Nucleophilic catalysis of nitrosation:

relationship between nitrosating agent

equilibrium constant and catalyst nucleophilicity

Gabriel da Silva, Eric M. Kennedy* and Bogdan Z. Dlugogorski

Process Safety and Environment Protection Research Group, School of Engineering,

The University of Newcastle, Callaghan, NSW 2308, Australia; Fax: (+61 2) 4921

6920, E-mail: Eric.Kennedy@newcastle.edu.au

This paper develops a relationship between the equilibrium constant for the formation

of a nitrosating agent and nucleophilicity of the catalyst, to predict equilibrium

constants which until present have proven unobtainable by experimental means. This

relationship is deduced from a fundamental consideration of the Gibbs free energy of

formation of relevant species and includes Edwards’ nucleophilic parameter. A large

set of experimental measurements collected from the literature is applied to obtain the

parameters of the model. Subsequently, the relationship is employed to estimate the

equilibrium constants for the formation of nitrosyl iodide and nitrosyl acetate,

allowing the examination of their reactivities with various amine substrates.

Introduction

It is well known that, nitrosation reactions are catalysed by a range of nucleophilic

species (designated X-), thought largely to follow the mechanistic interpretation of

Ridd1. The mechanism involves the nucleophile dehydrating nitrous acid to form a

nitrosating agent of the form ONX, according to equation (1). The equilibrium

constant for this reaction, KONX, is given by equation (2).

HNO2 + X- + H+ ↔ ONX + H2O (1)

]][H][XHNO[]ONX[

2ONX +−=K (2)

Catalysts that have previously been utilised for nitrosation reactions include certain

halides (bromide, chloride and iodide) and some sulphur containing compounds

(thiocyanate, thiourea and thiosulphate). The nitrosating agents formed from these

catalysts subsequently affect the nitrosation of a substrate (designated S) according to

equation (3), where kN is the rate constant for the second-order nitrosation reaction.

ONX + S → ONS+ + X- (3)

During nitrosation under mildly acidic conditions, formation of the nitrosating species

is generally found to be at equilibrium, while the nitrosation reaction itself is rate

determining. This has led to the establishment of the following rate equation to

describe the overall rate of nitrosation.

KONX

kN

]][H][X[S][HNO2NONX+−= kKr (4)

Equation (4) shows that the efficiency of a particular catalyst is partitioned between

its equilibrium and rate constants. Of these two constants, KONX shows the greatest

variation between catalysts, thus making it the critical rate-determining factor. As

such, knowledge of the equilibrium constant is crucial in predicting the effect of a

particular catalyst. Also, to determine the overall rate of nitrosation, one must first

establish the equilibrium constant of the particular catalyst used. In spite of this

requirement, equilibrium constants for a number of common nitrosating agents have

not been well established in the literature. Other equilibrium constants, such as those

for nitrosyl iodide and nitrosyl acetate, are minuscule and cannot be obtained using

conventional experimental techniques, and only their rough estimates are available.

The next section of this paper presents a derivation of a thermodynamic model to

predict values of KONX based on Edwards’ nucleophilic En parameter. This is

followed by a review of literature on the available experimental measurements of

KONX to justify a linear relationship between ln.KONX and En. Finally, the model is

applied so as to provide previously unobtainable equilibrium constants, which are

then used to facilitate a kinetic re-analysis of some existing rate data.

Theoretical

It is well appreciated that KONX increases with increasing nucleophilic strength, yet

there have been no prior attempts to develop a quantitative relationship. Many scales

have been proposed to quantify nucleophilic strength, with perhaps the more

commonly used being those of Pearson2 and Swain and Scott3. These scales are

kinetic in nature and are not expected to apply to the current system. A

thermodynamic measure of nucleophilicity is, however, provided by Edwards’

nucleophilic parameter4, En. While this parameter has been applied previously with

considerable success, it has been assigned little fundamental significance.

