Question

10. Suppose there are two identical gas cylinders. One contains the monatomic gas xenon (Xe), and the other contains an equal mass of the monatomic gas radon (Rn). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio KEX/KERn of the average kinetic energy of an atom of xenon to the average kinetic energy of an atom of radon.

Answer 1

Using ideal gas equation and equation for KE using temperature,we can solve this question.
we know, ideal gas eqn 1. PV = nRT Now, for both gases, pressure and volume is same PV = PzV₂ = n, RT, = M₂ RT2 NRT, a ne RTL [n,T, = n2 T2

131 We know, n, is number of moles of xenon n is number of noks of Radon. Given that their mass is same. let that be m grams No. of moles of Xenonthif M (Atomic mass No. of) Xenon - 131 No. of moles of Radon (m2) = m Voof moes (Atomic mass wo of) 222 L Raden 222 : Thitia net a substituting xTi = M XT 2 9.22 131 222 Averrage molecular energy = 3 - Ratio of average Kit. - 3/kT, I _ 131 131 = 0.59