nitrobenzaldehydes synthesis from benzyl alcohol in a microreactor. Org. Process Res. Dev. 2017, 21(3), 357. [31] Di Somma, I.; Marotta, R.; Andreozzi, R.; Caprio V. Nitric acid decomposition kinetics in mixed acid and their use in the modeling of aromatic nitration. Chem. Eng. J. 2013, 228, 366. [32] Zaldivar, J.M.; Barcons, C.; Hernandez, H.; Molga, E.; Snee, T.J. Modelling and optimization of semibatch toluene mononitration with mixed acid from performance and safety viewpoints. Chem. Eng. Sci. 1992, 47(9-11), 2517.



[33] Marziano, N.C.; Tomasin, A.; Tortato, C.; Zaldivar, J.M. Thermodynamic nitration rates of aromatic compounds. Part4. Temperature dependence in sulfuric acid of HNO3→NO2+ equilibrium, nitration rates and acidic properties of the solvent. J. Chem. Soc. Perk. T. 2 1998, 1973. [34] Edwards, H.G.M.; Turner, J.M.C.; Fawcett, V. Raman spectroscopic study of nitronium ion formation in mixtures of nitric acid, sulfuric acid and water. J. Chem. Soc. Faraday T. 1995, 91(10), 1439. [35] Song, Y.; Chen, C.C. Symmetric electrolyte nonrandom two-liquid activity coefficient model. Ind. Eng. Chem. Res. 2009, 48, 7788. [36] Bollas, G.M.; Chen, C.C.; Barton, P.I. Refined electrolyte-NRTL model: activity coefficient expressions for application to multi-electrolyte systems. AIChE J. 2008, 54(6), 1608. [37] Chen, C.C.; Song, Y. Generalized electrolyte-NRTL model for mixed-solvent electrolyte systems. AIChE J. 2004, 50(8), 1928. [38] Davis, W.; De Bruin, H.J. New activity coefficients of 0-100 per cent aqueous nitric acid. J. Inorg. Nucl. Chem. 1964, 26(6), 1069. [39] Redlich, O.; Duerst, R.W.; Merbach, A. Ionisation of strong electrolytes. XI. The molecular states of nitric acid and perchloric acid. J. Chem. Phys. 1968, 49, 2986. [40] Robertson, E.B.; Dunford, H.B. The state of the proton in aqueous sulfuric acid. J. Am. Chem. Soc. 1964, 86(23), 5080. [41] Tomikawa, K.; Kanno, H. Raman study of sulfuric acid at low temperatures. J. Phys. Chem. A 1998, 102, 6082. [42] Fraenkel, D. Sctructure and ionization of sulfuric acid in water. New J. Chem. 2015, 39, 5124. [43] Sampoli, M.; De Santis, A.; Marziano, N.C. On the relationship between the dissociation of indicators in non-ideal acid solution and the dissociation of the acid itself. J. Chem. Soc. Chem. Comm. 1985, 110. [44] Khudhairy, D.; Zaldivar, J.M., Commission of European Communities, Joint Research Centre Ispra Sita, Technical note I.89.90, 1989. 20 ACS Paragon Plus Environment

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[45] Hoggett, J.G.; Moodie, R.B.; Penton, J.R.; Schofield, K. Nitration and aromatic reactivity. Cambridge University Press Rhadon, 1971. [46] Walrafen, G.E.; Yang, W.H.; Chu, Y.C. High-temperature raman investigation of concentrated sulfuric measurement of H-bond ∆H values between H3O+ or H5O2+ and HSO4-. J. Phys Chem A 2002, 106, 10162. [47] Deno, N.C.; Peterson, H.J.; Sacher, E. Nitric acid equilibria in water-sulphuric acid. J. Phys. Chem. 1961, 65, 199. [48] Kruus, P., Hayes, A.C., Adams, W.A. Determination of ratios of sulfate to bisulfate ions in aqueous solutions by raman spectroscopy. J. Solution Chem. 1985, 14(2), 117. [49] Mosier, N.S.; Ladisch, C.M.; Ladisch, M.R. Characterization of acid catalytic domains for cellulose hydrolysis and glucose degradation. Biotechnol. Bioeng. 2002, 79(6), 610. [50] Kawamoto, H.; Saito, S.; Hatanaka, W.; Saka, S. Catalytic pyrolisis of cellulose in sulfolane with some acidic catalysts. J. Wood Sci. 2007, 53, 127. [51] Shin, T.R.; Jung, S.M.; Jeon, I.Y.; Baek, J.B. The oxidation mechanism of highly ordered pyrolytic graphite in a nitric acid/sulfuric acid mixture. Carbon 2013, 52, 493. [52] Allinger, N.L.; Cava, M.P.; De Jongh, D.C.; Johnson, C.R.; Lebel, N.A.; Stevens, C.L. Organic Chemistry. Worth Publishers Inc, 1972. [53] Perrin, D.D. Ionisation constants of inorganic acids and bases in aqueous solution. International Union of Pure and Applied Chemistry, second ed., Pergamon Press, pp.76, 1986. [54] Marziano, N.C.; Tomasin, A.; Traverso, P.G. The MC activity coefficient function for acidbase equilibria. Part 5. The MC activity coefficient for a reliable estimate of thermodynamic values. J. Chem. Soc. Perk. T. 2 1981, 7, 1070.



702x280mm (96 x 96 DPI)

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Fig. 1. Investigated experimental conditions in the literature and this work for nitronium ion determination. Each side of the triangle reports all of the possible molar fraction composition of the corresponding binary mixtures. 110x83mm (96 x 96 DPI)



Fig. 2. [NO2+] molar concentration vs H2SO4 molar percentage (S%) at varying nitric acid molar percentage (N%). (ж) 5%; (○) 10%; (♦) 20%; (△) 30%; (□) 40%; (X) 50%; (●) 70%; (▲) 80%. Experimental data from Albright et al., (1996) and Edwards et al., (1994). 123x97mm (96 x 96 DPI)


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Fig. 3. Dependence of the parameters of eq.1 on the nitric acid molar percentage N%. 170x51mm (96 x 96 DPI)



Fig. 4. a) comparison of the overestimated NO2+ concentrations calculated using the model proposed by Albright et al., (1996) and the sigmoidal model, and the lower concentrations calculated by experimental indirect measurement and HR function. b) Comparison between the NO2+ concentrations calculated using experimental indirect measurements and HR function (zoom in). 115x153mm (96 x 96 DPI)


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Fig. 5. Comparison of the bisulphate Raman peak at varying sulfuric acid concentration without nitric acid (continuous line) and with added nitric acid (dashed lines). The initial nitric acid concentrations are 1, 3, and 5 mol•L-1 for sulfuric acid concentrations of 2.11, 5 and 10 mol•L-1, respectively. 113x91mm (96 x 96 DPI)



Fig. 6. Experimental (symbols) and calculated (continuous lines) molar concentrations for ionic and neutral species at the equilibrium. 102x148mm (96 x 96 DPI)


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