Collisions, number

The reaction constant k was related to a collision number Z, the number of reactant molecules colliding/unit time, and an activation energy E by the Anhenius equation... 

A typical value of the collision number is 10 °s in gases at one atmosphere pressure and room temperature, and the number of successful collisions which can bring about the chemical reaction is equal to this number multiplied by the Anhenius or probability factor, exp(— /f 7 ), where E is the activation energy, the critical collision energy needed for reaction to occur. 

If hvQ is small compared with kT, the partition function becomes kT/hvQ. The function kT jh which pre-multiplies the collision number in the uansition state theoty of the bimolecular collision reaction can therefore be described as resulting from vibration of frequency vq along the transition bond between the A and B atoms, and measures the time between each potential n ansition from reactants to product which will only occur provided that die activation energy, AEq is available. 

The collision tlieory for bimolecular reactions assumes that a chemical reaction occurs when two molecules collide with enough energy to penetrate the molecular van der Waals repulsive forces, thus combining together. For the bimolecular collisions of unlike molecules A, the collision number is ... 

The steric factor, p, is presumably temperature-independent The collision number, Z, is relatively insensitive to temperature. For example, when the temperature increases from 500 to 600 K, Z increases by less than 10%. Hence to a good degree of approximation we can write, as far as temperature dependence is concerned,... 

The vibrational relaxation of simple molecular ions M+ in the M+-M collision (where M = 02, N2, and CO) is studied using the method of distorted waves with the interaction potential constructed from the inverse power and the polarization energy. For M-M collisions the calculated values of the collision number required to de-excite a quantum of vibrational energy are consistently smaller than the observed data by a factor of 5 over a wide temperature range. For M+-M collisions, the vibrational relaxation times of M+ (r+) are estimated from 300° to 3000°K. In both N2 and CO, t + s are smaller than ts by 1-2 orders of magnitude whereas in O r + is smaller than t less than 1 order of magnitude except at low temperatures. 

Since there are no experimental values of Z for M+-M collisions available at present, we first calculate Z for the M-M collisions for N2, CO, and 02 whose experimental values are well established 7,21). After establishing the usefulness of this approach for the M-M collisions, we then calculate the collision numbers for the M +-M systems, Z+. 

Figure 4. Calculated values of the reduced collision number Z as a function of temperature for N2+-N2, 02+-02, and CO+-CO...

Because the total collision number, Cj, is the sum of the number of particle-particle collisions, Cp, and the number of particle-wall collisions, C, we can define the particle-wall collision ratio, M, as below. 

As we are particularly interested in surface reactions and catalysis, we will calculate the rate of collisions between a gas and a surface. For a surface of area A (see Fig. 3.8) the molecules that will be able to hit this surface must have a velocity component orthogonal to the surface v. All molecules with velocity Vx, given by the Max-well-Boltzmann distribution f(v ) in Cartesian coordinates, at a distance v At orthogonal to the surface will collide with the surface. The product VxAtA = V defines a volume and the number of molecules therein with velocity Vx is J vx) V Vx)p where p is the density of molecules. By integrating over all Vx from 0 to infinity we obtain the total number of collisions in time interval At on the area A. Since we are interested in the collision number per time and per area, we calculate... 

Here we have utilized Eq. (147) and assumed that the electronic ground state of the transition state has been raised by AE (to refer partition functions to the transition state s own ground state) and qto-vih is referred with respect to the bottom of the potential, as in Fig. 3.10. Expression (156) shows that the adsorption rate per area is the collision number for that area times a factor So(T), the so-called sticking coefficient, which must always be smaller than one. The sticking coefficient describes how many of the incident atoms were successful in reaching the adsorbed state... 

In fact, although termolecular collision numbers are certainly much smaller than bimolecular collision numbers, they are sufficient to ensure the reversibility of the reactions. Following Tolman s15 approach,16,17 for a reaction... 

Rate constant temperature dependence Processing threshold Calculation of rate constants at different temperatures, including collision numbers and concentrations of species in steady state Calculation of the rate of photodissociation and cosmic ray-induced molecular processing from photon and particle fluxes... 

Calculate the collision number ZAb (m-3 s-1) for the collision between two hydrogen molecules and the collisions per molecule for ... 

Collision number The number of times per second, on average, that molecules collide with one another. 

The expression on right hand side of equation (4.23) is known as collision number Z. The frequency factor of the reaction is, therefore, identified with collision number. In reactions between two like molecules, the expression for the frequency factor becomes... 

If the collision is occurring between two unlike molecules A and B of masses and then the expression for the collision number... 

Tab. 5 Diffusion coefficient, heterogeneous rate constant ks, collision number Zheti free enthalpy of activation DG j and standard free enthalpy of activation DG 298 for the reduction of 10 M a-l<4SiWi2O40 in DMF containing 0.1 M LiCl04 (taken from Ref 49)...

In all factors are collected which are independent of the momentary energetic state of the reactants, like collision numbers, geometrical and also normalizing factors [e.g. A from Eqs. (20, 22)] etc. The x(E) in the integrals represent the transition probability for electrons in case the condition of energy conservation is fulfilled (Emitiai =-Efinai)- The D(E) functions denote the densities of vacant or occupied electron states in the electrode. 

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