We propose that the thermodynamic potential of a nucleophile can be obtained from

the free energies of formation of both X- and X2. This idea is represented by equation

(5) with the corresponding free energy change of the reaction expressed by equation

(6).

ON + αnX- +

−

21 nα X2 ↔ ONX + αne- (5)

oooooON,X,nX,

nONX,5 22

1ffff GGGGG ∆−∆−∆

−

−∆=∆ −αα (6)

Here, αn is a parameter that measures the ON-X bond order, and lies somewhere

between zero (X-) and unity (X-X). We propose that for a wide range of catalysts αn

is approximately constant, and will argue this point further in discussion section. It

will be shown later in the current chapter that, this implies a linear relationship

between KONX and En.

We now introduce equation (7), which leads to the formulation of Edwards’ En

parameter. The standard free energy change for this reaction is expressed in equation

(8)

2X- ↔ X2 + 2e- (7)

ooo−∆−∆=∆ X,X,7 2

2 ff GGG (8)

Upon substitution of equation (8) into equation (6) and some rearrangement, we

obtain equation (9).

oooooON,57

nX,ONX, 2

1fff GGGGG ∆+∆+∆

−

+∆=∆ −

α (9)

Edwards noticed that nucleophilic strength was a function of the standard electrode

potential Eo, which is related to the free energy change of reaction (7) by equation

(10), where v is the number of electrons transferred in the reaction (in this case 2) and

F is the Faraday constant (96.485 C mol-1). Equation (10) may now be substituted

into equation (9), to produce equation (11).

ovFEGo −=∆ 7 (10)

( ) oooooON,5X,ONX, 1 fnff GGEFGG ∆+∆+−−∆=∆ − α (11)

The Edwards nucleophilic constant is related to the standard electrode potential by

equation (12), where the numerical constant of 2.6 corresponds to the electrode

potential of water. Nucleophilic En constants have been tabulated for most common

nucleophilic species, including those used to catalyse nitrosation4.

60.2n += oEE (12)

We may replace the standard electrode potential in equation (11) with Edwards’

nucleophilic constant, as illustrated by equation (13).

( ) ooooON,5nnnX,ONX, )1(60.21 fff GGFEFGG ∆+∆+−+−−∆=∆ − αα (13)

We now turn our attention to the formation reaction for ONX, as given by equation

(1). The standard free energy change for this reaction is specified by equation (14).

oooooo−+ ∆−∆−∆−∆+∆=∆ X,H,HONO,OH,ONX,1 2 fffff GGGGGG (14)

Replacing the standard free energies of formation of H2O(l) (-237.129 J mol-1),

HNO2(aq) (-55.649 J mol-1) and H+(aq) (0 J mol-1), we obtain equation (15); all

thermodynamic values invoked in this paper have been taken from reference 5 and

apply to aqueous solution.

480181X,ONX,1 −∆−∆=∆ −ooo

ff GGG (15)

Substituting (13) into (15) leads to:

( ) 480181)1(60.21 ON,5nnn1 −∆+∆+−+−−=∆ ooofGGFEFG αα (16)

Equation (16) may be further simplified to give equation (17), by substituting the free

energy of formation of ON(aq). This has been determined as 111.300 J mol-1 from the

gas phase value of 86.600 J/mol, along with the known Henry’s constant of 1.9×10-3

M atm-1 6.

( ) 18070)1(60.21 5nnn1 −∆+−+−−=∆ oo GFEFG αα (17)

Using the relationship between o1G∆ and KONX, equation (17) is transformed into

equation (18).

( ) 18070)1(60.21ln 5nnONX +∆−−−−= oGFEFKRT n αα (18)

With a minor rearrangement, we obtain equation (19) that takes the form of a linear

relationship between ln.KONX and En. As such, a plot of ln.KONX vs En should give a

straight line, where the slope may be used to calculate αn, and the intercept to obtain

oG5∆ .

