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# Lecture30A - Gas Dynamics and Reactions(27.4-7 In the gas...

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Lecture 30 1 Gas Dynamics and Reactions (27.4-7) In the gas phase, unless a molecule is unstable, “something” must occur for a reaction to occur. There are basically two paths: a molecule strikes a surface (reacts and/or dissociates); a molecule strikes another molecule (reacts and/or dissociates). Kinetic gas theory can tell us the rate at which these collisions take place. 1 st gas-surface collisions Fig 27.5 As you might expect, the number of collisions will be proportional to the gas speed, u, and density, ρ=N/V (# density). { ( 29 lengthof cylinder In a small cylinder: volume element cos Note as /2, volume 0 A udt θ π = Θ →

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Lecture 30 2 ( 29 Now A cos is proportional to the number of molecules in the cylinder in a time interval dt. udt ρ θ ( 29 ( 29 cos includes only those with speeds between u and u+du A udt F u du ρ θ ( 29 ( 29 sin cos further selects that fraction travelling 4 towards the surface within solid angle and +d , and and +d . d d A udt F u θ θ φ ρ θ π θ θ θ φ φ φ ( 29 ( 29 coll sin cos 4 dN # of molecules colliding within area, A, from the specified direction in a time interval dt. coll d d A udt F u dN θ θ φ ρ θ π = = so collision rate on surface coll dN dt = collision rate per unit area for those in the speed range 1 and for our selected direction coll coll dN dz u u du A dt = = +
Lecture 30 3 ( 29 cos sin 4 coll dz uF u du d d ρ θ θ θ φ π = We'll average over all speeds and directions, noting that (see figure 27.5) 0 /2, limited range for ! θ π θ ( 29 / 2 2 0 0 0 1/ 2 2 cos sin 4 4 coll u u z uF u du d d π π π ρ ρ θ θ θ φ π = = 1 4 2 4 3 1 4 4 2 4 4 3 123 14 3 2 1/ 2 4

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Lecture30A - Gas Dynamics and Reactions(27.4-7 In the gas...

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