Collision rate like molecules

The molecules in a gas mixture continually collide with each other, and the diffusion process is strongly influenced by this collision process. The collision of like molecules is of little consequence since both molecules are identical and it makes no difference which molecule crosses a certain plane. The collisions of unlike molecules, however, influence the rate of diffusion since unlike molecules may have different masses and thus different momeniums, and thus the diffusion process is dominated by the heavier molecules. The diffusion coefficients and thus diffusion rales of gases depend strongly on temperature since the temperature is a measure of the average velocity of gas molecules. Therefore, the diffusion rales are higher at higher temperatures. 

For a bimolecular reaction, the rate depends on the number of collisions in unit time in Section 30.5 it was shown that the number of collisions between like molecules is... 

If the diameter of HI (obtained from viscosity) is cr = 435 pm, estimate the rate of decomposition of HI at 700 K using the kinetic theory expression for the number of collisions between like molecules and the values of the activation energy obtained in Problem 33.2. 

A bimolecular reaction which would proceed with comparable velocity at the same temperature as this reaction would have a heat of activation of about 60,000 calories, as may be inferred from the table on page 96. Now termolecular collisions are about 1,000 times less frequent than bimolecular collisions at atmospheric pressure. Thus if we have a bimolecular reaction and a termolecular reaction with equal heats of activation, the rate of the latter should be at least 1,000 times smaller than that of the former at the same temperature. It will probably be more nearly 10,000 times slower, since a larger proportion of the ternary collisions are likely to be ineffective on account of unfavourable orientation of the molecules during impact. Conversely, if a termolecular reaction and a bimolecular reaction are to take place at equal rates at the same temperature, then the heat of activation of the termolecular reaction would need to be the smaller by an amount AE, such that e ElRT = 1,000 to 10,000. Thus, other things being equal, the heats of activation of termolecular reactions ought to be about 5,000 calories less at the ordinary temperature, and about 15,000 calories less at 1,000° abs., than those of bimolecular reactions. We have also to allow for the diminished duration of collisions at higher temperatures, which we can do by comparison with the nitric oxide oxidation. 

A bimolecular reaction rate is proportional to the frequency of collisions between the two molecules of the reacting species. It is known from kinetic theory that the frequency of collisions between two like molecules, A, is proportional to [A]2, and the frequency of collisions between an A and a B molecule is proportional to the product of the concentrations, [A] [B]. If the species whose molecules collide are starting materials in limited concentrations, the reaction is second-order. This reaction follows the rate equation of either type (5) or (2), Table 20-1. 

Pan states that CH4 is more reactive than ammonia so that there is likely to be some mass transfer limitation on methane as well as ammonia. Making an assumption that the surface mole fractions of reactants will be of the order of half the bulk gas-phase levels, approximate reaction probabilities for NH3 and CH4 can be calculated. Collision rates are about 2 x 10 molecules cm" s" so that the reaction probability for ammonia and methane is about 10" and for oxygen about 2.5 x 10". These are sufficiently close to the values for independent oxidation of CH4 and NH3 to make it likely that the same surface reactions are also involved in the co-oxidation. 

At the point of zero charge, there is no repulsive electrical force on the particles and so the full adhesion between the grains is developed. If this adhesion is strong, then each Brownian collision between singlet particles will produce a doublet. This was the case considered by Smoluchowski in 1917 and extended by Fuchs in 1934. The theory was based on the idea that colloidal particles behave like molecules which can react to form abimolecular compound. Thus the rate of appearance of doublets dAf /df is proportional to the square of singlet concentration N per unit volume by the law of mass action, and is limited by the Brownian diffusion coefficient to give... 

It was recognized early in the history of heterogeneous catalysis that, in many instances, only a relatively small proportion of the surface was catalytically active. The pre-exponential rate factor was seen to be very small in relation to likely collision frequencies of molecules adsorbed on the surface, taking into account steric requirements, while poisoning (inhibition of the catalysed reaction) could result from surprisingly low levels of specific impurities (see below). Hence the term active sites was coined to describe those localities on the surface which would induce the desired chemical reaction. 

Simple collision theory can, in fact, be modified and extended to reactions in solution. In solutions, which contain solvated molecules and ions rather than simple molecules or atoms, interactions are known as encounters rather than collisions. It would be expected that encounter rates should be smaller than collision frequencies because the solvent molecules reduce the collision rate between reactants. However, encounters may be more likely than collisions where molecules are trapped in a temporary cage of solvent molecules (Figure 6.20). 

Since the molecules in a liquid are much closer together than in a gas, and since they are moving just as rapidly on the average as in a gas at the same temperature, the rate of collisions in a liquid is much greater than in a gas. There is some ambiguity in defining a collision between two molecules in a liquid, because the molecules are not exactly like hard spheres and there is no unique instant of contact between them. However, if some definition of a collision is adopted, the rate of collisions between liquid molecules can be estimated. ... 

---