The air tanks used by a certain fire department each contain 60.0 L of air at a

Question

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.

Explanation / Answer

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

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