Question

A 1.00 m3 box is filled with 54.1 moles of air (MM = 0.0289 kg/mole). The rms speed of the molecules is 549 m/s. What is the pressure of the molecules? 

Answer 1

$$p=\frac {Nmv^2}{3V}$$

$$m=\nu\times MM=54.1\times0.0289=1.56 kg$$

$$N=\nu\times N_A=54.1\times 6.02\times10^{23}=3.26\times10^{25}$$

$$p=\frac {3.26\times 10^{25} \times 1.56 \times 549}{3\times 1}=9.3\times10^{27} Pa$$