THE HYDROGEN-BROMINE REACTION

The hydrogen-bromine reaction is a classic example of a free radical reaction having been shown by Bodenstein et al. to have a much different kinetic behavior from the hydrogen-iodine reaction. Kassel has reviewed critically the early work. Other more recent reviews have also appeared  

Bodenstein and Lind have studied the thermal reaction between H2 and Br2 to form HBr. Their careful study showed this reaction to be of apparently much greater complexity than the H2-I2 reaction. As was pointed out later in the interpretations of this data by Christiansen, Herzfeld, and Polanyi the reaction proceeds by a free radical chain mechanism involving bromine and hydrogen atoms. Assuming the bromine atom concentration to be governed by the Br2 = 2Br thermal equilibrium, the mechanism of HBr formation is 

Steady-state analysis of this mechanism furnishes 

The most self-consistent value of k /k found by Bodenstein and Lind was 10, independent of temperature. This result together with K and k furnishes ki, the rate coefficient for reaction (2), as given in Table 6. It should be noted that /c2 is not sensitive to k jk if [HBr] is small. 

KINETIC DATA FOR THE OVERALL REACTION OF HYDROGEN AND BROMINE AND FOR THE REACTION Bt2-1-H2 FROM THE RESULTS OF BODENSTEIN AND LIND  

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In the case of the hydrogen-bromine reaction, each of the elementary propagation reactions led to the formation of a single chain carrier. This type of reaction is said to be a straight or linear chain reaction. Some mechanisms involve elementary propagation reactions in which more than a single chain carrier is formed by the reaction. This type of reaction is known as a branching reaction. Examples of such reactions are... 

A reaction, A + B = 2C, has a rate equation of the same form as that of the hydrogen-bromine reaction studied in problem P2.03.15, namely,... 

In a not too complicated case, e.g., in the case of the hydrogen-bromine reaction investigated so thoroughly by the Bodenstein school, it can be shown with certainty that its well known mechanism is really the only one which conforms with the (very accurate) experiments by Bodenstein and Lind and later experimenters. In this and often in more complicated cases, too, the calculations permit expressing the time from the beginning of the experiment by means of the sum of a number of known functions of the degree of advancement x, each multiplied by a constant. 

In the well-known mechanism for the hydrogen-bromine reaction one may for instance not be inclined to consider the bromine atoms as a catalyst. As a matter of fact their concentration can be increased at will within limits by irradiation of the mixture (16) which causes a definite increase of the velocity of the overall reaction, an effect which may very well be called catalytic. 

The case is different when the catalyst is formed by the system itself. In these cases one extra condition is required to determine the velocity. In the hydrogen-bromine reaction the bromine atoms are formed by the dissociation of bromine molecules and disappear by the reversed reaction. Steady course of the reaction thus requires that chemical equilibrium in regard to that reaction is reached. 

In all there are 10 possible combinations of the above 5 equations in sets of 3 each. Of the 10 sets only 5 can be combined to result in the overall reaction, and the only one of these which can be reconciled with the kinetic experiments is the first one above, which proves our case cf. Skrabal s somewhat different considerations (35b). In the hydrogen-bromine reaction we may use the expression that reaction chains are started by the formation of bromine atoms from molecules and broken by their disappearance by the reverse reaction. 

To illustrate the relation between the different flows and the two reaction velocities, we remark that the flows 23, 34, and 45 are obviously the velocity of the main reaction, r, while the flows 12 and 50 equals the velocity s of the side reaction. This is shown in Fig. 5 by means of letters and arrows. The diagram also shows the symbolic analogy between our flows and real physical flows. Thus we may speak of sources and sinks, 1 being a source and 0 a sink, and of translational and rotational flows for example, we may say that the flow s62 is a superposition of a translational flow ( — s) and a rotational flow (r). s may be assumed to be always positive. The case s = 0 is in principle the same as the one treated above (p. 322), where we may speak of catalysis with X2 as a catalyst. As the chain (23452) is broken in this case only by the reaction 21, the chain length then has its maximum, but its numerical value cannot be defined unless we know the kinetics of the reactions (12) and (21), which may be unknown compare the discussion in the literature of the hydrogen-bromine reaction (see also p. 334). 

It must be remembered that at times the same pair of intermediates occurs in two different partial reactions (cf. the hydrogen-bromine reaction). In such cases the two pairs of symbols must be chosen so that they are visually different, either by numbering the partial reactions or, if numbering of states is preferred, by using a dash to distinguish one reaction from the other. 

A well-known example of the first case is the hydrogen-bromine reaction where the concentration of the intermediate Br is determined by its equilibrium value in the case of the reaction in the dark and in the photochemical case the stationary value resulting from the dissociation by light and the recombination (16), the latter being independent of the illumination. In such cases the sequences are strictly speaking not linear but branched and shall not be discussed further in this section. 

Under these circumstances it is probably better to describe Kistia-kowsky s work in detail rather than Bodenstein s, although it must be remembered that the close similarity of the kinetics that Kistiakowsky studied to those of the hydrogen-bromine reaction made less necessary a closely detailed proof of every step. The occurrence of these reactions in the photobromination of methane was shown by measuring the rate of disappearance of bromine photometrically to establish the kinetics. From the plot of [Br2] against time the initial rate of disappearance of bromine was obtained as a function of the initial pressures of the reactants [GH4] and [Br2], and found to fit the equation... 

The classical example of a complex straight-chain reaction for which the results of the steady-state approximation agree with experimental measurements is the hydrogen-bromine reaction H2 T Br2 2HBr [5]. The inferred mechanism is... 

KINETIC DATA FOR THE HYDROGEN-BROMINE REACTION FROM THE RESULTS OF... 

The quasi-steady-state method comes from Bodenstein (1913), Christiansen (1919), Herzfeld (1919) and Polanyi (1920). Fuller accounts of research on the hydrogen-bromine reaction are given by Benson (1960) and Campbell and Fristrom (1958). 

The kinetic law for the hydrogen-bromine reaction is considerably more complicated than that for the hydrogen-iodine reaction. The stoichiometry is the same. 

The initial rate of the hydrogen-bromine reaction is given by... 

The thermal and photochemical reactions between molecular hydrogen and chlorine show some resemblance to the hydrogen-bromine reactions, but the mechanisms are more complex. Since it is easier to understand its main features, we will consider first the photochemical reaction. The mechanism has to account for the profound effect of oxygen... 

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