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Q. What is the rms speed of nitrogen molecules contained in a 7.0 m3 volume at 4.20 atm if the total amount of nitrogen is 1600 mol?

I figured I would have to use this equation to solve it:

V rms = (3KT/m)^(1/2)

But first I would need to find T, so I found it through this equation:

PV=nRT

(4.20 atm)(1.013e5 N/m^2/atm)(7.0m3) = (1600 mol)(8.315 J/mol K)(T)

and T = 223.9 K

I also needed to find m

m (N2) = (28)(1.66 x 10e-27) = 4.648e-26 kg

Then I subsitituted them all back into the original equation

V rms = [(3*1.38e-23 J/K*223.9 K)/(4.648e-26 kg)]^(1/2)

V rms = 446.5 m/s

But that isn’t the right answer. I don’t know what I am doing wrong, but I was wondering if anyone could help point me in the right direction, it would be greatly appreciated.

Thank you!!