A closed vessel with rigid walls contains 1 mol of ²³⁸₉₂U and 1 mol of air at 298 K. Considering complete
decay of ²³⁸₉₂U to ²⁰⁶₈₂Pb , the ratio of the final pressure to the initial pressure of the system at 298 K is
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92
238
U decays to
82
206
Pb by a series of alpha and beta emissions.
The number of alpha particles emitted by 1
92
238
U atom is
4
238−206
=8.
Hence 1 mole of
92
238
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.
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