Kinetics of solvolysis in water of four secondary alkyl nitrates

Ross ELMORE ROBERTSON, KALVELIL MATTHEW KOSHY, ADRIANNE ANNESSA, A N D JAN N. ONG Departt~tetlt of Cltentistry, University of Colgcrry, Calgary, Alm., Ccrtlcr(1r T2N IN4

JOHN MARSHALL WILLIAM SCOTT Depcrrttnetlt of Chertristry, Met?~oriol Ut~ivrrsi ty , St. Johtl's, Nfld., Ccrtlcrclcr AIC 5S7

A N D

MICHAEL JESSE BLANDAMER Depcrrtttretlt of Chet~~is t ry , The Uniuersity, Leicestrr, Et~glotlcl

Received November 24, 1981

Ross ELMORE ROBERTSON, KALVELIL MATTHEW KOSHY, ADRIANNE ANNESSA, JAN N. ONG, JOHN MARSHALL WILLIAM SCOTT, and MICHAEL JESSE BLANDAMER. Can. J. Chem. 60, 1780 (1982).

Kinetic data are reported for the solvolysis in water of propane-2-nitrate, butane-Znitrate, cyclopentyl nitrate, and cyclohexyl nitrate. In each case, the dependence of rate constant on temperature is analysed in terms of two mechanisms for the solvolytic reaction. First it is assumed that the rate constant describes a single step reaction, the analysis leading to estimates of the heat capacity of activation AC,*. Three different analytical methods are discussed in this regard. Second it is assumed that the rate constant describes a two stage mechanism, the first stage being reversible. In this case the explanation of the AC,* term calculated according to the first mechanism is quite different. We comment on the alternative explanations of trends in activation parameters.

Ross ELMORE ROBERTSON, KALVELIL MATTHEW KOSHY, ADRIANNE ANNESSA, JAN N. ONG, JOHN MARSHALL WILLIAM SCOTT et MICHAEL JESSE BLANDAMER. Can. J . Chem. 60, 1780 (1982).

On rapporte des donnees cinetiques pour la solvolyse des nitrates de propyle-2, de butyle-2, de cyclopentyle et de cyclohexyle dans l'eau. Dans chaque cas, on analyse I'effet de la temperature sur la constante de vitesse en fonction de deux mCcanismes pouvant rCgir la reaction de solvolyse. On admet premierement que la constante de vitesse decrit une reaction en une seule Btape, I'analyse conduisant une evaluation de la capacite calorifique d'activation, AC,'. De ce point de vue, on discute trois mtthodes analytiques differentes. Deuxiement, on admet que la constante de vitesse decrit un mecanisme en deux etapes, la premikre &ant reversible. Dans ce cas, I'explication du terme AC,' calculi selon le premier mecanisme est tout i fait differente. Nous comrnentons d'autres explications relatives aux tendances des parametres d'activation.

[Traduit par le journal]

An extensive body of information describes the kinetics of solvolysis of simple organic esters in water (1). For the most part, the dependence of rate constant, k , on temperature has been analysed using the Valentiner equation (2,3) thereby leading to estimates of the thermodynamic activation pa- rameters including the enthalpy of activation AH* and the heat capacity of activation LC,*. The latter quantity attracted considerable interest because, it was argued (I), a major contribution to the sign and magnitude of AC,* stems from reorganisation of solvent around the substrate on activation. How- ever, certain features (4), previously unrecognised (I), of the Valentiner equation (2) prompted a reconsideration (5) of the methods of analysing the dependence of rate constant on temperature. We draw attention to these and other features of the Valentiner equation in this paper. A consequence of this reconsideration has been an investigation of other methods of data analysis with reference to the kinetics of solvolysis in water (5-7) and in mixed solvents (8) and to kinetic solvent isotope effects (9). For the most part this exercise has involved reexamining previously published data (1). In this communication, we report kinetic- data for the

solvolysis of four secondary nitrates in water. Originally, the experimental investigation was prompted by the need for a comparison between the activation parameters for these nitrates and those reported (10) for 2-adamantyl nitrate. How- ever, as indicated above, the developments on the analytical side have overtaken events.

Results The rate constants were determined by the

conductance method (1). First order rate constants at several temperatures are summarized in Tables 1-4. We report the averaged rate constants at each temperature but in the analysis we used the indi- vidual rate constants obtained from 3 or more determinations at each temperature.

