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

1391 minutes

Step-by-step 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=(nRT)/(p)=((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=(V)/(r)=(44.5)/(0.032)=1391 min`