Two moles of an ideal gas X occupying a volume V exerts a pressure P. The same pressure is exerted by one mole of another gas Y occupying a volume 2V. If the molecular weight of Y is 16 times the molecular weight of X, find the ratio of the rms speeds of the molecules of X and Y.

Two moles of an ideal gas X occupying a volume V exerts a pressure P.

1.	Two moles of an ideal gas X occupying a volume V exerts a pressure P. The same pressure is exerted by one mole of another gas Y occupying a volume 2V. If the molecular weight of Y is 16 times the molecular weight of X, find the ratio of the rms speeds of the molecules of X and Y.
Answer» Solution :`V_(RMS)=sqrt((3PV)/(n M)) (m/M=n), v_(1 rms)/v_(2 rms)=sqrt((V_(1))/V_2 n_2/n_1 M_2/M_1)` `v_(1 rms)/v_(2 rms) =sqrt((V)/(2V)) (1/2) (16)/1), (v_(1 rms))/(v_(2 rms))=2`