Question

The best vacuum attained so far in a laboratory is ${10}^{-10}\text{mm}$ of $Hg$. The number of molecules of gas remaining per $c{m}^3$ at $20{}^{\circ }\text{C}$ in this vacuum is:

• A. $3.29\times {10}^4$ molecules
• B. $3.29\times {10}^5$ molecules
• C. $3.29\times {10}^6$ molecules
• D. $3.29\times {10}^7$ molecules

Answer 1

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

Given Pressure,
= ${10}^{-10}$ mm Hg = $\frac{{10}^{-10}}{760}$ atm,
V = 1 $c{m}^3$ = ${10}^{-3}L$, T = 293 K

We know that,
$PV=nRT$
$\Rightarrow n=\frac{{10}^{-10}}{760}\times \frac{{10}^{-3}}{0.082\times 293}$
$=5.46\times {10}^{-18}$ mol

$\therefore$ Number of molecules
$=5.46\times {10}^{-18}\times 6.023\times {10}^{23}=3.29\times {10}^6\text{molecules}$