Question

The speed of molecules is a measure of their average kinetic energy. 

(a) What is root mean square speed? 

(b) Give the equation for root mean square speed. 

(c) Calculate the following:

(i) Root mean square speed of methane molecule at 27°C. 

(ii) Most probable speed of nitrogen molecule at 25°C

Answer 1

(a) It is the square root of the mean of the squares of speeds of various molecules of the gas at a given temperature.

(b)  U_rms = \(\sqrt{\frac{u_1^2+u_2^2+...+u_n^2}{n}}\)  

OR U_rms = \(\frac{\sqrt{3RT}}{M}\)  

OR U_rms = \(\sqrt{\frac{3pV}{M}}\) 

(c) (i)  U_rms = \(\sqrt{\frac{3\times8.314\,JK^{-1}mol^{-1}\times\,300K}{16\,g\,mol^{-1}}}\) 

=21.63 ms^-1

(ii) U_mp = \(\sqrt{\frac{2RT}{M}}\)

U_mp = ^{\(\sqrt{\frac{2\times8.314\,JK^{-1}mol^{-1}\times\,298K}{14\,g\,mol^{-1}}}\)} 

= 18.81 ms^-1