Answer: 29.232 kg
Explanation: First, we must calculate the volume of the room. From the dimensions given in the exercise, we can assume that the room is box-shaped so its volume will be:
[tex]V=4.0m *3.5 m*2.4 m=33.6 m^3[/tex]
Since the density of nitrogen in air is given in grams over liter, we must change the volume units from cubic meters to litres.
[tex]V=(33.6m^3)*(\frac{1000L}{1 m^3} )=33600 L[/tex]
Now we just have to multiply the volume of the room by the density of nitrogen:
[tex]Mass= 0.87 \frac{g}{L} *33600L=29232 g[/tex]
To report this mass in kilograms, unit conversion is applied:
[tex]Mass=29232g*\frac{1 kg}{1000 g} =29.232 kg[/tex]