At 20°C, two balloons of equal volumes and porosity are filled to a pressure of 2 atm, one with 14 kg N2 and other with 1 kg of H2. The N2 balloon leaks to a pressure of half atm in 1hr. How long will

Question

At 20°C, two balloons of equal volumes and porosity are filled to a pressure of 2 atm, one with 14 kg N2 and other with 1 kg of H2. The N2 balloon leaks to a pressure of half atm in 1hr. How long will it take for H2 balloon to reach at pressure of half atm?

TestHub · Accepted Answer

Moles effusing per unit time ∝ P/√(M); with n = PV/RT at fixed V and T, dP/dt ∝ P/√(M), so pressure decays exponentially and the time for a given pressure ratio scales as t ∝ √(M). For the same ratio 2 → 0.5 atm: t(H 2 ) = 1 h × √(2/28) = 0.267 h = 16 min. Confirms Ans: (c) 16 min.

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