Answer to Question #183565 in Mechanics | Relativity for jay

Question

The pressure of air in a reasonably good vacuum might be 2.0 x 10^-5 mmHg. What mass of air exists in a 250 mL volume at this pressure and 25℃?

Take M = 28kg/kmol for air.

Answer 1

A good vacuum is a state when the concentration of atoms/molecules is low and, therefore, the distance between atoms/molecules is big. They almost don't interact with each other, so ideal gas might be a reasonable approximation for this situation.

The ideal gas equation is given by

$\displaystyle pV = \frac{m}{M} RT$

We can find mass from this as

$\displaystyle m = \frac{pVM}{RT}$

$\displaystyle m =\frac{2.0 \cdot 10^{-15} \cdot 133.32 \cdot 250 \cdot 10^{-6} \cdot 28 \cdot 10^{-3}}{8.31 \cdot 298} = 7. 5371 \cdot 10^{-22} \;kg$

Answer: $7. 5371 \cdot 10^{-22} \;kg$