A spherical balloon of volume V contains Helium gas at a pressure P. How many  moles of Helium are there in the balloon if the average kinetic energy of the  Helium atoms is  K−.

We know, vRMS=3kTm=3RTM=3PVmass  of  gas ,      (1)where m, M are mass of each molecule, molar mass of gas respectively.⇒12mvRMS2=3kT2=K− Also, from (1), K−=12mvRMS2=3mPV2mass  of  gas But, mass  of  gasm=N (number of molecules).⇒K−=3PV2N⇒N=3PV2K− Now, number of moles =  n=NNA=3PV2K−NA