Answer to Question #183556 in Mechanics | Relativity for jay

Question

The pressure or air in a reasonably good vacuum might be 2.0 x 10^-5 mmHg. What mass of air exists in a 250mL volume at this pressure and 25⁰C? Take M=28 Kg/kmol for air.

Answer 1

Let's assume that air in the given conditions can be an ideal gas. Then

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

Converting everything to SI units

$p =2.0 \cdot 10^{-15} \cdot 133.32 = 266.64 \cdot 10^{-15}\; Pa$

$V= 250 \cdot 10^{-6} \; m^3$

$T = 25 + 273 =298\; K$

$M = 28 \cdot 10^{-3}\; kg/ mol$

$\displaystyle m = \frac{pVM}{RT} = \frac{266.64 \cdot 10^{-15} \cdot 250 \cdot 10^{-6} \cdot 28 \cdot 10^{-3}}{8.31 \cdot 298} =753.7 \cdot 10^{-24} \; kg = 7. 537 \cdot 10^{-22} \;kg$

Answer: $7. 537 \cdot 10^{-22} \;kg$