The best vaccum so far attained in laboratory is $10^{-10}mm$ of Hg. How many molecules of gas remain per $cm^3$ at $20^{\large\circ}C$ in this vaccum?

$\begin{array}{1,1}(a)\;3.29\times10^4 \;molecules\\(b)\;3.29\times10^6 \;molecules\\(c)\;3.29\times10^{10} \;molecules\\(d)\;3.29\times10^5 \;molecules\end{array}$

For gaseous mixture at vaccum
$P = 10^{-10} mm =\large\frac{10^{-10}}{760} atm$
$V = 10^{-3} \;litre$
n = ?
R = 0.0821 litre atm $K^{-1}mol^{-1}$
T = 293 K
PV = nRT
$\therefore n = \large\frac{10^{-10}\times10^{-3}}{760\times0.0821\times293}$
$= 5.47 \times 10^{-18}$
$\therefore$ No. of molecules per mL $= 5.47\times10^{-18}\times6.023\times10^{23}$
$= 3.29 \times10^6$ molecules