( )RT

FGE

RTFK

)1(60.2180701ln n5n

nONX

αα −−∆−+

−

=o

(19)

Review of Experimental Measurements

A comprehensive review of literature values of KONX has been undertaken to identify

the experimental measurements required to calculate the parameters of the model.

Note that all equilibrium constants quoted in the current manuscript invoke the

standard state of a hypothetical ideal solution of unit molality, and, unless otherwise

stated, are at 25oC.

Nitrosyl Chloride

The equilibrium constant for formation of nitrosyl chloride has been experimentally

studied by Schmid and Hallaba7, who determined it to be 1.1×10-3 M-2. Turney and

Wright8 used thermodynamic cycles in determining the equilibrium constant to be

6×10-4 M-2, somewhat smaller than the experimentally determined value. A

thermodynamic estimate may also be made from the free energy change of the

reaction (16.9 J/mol) as calculated from standard free energies of formation. This

gives a thermodynamic equilibrium constant of 1.1×10-3 M-2, agreeing with the

experimentally derived value.

Nitrosyl Bromide

Schmid and Fouad9 experimentally determined the equilibrium constant for nitrosyl

bromide as 5.1×10-2 M-2. Turney and Wright8 have again assigned the equilibrium

constant a thermodynamic value of 9×10-2 M-2. Both the experimental and calculated

values are seen to exhibit reasonable agreement.

Nitrosyl Thiocyanate

The earliest, and the most often cited, determination of the equilibrium constant for

nitrosyl thiocyanate formation is that of Stedman and Whincup10 who conducted tests

in perchloric-acid media over a range of ionic strengths. Using an estimate of the

activity coefficient, the equilibrium constant was evaluated as 32 M-2 at 20oC. The

enthalpy change for the reaction was also determined to be -12 kJ/mol, allowing us to

adjust the equilibrium constant to 29 M-2 at 25oC. Further experiments were

conducted in sulphuric-acid media, where the equilibrium constant was determined to

be 18.5 M-2 at 20oC (i. e. 17.0 M-2 at 25oC), though it was reported that this value was

unduly influenced by solution activity. Jones et al.11 determined an average value of

9.9 M-2 for nitrosyl thiocyanate over a range of perchloric acid concentrations,

contrasting somewhat with the values of Stedman and Whincup10. We used the free

energies of aqueous thiocyanate and nitrosyl thiocyanate formation to determine the

equilibrium constant as 30.8 M-2, agreeing well with the widely accepted value of

Stedman and Whincup10.

S-Nitrosothiourea

While thiourea yields one of the more efficient nitrosating agents, the equilibrium

constant for its formation remains poorly resolved. Al-Mallah et al.12 determined it as

5.000 M-2, at an ionic strength of 0.3. Adjusting for activity coefficients using the

Debye-Hückel approximation, we obtain a corrected value of 9.500 M-2.

Nitrosyl Thiosulphate Ion

Garley and Stedman13 conducted experiments into the formation of the nitrosyl

thiosulphate ion in weakly acidic solutions, and obtained an average equilibrium

constant of 1.66×107 M-2. Again, we have adjusted this result to account for activity

coefficients using the Debye-Hückel approximation, yielding a thermodynamic

equilibrium constant of 1.82×107 M-2. Abia et al.14 also determined the equilibrium

constant for the formation of nitrosyl thiosulphate, obtaining an average value of

2.5×106 M-2. Once adjusted for solution activity, this gives a value of 4.3×106 M-2,

being somewhat lower than that of Garley and Stedman13.

Dinitrogen Trioxide

During nitrosation in the absence of a nucleophilic catalyst, reaction proceeds through

the nitrosating agent dinitrogen trioxide. The formation reaction for dinitrogen

trioxide is generally written as in equation (20).

