Question

The lowest pressure (the best vaccum) that can be created in laboratory at ${20}^{\circ }C$ is ${10}^{-10}mm$ of $Hg$. At this pressure, the number of ideal gas molecules per $c{m}^3$ will be

• A. $3.22\times {10}^{12}$
• B. $1.61\times {10}^{12}$
• C. $3.29\times {10}^6$
• D. $3.22\times {10}^5$

Answer 1

Answer: (C)

$3.29\times {10}^6$

For gaseous mixture at vaccum

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

$V={10}^{-3}litre$

$n=?$

$R=0.0821litre{K}^{-1}mo{l}^{-1}$

$T=293K$

$PV=nRT$

$\therefore n=\frac{PV}{RT}=\frac{{10}^{-10}\times {10}^{-3}}{760\times 0.0821\times 293}=5.47\times {10}^{18}$

$\therefore$ Number of molecule per $mL=5.47\times {10}^{-18}\times 6.023\times {10}^{23}=3.29\times {10}^{6}molecule$