Question

# A closed vessel with rigid walls contains 1 mol of $$^{238}_{92}U$$ and 1 mol of air at 298 K. Considering complete decay of $$^{238}_{92}U$$ to $$^{206}_{82}Pb$$, the ratio of the final pressure to the initial pressure of the system at 298 K is:

Solution

## $$^{238}_{92}U$$ decays to $$^{206}_{82}Pb$$ by a series of alpha and beta emissions.The number of alpha particles emitted by 1 $$^{238}_{92}U$$ atom  is $$\dfrac {238-206}{4}=8$$.Hence 1 mole of $$^{238}_{92}U$$ will produce 8 moles of He.Initially, only air was present.Hence, an initial number of moles of gaseous substances $$=1$$ mole.The final number of moles of gaseous substances $$=1$$ mole air $$+8$$ mole He $$=9$$ moles.The pressure of the gas is directly proportional to the number of moles of gas.Hence, the ratio of the final pressure to the initial pressure of the system at 298 K is $$9:1$$.Chemistry

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