Question

When all the molecules are in motion, then the collision rate is determined by​

Answer 1

Answer:

Explanation: According to Kinetic Molecular Theory, the collision frequency is equal to the root-mean-square velocity of the molecules divided by their mean free path. If the molecules have diameter d, then we can use a circle of diameter σ=2d to represent a molecule's effective collision area.

Answer 2

Answer:

The collision rate of gas molecules is determined by the ratio of average speed and mean free path.

Explanation:

Collision rate

Collision rate is the number of collisions of molecules per unit time.

Derivation of collision rate

Let the gas molecules have spherical shape. These molecules are colliding to other molecules frequently. Suppose these molecules have diameter d. Let single molecule has average speed v. These molecules collide with other molecules by making a cylindrical volume having radius equal to diameter of the molecule. So, volume swept by the molecule in time t is

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pi {d}^{2} vt$

Let n be the number of molecules per unit volume. So, the number of collisions per unit volume in time t is

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n\pi {d}^{2} vt$

The rate of collision is given by dividing the above equation by t

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:n\pi {d}^{2} v$

Time between two succesive collision is

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{n\pi {d}^{2} v}$

Mean free path is the average distance between two succesive collision is given by l

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:l = v \frac{1}{n\pi {d}^{2} v}$

But v/l is collision rate r. So

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:r = \frac{v}{l \:}$

Therefore, collision rate is the ratio of average speed and mean free path.