One mole of diatomic gas is being heated in a closed tank from 300K up to 1000 K. During the process part of the molecules dissociate. At 1000 K the energy of the diatomic molecules are only half of that of the whole gas. By what factor has the gas pressure increased $\frac{P_{final}}{P_{initial }}$? (The oscillation of the molecules are not to be taken in account.)

detailed solution

Correct option is A

Let x mole of the gas dissociate at 1000 K          No. of mole of diatomic gas molecule =1-x          No. of moles of monatomic gas molecules=2 x X          Energy of diatomic molecules = 12(energy of monatomic molecule + energy of the diatomic molecule)Energy of diatomic molecules = energy of monatomic molecule1-x5R2= 2x3R2⇒5-5x =6x⇒x=511total no of moles now 1-x+2x=1+x =1+511=1611 pressure of a gas is directly proportional to no of moles and temperature soPfinalPinitial=n2n1T2T1=161111000300=16033