Pressure on a wall exerted by a gas

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Homework Statement

4.80×10^23 nitrogen molecules collide with a 16.0 cm^2 wall each second. Assume that the molecules all travel with a speed of 410 m/s and strike the wall head on. Answer in pascals

Homework Equations

P=mv/A

The Attempt at a Solution

Ordinarily I would use P=1/3(N/V)mv(rms)^2

but, I am not given the volume. I figure I should just use momentum/area / 1 second?
MV will give me Newton * Seconds. Since we are looking at just 1 second, it should work right?

Heres what I did:

Converted 6.022*10^23 molecules to grams by:

6.022*10^23 N2 / 6.022*20^23 * 28g = 22.318g = 0.0023Kg

Convert 16cm^2 to 0.0016m^2

noww:

(0.0023Kg)(410)/(0.0016m^2) = 5719 Pa

This answer is wrong tho.

What am I doing wrong here?

Thank you!

 

[ehild]

The molecules collide elastically with the wall. The change of momentum is 2mv. ehild