A bulb filled with $He$ (molar mass 4) at $1.00 atm$ leaks through a pinhole into vacuum and its pressure falls to $0.80 atm$ in $100 s$ . If the same bulb at the same temperature is filled with $CH X_{4}$ (molar mass 16) at $1.00 atm$ , the time in seconds (nearest integer) for its pressure to fall to $0.80 atm$ is

Numerical answer type, answer in s, tolerance 1.

Answer: 200 s

The effusion rate is proportional to

p / M

, so the pressure decays exponentially with a time constant proportional to

M

. The time for the same fractional drop scales as

M

t_{CH X_{4}} = 100 \times 16/4 = 200 s