Question

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

Answer 1

$PV=nRT$

$\frac{PV}{nT}=R$ ($R$ here is a constant)

$\therefore \frac{P_1{V}_1}{n_1{T}_1}=$$\frac{P_2{V}_2}{n_2{T}_2}$

$P_1=760mm$ of $Hg$

$V_1=22400c{m}^3$

$T_1=273K$

$P_2={10}^{-11}mm$ of $Hg$

$T_2=300K$

$n_1=6.02\times {10}^{23}$

$\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}molecules/c{m}^3$