Answer to Question #159348 in Physical Chemistry for han

Question

The following Table 1 shows kinetic study values obtained from second order the gas phase reaction.

X₂  + H₂    → 2HX

Table 1

T (K) k(cm³ mol^-1 s^-1

600 4.6 x 10²

700 9.7 x 10³

800 1.3 x 10⁵

1000 3.1 x 10⁶

[Average molar mass of reactant is 128 g mol^-1]

Find:

i. The collision frequency at 700 K (in m³ s^-1).

ii. The collisions diameter.

Answer 1

Collisional Frequency is the average rate in which two reactants collide for a given system and is used to express the average number of collisions per unit of time in a defined system.

In every cylindrical collision volume Vc=σ⋅λ there is by definition just one particle, namely the particle with which the moving particle collides. Then the moving particle will change its direction and define a new collision volume, again with a “target” particle with which it will collide.

The mean free path is the distance that a molecule travels between collisions. The mean free path is determined by the criterion that there is one molecule within the "collision tube" that is swept out by a molecular trajectory. The criterion is: λ (N/V) π r² ≈ 1, where r is the radius of a molecule.

Collisions diameter = The distance between the centers of two colliding molecules when at their closest point of approach.

The distance between the centers of two molecules taking part in a collision at the time of their closest approach.