2HNO2 ↔ N2O3 + H2O (20)

The equilibrium constant for equation (20) has been well studied both from

thermodynamic15,16 and experimental17,18 standpoints, returning respective KONX

values of 2.3×10-3, 9.0×10-3, 3.0×10-3 and 7.5×10-3 M-2. However, these studies have

expressed the equilibrium constant in the form of equation (20), rather then in the

form of equation (21), with nitrous acid reacting with a nitrite ion.

HNO2 + NO2- + H+ ↔ N2O3 + H2O (21)

We now see that equation (21) resembles equation (1), where the nitrite ion is acting

as the nucleophile. To adjust the free energy change of the reaction (and subsequently

the equilibrium constant) from the form of equation (20) to that of equation (21), we

simply replace the free energy of formation of nitrous acid (-55.600 J/mol) with that

of a nitrite ion (-37.200 J/mol). This yields thermodynamic equilibrium constants of

3.8, 15.1, 5.0 and 12.6 M-2 for the four studies mentioned above. We may also

determine the equilibrium constant to be 4.9 M-2 from the free energies of formation

of the reacting species.

Discussion

The equilibrium constants reviewed in the previous chapter are plotted in figure 1 as a

function of En, together with the equilibrium constant for OH- acting as the

nucleophile, which is, by definition, unity. The linear relationship of equation (19) is

also drawn in figure 1, in the least-square sense, to produce the linear relationship of

equation (22). The comparison of equations (19) and (22) yields αn = 0.46 and oG5∆

= 8.906 J/mol, with αn indicating that the ON-X bond order is intermediate between

that of X2 and X-.

Figure 1. Comparison of the model with the experimental measurements.

35.2988.17ln nONX −= EK (22)

As both of the parameters plotted in figure 1 are related to thermodynamic properties,

our relationship may be considered a linear free energy relationship (LFER). A LFER

of this form generally indicates that a single mechanism dominates interaction within

Nitrosyl Thiocyanate

Nitrous Acid

En

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

lnK O

NX

-10

-5

0

5

10

15

20

Cl-

Br-

OH-

NO2-

SCN-

SC(NH2)2

S2O32-

the reaction series. Interpreting figure 1 in this context reveals that bond order is the

dominant factor in determining the magnitude of KONX, and that other interaction

mechanisms do not play a significant role. This is particularly interesting when one

considers the range of species to which the relationship has been applied, including

both the nitrosyl halides and the sulphur-centred nitrosating agents. This range also

contains a number of larger molecules(e. g. thiourea and thiosulphate), species

possessing two possible nucleophilic sites (such as the S and N atoms in thiocyanate

and thiourea) and those with negative, neutral and positive charges. In spite of this

wide range of species, no secondary effects such as those attributable to steric or

resonance factors seem to significantly influence nucleophilicity.

Table 1 shows the equilibrium constants calculated from the model, along with

literature values for each catalyst. As expected, all of the equilibrium constants used

to calculate the parameters of the model are well predicted, usually within the ten-fold

variation witnessed in the experimental measurements. Included in table 1 are

estimates for the equilibrium constants of nitrosyl fluoride, nitrosyl nitrate and

nitrosyl sulphate formation; three compounds which have previously been found to

have little or no catalytic effect on nitrosation22,23. The relatively low equilibrium

constants predicted for nitrosyl fluoride and nitrosyl sulphate disclose the reason why

these agents do not catalyse nitrosation. The literature value for the formation of

nitrosyl nitrate, which is six orders of magnitude greater than that predicted here, is

clearly in error, as the nucleophilic catalysis of nitrosation by the nitrate ion cannot be

observed in experiments as a consequence of the low equilibrium constant.

Table 1. Comparison of literature and predicted equilibrium constants for common

nitrosating agents. Calculations made using En values of reference 4, except that of

ONF, which is taken from reference 19.

