The lowest pressure (the best vaccum) that can be created in laboratory at $27^{o} C$ is $10^{- 11} m m$ of $H g$ . At this pressure, the number of ideal gas molecules per ${c m}^{3}$ will be _____.

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Solution

$P V = n R T$

$\frac{P V}{n T} = R$ ( $R$ here is a constant)

$∴ \frac{P_{1} V_{1}}{n_{1} T_{1}} =$ $\frac{P_{2} V_{2}}{n_{2} T_{2}}$
$P_{1} = 760 m m$ of $H g$
$V_{1} = 22400 c m^{3}$
$T_{1} = 273 K$
$P_{2} = 10^{- 11} m m$ of $H g$
$T_{2} = 300 K$
$n_{1} = 6.02 \times 10^{23}$
$\frac{n_{2}}{V_{2}}$ $= \frac{P_{2} n_{1} T_{1}}{P_{1} V_{1} T_{2}}$
$\frac{n_{2}}{V_{2}}$ $= \frac{10^{- 11} \times 6.02 \times 10^{23} \times 273}{760 \times 22400 \times 300} = 0.332 \times 10^{6} m o l e c u l e s / c m^{3}$

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