Calculate the number of gasesous molecules left in a volume of `1 mm^(3)` if it is pumped out to give a vacuum of `10^(-6)mm Hg` at `298 K`.

Explanation

Given:
`V=1 mm^(3)=10^(-6) dm^(3)`
`P=10^(-6) mm Hg=(10^(-6) mm Hg)((101.325 kPa)/(760 mm Hg))`
`=1.333xx10^(-7)kPa`
` :. ` Amount of gas `n=(PV)/(RT)`
`=((1.333xx10^(-7)kPa)(10^(-6)dm^(3)))/((8.314 kPa dm^(3) K^(-1) mol^(-1))(298 K))`
`=5.38xx10^(-17) mol`
Therefore, number of molecules:
`N=nN_(A)=(5.38xx10^(-17)mol)(6.023xx10^(23) mol^(-1))`.
`=3.240xx10^(7)`