Rate of Surface Collisions

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 

The number of surface collisions at p=l bar and T = 300 K is thus rcoii-surf = 1-08 X 10 m s for hydrogen and 2.88 x 10 m s for nitrogen. Since there are typically 1.5 x 10 surface atoms per m, a surface atom will on average be hit a billion times per second under ambient conditions. This, however, does not necessarily mean that the gas molecule reacts, particularly if the reaction is an activated process. 

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If this is multiplied by a surface area a, the result is the rate of surface collisions. Then by analogy with Equation (42), we may take ka as... 

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