Question

At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilomole of oxygen has a mass of 32kg.

Answer 1

Answer on Question 40305, Physics, Molecular Physics | Thermodynamics

Question: At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilomole of oxygen has a mass of 32kg. Solution. From the fact that 1 kilomole of oxygen has a mass of 32kg we can find the mass of molecule of oxygen. Indeed, we know how many molecules are in 1 kilomole, hence

$m=10^{3}\cdot N_{A}32=\frac{32}{6.022\cdot 10^{26}}=5.3\cdot 10^{-26}$

Now we just use formula that connects rsm velocity and temperature

$v_{\rm rms}=\sqrt{\frac{3kT}{m}}$

where $k$ is Boltzmann constant. Hence

$T=\frac{mv_{\rm rms}^{2}}{3k}=\frac{5.3\cdot 10^{-26}\cdot 640^{2}}{3\cdot 1.38\cdot 10^{-23}}\approx 723.6\,K$