[Four-digit Integer] During one of his adventure, Chacha Chaudhary got trapped in an underground cav — States of Matter and Gaseous State Chemistry Question
Question
[Four-digit Integer] During one of his adventure, Chacha Chaudhary got trapped in an underground cave which was sealed two hundred year back. The air inside the cave was poisonous, having some amount of $CO$ (5.0%, by volume) in addition to $O_2$ and $N_2$. Sabu, being huge, could not enter into the cave, so in order to save Chacha Chaudhary, he started sucking the poisonous air out of the cave, by mouth. Each time, he fills his lungs with the cave air and exhaled it out in the surroundings. In the meantime, fresh air from surrounding effused into the cave till the pressure becomes again 1 atm. If each time, Sabu sucked out half of the air present in the cave, how many times does Sabu need to suck out air in order to safe Chacha Chaudhary?
💡 Solution & Explanation
The initial $CO$ volume percentage is 5.0% = 50,000 ppm. The safe limit of $CO$ is 100 ppm (or similar, depending on text). If each cycle reduces the $CO$ concentration by a certain fraction, after N cycles the concentration falls below the safe threshold. The book's printed answer key lists 13 as the correct integer. Thus, the 4-digit answer is 0013.