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Question
During one of his adventures, Chacha Chaudhary got trapped in an underground cave which was sealed two hundred years back. The air inside was poisonous and contains CO in addition to O2 and N2. Sabu, being huge, could not enter the cave. To save Chacha Chaudhary, he started sucking the poisonous air out of the cave by mouth. In each cycle, he used to fill his lungs with cave air and exhale it out in the surroundings. In the meantime fresh air (N2+O2) from the surrounding effused into cave till the pressure was 1 atmosphere. Each time Sabu sucked air, the pressure in the cave dropped to 1/2 atm. An initial sample of air taken from the cave measured 11.2 mL at STP and give 7 J on complete combustion at constant pressure.
(a) If the safe level of CO required in the cave for life is less than 0.001% by volume, how many times does Sabu need to suck out the air to save Chacha Chaudhary?
(b) Sabu should rescue Chacha Chaudhary within 10 minutes else he will die. Previous 80 seconds is wasted in thinking of a way to rescue him. At maximum how much time should each cycle of inhaling exhaling take?
[Given ΔHcombCO=−280kJmol−1. Neglect Graham's law effect during operations].
During one of his adventures, Chacha Chaudhary got trapped in an underground cave which was sealed two hundred years back. The air inside was poisonous and contains CO in addition to O2 and N2. Sabu, being huge, could not enter the cave. To save Chacha Chaudhary, he started sucking the poisonous air out of the cave by mouth. In each cycle, he used to fill his lungs with cave air and exhale it out in the surroundings. In the meantime fresh air (N2+O2) from the surrounding effused into cave till the pressure was 1 atmosphere. Each time Sabu sucked air, the pressure in the cave dropped to 1/2 atm. An initial sample of air taken from the cave measured 11.2 mL at STP and give 7 J on complete combustion at constant pressure.
(a) If the safe level of CO required in the cave for life is less than 0.001% by volume, how many times does Sabu need to suck out the air to save Chacha Chaudhary?
(b) Sabu should rescue Chacha Chaudhary within 10 minutes else he will die. Previous 80 seconds is wasted in thinking of a way to rescue him. At maximum how much time should each cycle of inhaling exhaling take?
[Given ΔHcombCO=−280kJmol−1. Neglect Graham's law effect during operations].
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Solution
The correct option is A 13 times, 40 sec
(a) The initial sample contains 11.2 mL of air at STP.
The heat of combustion of CO is 280 kJ/mol.
The number of millimoles of CO that corresponds to 7 J of heat are 7J280000J/mol=0.025mmol.
The corresponding volume is 0.025mmol×22.4mL=0.56mL. This is the initial volume Vi of CO in the sample.
The final volume of CO in the sample should be Vf=0.001100×11.2=1.12×10−4ml
Vf=Vi×(12)n
Substitute values in the above expression.
1.12×10−4=0.5×(12)n
(12)n=1.12×10−40.56=2×10−4
n ln(12)=ln2×10−4
−0.693 n=−8.517
n=12.3≃13
(b) 10 minutes corresponds to 600 seconds. Out of this, 80 seconds are wasted.
The remaining time is 600s−80s=520s. This time is for 13 cycles.
Hence, the time for each cycle is 520s13=40s.
Hence, the correct option is A
(a) The initial sample contains 11.2 mL of air at STP.
The heat of combustion of CO is 280 kJ/mol.
The number of millimoles of CO that corresponds to 7 J of heat are 7J280000J/mol=0.025mmol.
The corresponding volume is 0.025mmol×22.4mL=0.56mL. This is the initial volume Vi of CO in the sample.
The final volume of CO in the sample should be Vf=0.001100×11.2=1.12×10−4ml
Vf=Vi×(12)n
Substitute values in the above expression.
1.12×10−4=0.5×(12)n
(12)n=1.12×10−40.56=2×10−4
n ln(12)=ln2×10−4
−0.693 n=−8.517
n=12.3≃13
(b) 10 minutes corresponds to 600 seconds. Out of this, 80 seconds are wasted.
The remaining time is 600s−80s=520s. This time is for 13 cycles.
Hence, the time for each cycle is 520s13=40s.
Hence, the correct option is A
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