Question

There poisonous gas that needs to be removed from a room. The room is at 1 atm and 270 C. A machine can remove the gas at 32 mL/minute. How long will it take to remove all the gas?

Answer 1

Answer:

1391 minutes

Explanation:

To solve the problem, we need to find first the volume of gas present in the room.

We can do it by using the equation of state for an ideal gas:

$pV=nRT$

where

p = 1 atm is the pressure

V is the volume

n = 1 mol is the number of moles (not given in the problem, so we assume its value)

$R=0.082 atm \cdot L/(mol \cdot K)$ is the gas constant

$T=270C+273=543 K$ is the temperature

Solving for V,

$V=\frac{nRT}{p}=\frac{(1)(0.082)(543)}{1}=44.5 L$

So, there are 44.5 L of gas in the room.

The gas can be removed at a rate of

$r=32 mL/min = 0.032L/min$

Therefore, the time it takes is:

$t=\frac{V}{r}=\frac{44.5}{0.032}=1391 min$