Macro/ micro connections- pressure

[Kmol6]

Homework Statement

A 1.3m×1.3m×1.3m cube of nitrogen gas is at 20∘C and 1.5 atm. Estimate the number of molecules in the cube with a speed between 700 m/s and 1000 m/s.

Homework Equations

P= (1/3) (N/V) (Mv²_rms)

The Attempt at a Solution

20^oc = 293 K
1.5 atm = 151950 Pa

Solving for N
N= 3PV/(mv²_rms)

N= 3(151950)(2.197) / (28 x 1220²)
N= 0.024 Molecules ?
This doesn't seem right?

 

[kuruman]

It looks like you need to use the Maxwell- Boltzmann distribution for this.