Question

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

• A. $3.22\times {10}^{12}$
• B. $1.61\times {10}^{10}$
• C. $3.22\times {10}^8$
• D. $3.29\times {10}^6$

Answer 1

The correct option is D $3.29\times {10}^6$

$P={10}^{-10}\text{mm}$ of $\text{Hg}=\frac{{10}^{-10}}{760}\text{atm}$
$V={10}^{-3}\text{litre}$
$R=0.0821\text{L/K-mol}$
$T=293\text{K}$

Now,
$PV=nRT$
$n=\frac{PV}{RT}$
$n=\frac{{10}^{-10}\times {10}^{-3}}{760\times 0.0821\times 293}=5.47\times {10}^{-18}\text{moles}$
$\therefore$ No. of molecules per ${\text{cm}}^3=5.47\times {10}^{-18}\times 6.023\times {10}^{23}=3.29\times {10}^6$