ONX KONX (literature), M-2 KONX (model), M-2 Reference(s)ONF - 1.5×10-15 -ONNO3 4×10-5 3.3×10-11 5ONSO4

- - 7.0×10-11 -CH3COONO ≈1.4×10-8 4.4×10-6 20ONCl 1.1×10-3; 6×10-4; 1.1×10-3 7.8×10-4 4; 5; This StudyONBr 5.1×10-2; 9×10-2 9.7×10-2 7; 5ONNO2 3.8; 15; 5.0; 13; 4.9 5.0 13; 14; 15; 16; This StudyONSCN 29; 17; 9.9; 31 30 8; 8; 9; This StudyONI >100 1.800 21(NH2)2CSNO+ 9.500 1.5×104 10S2O3NO- 1.8×107; 4.3×106 6.7×106 11; 12

Dix and Williams24 studied the iodide catalysed nitrosation of various aniline

derivatives, but were unable to present rate constants due to the absence of an

equilibrium constant for nitrosyl iodide. These rate constants have now been

estimated (using the equilibrium constant from table 1), and are presented in table 2.

Figure 2 shows how the rate constants for nitrosation via nitrosyl iodide vary as a

function of pKa. For comparison, we also included the published results obtained for

nitrosation via nitrosyl chloride and nitrosyl thiocyanate. It can readily be seen that,

nitrosyl iodide is the least reactive nitrosating agent, and that the reaction rates do not

approach the encounter-controlled limit (as they do for nitrosyl chloride). In other

words, nitrosation via nitrosyl iodide is controlled by chemical kinetics, rather than by

diffusion.

Table 2. Rate constants for the nitrosation of various aniline derivatives by nitrosyl

iodide.

kN, M-1 s-1

p-Methoxyaniline 2.6×107

p-Chloroaniline 2.9×106

Aniline 2.6×106

m-Methoxyaniline 1.9×106

p-Carboxyaniline 8.8×104

Figure 2. ln.kN versus pKa for the nitrosation of various aniline derivatives by ONI

(•), ONCl 24 (◊) and ONSCN 22 (□). Dashed line indicates the encounter-controlled

limit.

pKa

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

lnk n

4

5

6

7

8

9

10

Nitrosyl acetate is another compound for which a KONX value has not been

experimentally obtainable due to its low value. The only available value is an

estimate that has been inferred from the nitrosation of several secondary amines20.

Nitrosyl acetate has long been implicated in nitrosation reactions, and there exist

several studies on its role, many with considerable disagreement. A complex

mechanism has been proposed and validated20,27,28 in which nitrosyl acetate not only

acts as a nitrosating agent, but also catalyses the formation of dinitrogen trioxide.

Table 3 shows calculated rate constants for nitrosation via nitrosyl acetate, extracted

from the data of Casado et al.20 Included in the table, for comparative purposes, are

published data26 for nitrosation via dinitrogen trioxide. While the rate constants for

dinitrogen trioxide are all relatively constant at ca. 10-8 M-1 s-1, those for nitrosyl

acetate are considerably lower, and vary by approximately three orders of magnitude.

It appears as though nitrosation via dinitrogen trioxide proceeds at the encounter-

controlled limit, thus indicating that a similar limitation should operate for nitrosyl

acetate, due to its greater reactivity. The fact that the experimental results do not

support this observation seems to indicate either erroneous experimental data

(possibly due to the intricate kinetic analysis brought about by the complex reaction

mechanism) or incorrect mechanistic assumptions.

Table 3. Rate constants for the nitrosation of three secondary amines by nitrosyl

acetate, as compared to nitrosation via dinitrogen trioxide.

kN (CH3COONO), M-1 s-1 kN (N2O3), M-1 s-1

Morpholine 2.8×106 2.2×108

N-Methylaniline 5.6×105 4.0×108

Piperazine 3.5×104 1.3×108

Acknowledgements

We would like to thank Orica Pty. Ltd. for project funding, and the Australian

Research Council for the provision of a student scholarship to G. D.

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