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 PfinalPinitial ? (The$$ oscillation of the molecules are not to be taken in account.$$)

Question

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 PfinalPinitial ? (The$$ oscillation of the molecules are not to be taken in account.$$)

Infinity Learn · Accepted Answer

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 $$soPfinalPinitial=n2n1T2T1=161111000300=16033$$

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