An electronic vaccum tube is constructed and sealed at `27^@C` and `1.2 times 10^-6 cm Hg` pressure. The tube has a volume of `100 cm^3`. Calculate the number of gas molecules left in the tube.Avogadro number is `6.02 times 10^23`, and the gas occupies a volume of 22.4 litre at STP.

Explanation

Molar density at STP
`=(6.02 times 10^23)/(22.4 times 10^3)` molecules . `cm^-3`
Let the number of molecules left in the tube,after sealing be n.
From gas equation we have, `p_1/(p_1T_1)=p_2/(p_2T_2)`
Here, `p_1=1.2 times 10^-6 cmHg`
`p_1=n/100 mol ec ul es.cm^-3`
`T_1=273+27=300K`
`p_2=76 cmHg`
`p_2=(6.02 times10^23)/(22.4times10^3)mol e cu l es .cm^-3`
and `T_2=273 K`
`therefore(1.2 times10^6)/(n/100times300)=76/((6.02times10^23)/(22.4times10^3)times273)`
i.e.,`n=(1.2times10^-6times100times6.02times10^23times273)/(300times76 times 22.4 times 10^3)`
`=3.86 times 10^13`