Question

Estimate the number of molecules left in a volume of the size of a pinhead about $1$ cubic $mm$ when the air is pumped out to give a vaccum of ${10}^{-6}mmHg$ at ${25}^{o}C$.

Answer 1

$V=1m{m}^3={10}^{-6}lit$

$P={10}^{-6}mm$ of $Hg=\frac{{10}^{-6}}{760}atm$

$T={25}^{o}C=298K$

$n=\frac{PV}{RT}=\frac{{10}^{-6}\times {10}^{-6}}{760\times 0.0821\times 298}=5.378\times {10}^{-17}moles$

$1mole=6.023\times {10}^{23}molecules$

$\therefore$ no. of molecules $=3.24\times {10}^7$