Calculating Moles per Cubic Meter and Liters per Mole

(a) We are asked to find the number of moles per cubic meter, and we know from Example 13.7 that the number of molecules per cubic meter at STP is $2\text{.}\text{68}\times {\text{10}}^{\text{25}}$. The number of moles can be found by dividing the number of molecules by Avogadro’s number. We let $n$ stand for the number of moles,

(b) Using the value obtained for the number of moles in a cubic meter, and converting cubic meters to liters, we obtain

This value is very close to the accepted value of 22.4 L/mol. The slight difference is due to rounding errors caused by using three-digit input. Again this number is the same for all gases. In other words, it is independent of the gas.

The (average) molar weight of air (approximately 80% ${\text{N}}_2$ and 20% ${\text{O}}_2$ is $M=\text{28}\text{.}8\text{g}\text{.}$ Thus the mass of one cubic meter of air is 1.28 kg. If a living room has dimensions $5\text{m}\times \text{5 m}\times \text{3 m,}$ the mass of air inside the room is 96 kg, which is the typical mass of a human.