**Frequency of Collisions of Gas Molecules**

The number of collisions undergone by a molecule of gas in one second, i.e., the frequency of collisions, may be calculated from the mean free path and the average velocity. If a molecule travels, on an average, a distance *l* cm before being hit by another molecule and its average velocity is C; then the number of collisions that this particular molecule will undergo in one second in a volume of 1/mL is given by:

**C/ l = [√(8RT/πM) / {1/(√2πσ^{2}n)}]**

**= 4 σ ^{2}n √(πRT/M)**

Since there are n molecules in unit volume, the total number of collisions undergone by all the molecules in 1 mL is the product of the right hand side of equation above and n. But in this calculation each collision has been counted twice – once when the molecule hits another molecule and again when it is hit by another molecule. The correct number of collisions is obtained by introducing a factor ½ in the product, so that the frequency of collisions, Z, is given by-

**Z = (½ n) 4σ ^{2}n√(πRT/M)**

**= 2 4σ ^{2}n^{2} √(πRT/M)**

**Example:**

Calculate the frequency of collisions for oxygen molecules at 0°C and 1 atm pressure. Collision diameter = 3.64 x 10^{-8} cm.

Solution;

n = (6.02×10^{23}/22,414) = 2.58×10^{19}

Z = 2 (3.64 x 10^{-8})^{2} x (2.58×10^{19})^{2} x [√{(3.14)(8.32×10^{7}) x (273.16)}/32]

= 9.02 x 10^{28} mL^{-1}s^{-1}

It may be seen from the example that the frequency of collisions between molecules is rather high, about 10^{28} collations in 1mL in one second even at ordinary temperature. When the temperature increases the frequency of collisions also increases.