Homework SourseThe air tanks used by a certain fire department each contain
The air tanks used by a certain fire department each contain 60.0 L of air at a pressure of 200.0 atm and a temperature of 293 K. Assume the average fire fighter exhales 0.500 L of air per breath at a temperature of 310.0K, exhales 30.0 times per minute, that the exhaled air is at a pressure of 1.00 atm, and that the air behaves as an ideal gas. Calculate the time in hours before a fire fighter using such an air tank runs out of air.
The air tanks used by a certain fire department each contain 60.0 L of air at a pressure of 200.0 atm and a temperature of 293 K. Assume the average fire fighter exhales 0.500 L of air per breath at a temperature of 310.0K, exhales 30.0 times per minute, that the exhaled air is at a pressure of 1.00 atm, and that the air behaves as an ideal gas. Calculate the time in hours before a fire fighter using such an air tank runs out of air.
Solution
Applying P V = n R T
(200 x 101325 Pa) (60 x 10^-3 m^3 ) = n (8.314 ) (293)
n = 499.14 mol of gas is inside the tank.
for exhale air:
P V = n R T
(101325) (0.5 x 10^-3) = n\' ( 8.314) (310)
n\' = 0.0197 moles are exhaled per exhale.
in 1 min = 30n\' = 0.59 mol per min.
time in which tank will be empty = 499.14 mol / (0.59 mol /min) = 846.42 min
or t = 846.42 / 60 = 14.1 hrs
