Nitrogen pentoxide reaction rate

There is something strange about this nitrogen pentoxide reaction. The reaction is the best example of a first-order gas phase reaction that we have and yet, according to equation (1), two molecules of nitrogen pentoxide are involved. Why should this, then, not be a second order reaction If it is a second order reaction we should expect the specific reaction rate to change markedly with pressure and depend on collision frequency. The best answer is given as follows ... 

Tuazon et al. (1984a) investigated the atmospheric reactions of TV-nitrosodimethylamine and dimethylnitramine in an environmental chamber utilizing in situ long-path Fourier transform infared spectroscopy. They irradiated an ozone-rich atmosphere containing A-nitrosodimethyl-amine. Photolysis products identified include dimethylnitramine, nitromethane, formaldehyde, carbon monoxide, nitrogen dioxide, nitrogen pentoxide, and nitric acid. The rate constants for the reaction of fV-nitrosodimethylamine with OH radicals and ozone relative to methyl ether were 3.0 X 10 and <1 x 10 ° cmVmolecule-sec, respectively. The estimated atmospheric half-life of A-nitrosodimethylamine in the troposphere is approximately 5 min. 

In a purely photochemical reaction the absorption of radiant energy is plainly responsible for the activation. This suggested the possibility that thermal reactions are also due to activation by the thermal radiation which is present at every temperature. The argument was very forcibly presented by Perrin who showed that if the specific rate of a imimolecular gas reaction remains constant, with indefinite diminution in pressure, activation must be by radiation since the number of opportunities for activation by collision also diminishes without limit. In fact, the decomposition of nitrogen pentoxide, the first gas reaction shown to be unquestionably unimolecular, was found to have a specific reaction rate constant over a wide range of pressure, and apparently increasing at very low pressures. ... 

Where the rate of reaction depends upon the presence of an accidental catalyst, measurements are characterized by great lack of reproducibility. Many homogeneous reactions, on the other hand, have quite definite and reproducible rates. For example, the measurements of Bodenstein and of Kistiakowsky on the rate of decomposition of hydrogen iodide agree excellently, as do those of numerous investigators of the rate of decomposition of nitrogen pentoxide. 

Further tests of the influence of infra-red radiation on the reaction velocity have been made by Rice, Urey, and Washburne,f who exposed a molecular beam of nitrogen pentoxide to black body radiation of high temperature with a negative result, and by Kassel, J who also found that radiation of wave-length less than 5 n does not increase the reaction rate even at low pressures, where its effect relative to that of collisions might have been expected to be greater than at atmospheric pressure. 

Busse and Daniels have, moreover, found that hydrogen, carbon monoxide, bromine, and chlorine are without influence on the reaction. Certain organic vapours, which are themselves attacked by nitrogen pentoxide, bring about rapid decomposition. Hirst found that argon exerted no influence, while Hunt and Daniels showed that the presence of a large excess of nitrogen did not alter the rate of reaction at all. 

The only example of all the unimolecular reactions known where such a difficulty has actually arisen in an acute form is the decomposition of nitrogen pentoxide. It appears that at low pressures nitrogen pentoxide reacts at a rate which is considerably greater than the maximum possible rate of activation by collision, however great a value of n be assumed. There is a limit to the maximum rate theoretically possible, since, when n is increased beyond a certain point, the increase in the term E — EArrhenius + n- )RT produces a decrease in the calculated rate which more than compensates for the increase due to the term (E/RT)1l2n 1 multiplying the exponential term. 

The most satisfactory explanation is that the rate is increased beyond the maximum rate of activation by collision through the operation of a chain mechanism. The observations of Sprenger on the peculiar behaviour of nitrogen pentoxide at low pressures suggest strongly that chains are propagated. Moreover, if the rate of the azoisopropane reaction at the lowest pressures should prove to be greater than can be accounted for on the basis of the simple collision mechanism, a chain mechanism can be assumed without difficulty since the reaction is quite markedly exothermic. 

