Thermodynamics nitrogen molecules help

[houseguest]

Homework Statement

At 100 celsius the rms speed of nitrogen molecules is 576 m/s. Nitrogen at 100 celsius and a pressure of 2.0 atm is held in a container with a 10cm x 10cm square wall.

Homework Equations

rate of collisions: N_coll/ \Deltat = (N*A*v_x)/(2V) (this is from my textbook)
ideal gas law: N = PV/k_bT (k_b == Boltzmann constant)

The Attempt at a Solution

I took that equation and applied the ideal gas law to replace N,
number of collisions = (P*A*v_x)/(2*k_b*T)
= (2 * 101325 Pa)(.1*.1 m^2)(576m/s) / ( 2 * 1.38 * 10^-23 * (100+273.15) )

after plugging in the numbers I got 1.13 * 10^26, but that's wrong. I'm not sure why.

Thanks!

 

[kkaplanoz]

The equation that you use for the rate of collisions is asking for v_x, not v. v_rms is v. The relationship between the two is 3*v_x^2 = v_rms^2. This is because v_x^2+v_y^2+v_z^2=3*v_x^2=v^2.

 

[houseguest]

Ooooh yeeeeeaaah.

THANKS!