Question

Estimate how many collisions a water molecule undergoes at room temperature in 1 μs. Envision a liquid at a temperature of 1 K, where the distance between molecules and the molecular mass are the same as those of water at room temperature? Estimate how many collisions a molecule therein undergoes in 1 μs (at a temperature of 1 K).

Answer 1

Collision frequency formula:

R= universal gas constant = 8.314 J K^-1 mol^-1

T= room temperature = 25 degree Celsius = 25×273 =298 K

M= molar mass= 1 kg mol^-1

= 4.99 m s^-1

~ 5 m s^-1

R = 8.314 × 10^-5 bar m³ K^-1mol^-1

T = 298 K

= molecule' s effective collision area = 2d

For water d= 0.28 nm

= 2× .28 nm= .56×10^-9 M

N_A= 6.023×10²³ mol^-1

P = .317 bar at room temperature

=( 2477.57 ×10^-5 m)/(2.658×10⁵ )

= 93.2 nm

= (5 m s^-1 )/93.2 nm

= 53.6 ×10⁶ s^-1 =(53.6×10⁶)/ 1s

=53.6 × 10⁶ ×10^-6

Number of collisions per micro second = 53.6