It is to be noted that this is like the equation for a zero order reaction (11-12), but the rate is constant, not because it is independent of concentration but because the concentration is kept constant artificially. It was gratifying to find, as expected, that the quantity of crystals of nitrogen pentoxide in the vessel had no influence on the rate. This fact proves that the reaction being measured, is strictly a gas phase reaction and that there is no decomposition in the crystal itself and no catalysis by the crystal surface. 

Fig. 16.—Influence of pressure on the specific reaction rate k for the decomposition of nitrogen pentoxide at low pressures.

In spite of the large amount of work which has been done on nitrogen pentoxide, it is planned to carry out a still more precise measurement of the decomposition rate in the gas phase. The constancy of the energy of activation at different temperatures is a matter of great theoretical importance. Although few gas reactions in chemical kinetics are more accurately known, the present meas-... 

There are very few cases where one can compare directly the same reaction taking place by the same mechanism in both gas phase and solution. If at all temperatures the reactions have equal velocities in the two phases the values of 5 and of E are the same, and it may be safely assumed that the reaction mechanisms are identical and the solvent has no effect. Undoubtedly the simplest comparison exists in the unimolecular decomposition of nitrogen pentoxide and in this reaction the solvent has little effect. The unimolecular racemization of pinene at 200° proceeds at the same rate in the gas phase, in liquid pinene and in a solution of petrolatum. 

The simplest reaction which has been studied directly in the gas phase and in solution is the decomposition of nitrogen pentoxide.11 It is not a chain reaction and it is free from wall effects. The gas phase reaction seems to be free from complications and it has been checked in many laboratories. It is an excellent unimolec-ular reaction, the decomposition rate being exactly proportional to the concentration. This proportionality constant is nearly the same from 0.05 mm. to 1,000 mm. in the gas phase and up to an osmotic pressure of fifty atmospheres in solution, and the energy of activation is practically the same in the gas phase and in a group of chemically inactive solvents. 

Although the specific decomposition rate is much lower in nitric acid solution the decomposition still follows the first order law because the number of simple molecules which decompose is always proportional to the total concentration of nitrogen pentoxide at any time, and this is the criterion of a unimolecular reaction. 

The stoichiometry is more complicated here because 2 mol of dinitrogen pentoxide produce 4 mol of nitrogen dioxide and 1 mol of oxygen. So, it is no longer true that the rate of decrease of the reactant concentration equals the rates of increase of the product concentrations. However, this difficulty can be overcome if, in order to define the reaction rate, we divide by the coefficients from the balanced equation. For this reaction, we get the following. 

The technique and the reaction system developed for the foregoing reaction was then applied to the study of a unimolecular reaction. The decomposition of nitrogen pentoxide has been found to remain unimolecular over enormous variations in pressure.12 But what is of most concern to the immediate problem is that it seems to remahji unaffected at extremely low pressures. Hunt and Daniels13 found that the decomposition rate was unchanged even when the partial pressure of nitrogen pentoxide... 

Summary.—The mechanism of the activation process in gaseous systems has been investigated from the point of view of (1) activation by radiation (2) activation by collision. An increase in the radiation density of possible activating frequencies has resulted in no increased reaction velocity. The study of the bimolecular decomposition of nitrous oxide at low pressures has led to the conclusion that the reaction is entirely heterogeneous at these pressures. A study of the unimolecular decomposition of nitrogen pentoxide between pressures of 7io mm. Hg and 2 X 10 3 mm. Hg shows no alteration in the rate of reaction such as was found by Hirst and Rideal but follows exactly the rate determined by Daniels and Johnson at high pressures. No diminution of the reaction velocity as might be ex-expected from Lindemann s theory was observed. 

The reaction mechanism for the decomposition of nitrogen pentoxide is complex, as described in Sec. 2-2. However, a satisfactory rate equation can be developed by considering the two reactions... 

In the decomposition of nitrogen pentoxide the situation w as even more inexplicable until it w as suggested that the reaction proceeds in steps and that the first-order rate constant must not be identified with a single elementary reaction (Ogg, J. Chem. Phys. 1947,15, 337). 

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