# 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?