# Collision Frequency of a Gas

Oxygen Molecules collide with a 19.0 cm^2 wall. Assume that all molecules travel with a speed of 490 m/s and strike head on. How many collisions are there per second if the oxygen pressure is 1.00atm?

Pressure = Force/Area
Force = 2*Mass*Velocity
Collision Frequency = PI*Molecular_Diameter^2*Average_Velocity*Number_of_Molecules_per_Unit_Volume
Collision Frequency also = Velocity_Average/Mean_Free_Path
Pressure*Volume = Number_of_Molecules*Boltzmann's_Constant*Temperature
Average Velocity = sqrt(8*Boltzmann's Constant*Temperature/(PI*Mass))

A previous problem calculated the number of molecules per unit volume from the ideal gas law: N/V = P/(KbT). However, I need temperature, which I thought of getting from the average velocity equation: v_Ave = sqrt(8KbT/(PI*m)). However, I don't know the mass, so I've become stumped.

A friend worked with momentum. By Kinetic Theory, p = 2mv = Force*Time_Duration, for all molecules, N: p = 2mvN = Force*Time. By equating that force with that from P = FA, N/T = PA/(2mv), where T = 1 second, P = 1.013e5 Pa, v = 490m/s, A = .0019 m^2. But, he assumed m to be the molar mass of Oxygen, 32g. When I tried it, I received an answer of 6.1 collisions per second, which didn't make sense and was obviously wrong.

Any Suggestions?

## Answers and Replies

Maybe its asking for a real simple minded approach that treats the molecules as they were billiard balls, and not spinning, vibrating, etc.

I would just use mass here as 32gm/N, convert pressure in atm to pascals, and that in turn to total force over the 19 sq cm plate, and use your elastic collsion formula to see what the number is/second I'd not solve for mass explicitly but express it in terms of N/s (I got about 6.14 N/s where
N=6.02E23)