Analysis In common with almost all solvolytic reactions of

simple organic esters in water (I), plots of In k against T-l for the data given in Tables 1-4 are nonlinear. This observation can be accounted for in one of two ways; (A) the mechanism of reaction is a simple single-stage process but AC,* is nonzero (I), or (B) the mechanism of reaction is complex but

0008-4042/82/13 1780-06$0 1 .OO/O 01982 National Research Council of Canada/Conseil national de recherches du Canada

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TABLE 1. Kinetic data for solvolysis of propane-2-

nitrate in water

T (K) lo5 k (s-I)

TABLE 2. Kinetic data for solvolysis of butane-2-

nitrate

the individual enthalpies of activation are inde- pendent of temperature (6,7).

The mathematical analysis has been carried out using (i) computer programs (FORTRAN and GLIM (1 1) routines) for the CDC Cyber 73 at the University of Leicester and (ii) computer programs for a Hewlett-Packard 9825A desk-top computer.

A. Single stage rnechanistn The underlying assumption is that the rate con-

stant k describes a single stage process;

TABLE 3. Kinetic data for the solvolysis in water of

cyclopentyl nitrate

TABLE 4. Kinetic data for solvolysis in water of cy-

clohexyl nitrate

T (K) 10' k (s-I)

With this starting hypothesis, several methods can be used to fit the dependence of k on T. We consider here three approaches to the evaluation of the activation parameters.

In the Valentiner equation (2), the dependence of In k on T is expressed as shown in eq. [2].

[2] I n k = a , + ( a210 + a , In T

The outcome of the analysis for the four nitrates is summarized in Table 5. An estimate of the goodness of fit is provided by the quantity Q defined by eq. [3] where f is the number of degrees of freedom.

k [I] R-NO, 4 products [3] Q2 = (In k(obs) - In k ( ~ a l c ) ) ~ / f

TABLE 5. Analysis of kinetic data using Valentiner equation

AH* at T (K) AH* (298.15) Nitrate a ̂ I - 1 0 i 2 - a ^ 10' R (kJ mol-I) (kJ mol-I) ACp* (J mol-I K-I)

Propane-2- 123.3 1.902 13.41 4.688 115.8 353.326 122.41 - 119.8 (20.4) (0.105) (2.97) (0.01) (24.7)

Butane-2- 212.0 1.877 12.41 4.202 115.51 121.40 - 107.9 (25.9) (0.132) (3.78) (1 x (1.60) (3 1.5)

Cyclopentyl 175.5 2.100 20.98 3.75 112.732 120.11 - 174.4 (27.5) (0.136) (4.03) (0.02) (1.32) (33.5)

Cyclohexyl 205.2 2.365 24.99 3.97 122.454 159.01 -207.8 (13.2) (0.067) (1.9) (0.02) (2.97) (16.0)

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CAN. J. CHEM. VOL. 60, 1982

In all four cases AC,* is negative. A common feature of the data for 17 alkyl nitrates is shown in Fig. 1 which shows plots of a , against a , and a , against a,. We have commented elsewhere (4) on this phenomenon and examined the statistical sig- nificance underlying the linear dependences (12).

We have applied the polynomial suggested by Eyring and co-workers (13) to the analysis of kinetic data (7 ) , eq. [4 ] :

For the systems described here it was only significant to include all terms up to tn = 5 . The derived parameters are summarized in Table 6 , together with the corresponding standard errors and estimates of AH* (8) , AC,* ( O ) , dAC,*ldT, and d2AC,*ldT2.

The Clarke-Glew equation (14) uses a reference temperature but is based on a Taylor expansion of the enthalpy term about this reference tempera- ture;

The outcome of the analysis is summarized in Table 7 .

B . Two stage mechatzistn The assumption is that the mechanism of solvo-

lysis follows the scheme (15) shown in eq. [ 6 ] .

[61 Rx k,_ k2 (int) - products -k,

The measured first order rate constant k is related to k , and a (= k21k3) where k = k , l ( l + a ) . The simplification introduced here is that In k , and In a are linear functions of T-I. Hence

[71 In k = ( g , / T ) + g 2 - In [ 1 + exp (g3 /T + g4)l The temperature at which a = 1 is given by -g3!g4.

We have discussed elsewhere (12) the technique of fitting the data to eq. [7] using the Wentworth method (16). The results are summarized in Table 8. For each set of kinetic data there are two sets of solutions (17). Included in Table 8 are the calcu- lated activation parameters, AH, * and A M * (= AH3* - AH2*).

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ROBERTSON ET AL.

TABLE 7. Clarke-Glew equation

Nitrate 0 lo3 R* AH* (0) (kJ mol-I) -ACp+ (0) (J mol-I K-1)

Propane-2- 355.483 4.6883 118.481 (0.015)

Butane-2- 348.837 4.20 118.452 (0.014)

Cyclopentyl 338.54 4.33 115.56 (0.014)

Cyclohexyl 343.284 3.97 125.341 (0.008)

'Based on In k

FIG. 1. Parameters obtained using the Valentinerequation; (a) dependence of a , on a,, and (b) dependence of a , on a,; the substrates are 1. Methyl nitrate (21); 2. ally1 nitrate;' 3. benzyl nitrate (D,0);2 4. 1-adamantyl nitrate (10); 5. 2-adamantyl nitrate (10); 6. p-trifluoromethylbenzyl nitrate (22); 7. p-nitro- benzyl nitrate (22); 8. p-methylbenzyl nitrate (22); 9. p-chloro- benzyl nitrate (22); 10. 2,6-dimethylbenzyl nitrate (23); 11. m-methylbenzyl nitrate (23); 12. o-methylbenzyl nitrate (23); 13. tn-trifluoromethylbenzyl nitrate (22); 14. propane-2-nitrate; 15. butane-2-nitrate; 16. cyclohexyl nitrate; 17. cyclopentyl nitrate.

Discussion Details of the analysis in terms of the Valentiner

equation are presented for comparison with the results obtained for other substrates (1). Our reser-

IR. E. Robertson and E. C. F. KO. Unpublished data. ,K. M. Koshy and R. E. Robertson. Unpublished data.

vations over this approach stem from the plots shown in Fig. 1. We attribute these patterns to the fact that both T-I and In T are close to linear functions of T (11). For this reason the Clarke- Glew equation has merit in that the equation contains different functions of T, In T, and 0. Both sets of derived parameters (Tables 7 and 8) are in reasonable agreement. The value for AC,' (0) provides an important clue here in that the esti- mates and their standard errors overlap for each substrate. However, the polynomial equation leads to estimates of AC,' (0), together with the corres- ponding first and second temperature derivatives. Indeed, in all four systems, the analysis suggests that AC,* decreases with increase in temperature.

Granted that method A is a satisfactory explana- tion of the kinetic data, it is noteworthy that the calculated heat capacities of activation are signifi- cantly smaller than those previously reported for systems where the solvolysis involves a unimolec- ular process with extensive charge development in the transition state (10). The activation parameters are consistent with direct solvent participation in the activation process. In one extreme the data, here and in ref. 10, can be understood in terms of relatively little charge separation in the substrate but considerable nucleophilic involvement by sol- vent. At the same time it is possible that, in contrast to halides, there are special steric and related factors involved with the solvation of the leaving group in the case of alkyl nitrates. Hence it is possible to evolve numerous schemes such that the calculated activation parameters are composite quantities. Here is the link with mechanism B which breaks down the solvolytic reaction into component parts. Analysis in these terms raises new problems as indicated in Table 8. Thus for each nitrate there are two almost statistically equivalent solutions. For butane-Znitrate and cy- clopentyl nitrate results, solution (b) offers an intui- tively reasonable set of parameters where the ratio

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u is < 1.0 over the experimental range of tempera- tures. More importantly, A M * is positive and because we anticipate no marked difference be- tween the four substrates, we favour solution (a) for propane-2-nitrate and solution (a) for cyclohex- yl nitrate. However, for this latter system the two solutions are not wildly different because the temperature T(u = 1) falls within the experimental range. Indeed this system, cyclohexyl nitrate pro- vides an important clue to a major problem in this work.

According to Model A, the heat capacity of activation is a true heat capacity term. Because the partial molar heat capacities of apolar solutes in water are positive, it is not altogether surprising that AC,' is negative. According to Model B, the AC,* term is a n apparent quantity and no allow- ance is made for a contribution arising from the changes in real heat capacity of the substrate. Clearly this approximation is too sweeping and some compromise is sought. A line of argument would proceed as follows. Where the calculated (AC,*I quantity is large, a major part of that calculated heat capacity of activation stems from kinetic complexity. We anticipate that in these circumstances, the temperature T (ct = 1) is close to 'or within the experimental range (of cyclohexyl nitrate). Where the calculated lAC,* I is small (cf. propane-Z-nitrate), the mechanism of solvolysis is controlled by one step. Moreover, T (u = 1) where calculated according to method B lies some way removed from the experimental range. This com- promise view has much to commend it.

Experimental The alkylnitrates were prepared using methods based on

published procedures (18-20) combined with nmr measure- ments as a confirmation of purity.

Products In each study a separate experiment with the nitrate in water

in the ratio 1:4- 1:6 was sealed in a glass ampoule and reacted in a constant temperature bath in the experimental range for about 10 half-lives. The product was extracted with ether and iden- tified by vpc on a FFAP column. In each case the only significant product was the corresponding alcohol. In the case of cyclohex- yl nitrate, traces of cyclohexene in the original sample also appeared in the product.

Acknowledgement We thank the Royal Society for a travel award to

MJB.

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