Calculate the number of molecules in 1 cc of an ideal gas at `27^(@)C` a pressure of 10 mm of mercury. Mean kinetic energy of molecule at `27^(@)C` is `4 xx 10^(-14)` erg, the density of mercury is 13.6 `g//cc`.

Explanation

The pressure exerted by a gas is given by
`P = (2)/(3) `(KE per unit volume)
or `KE = (3)/(2) P`
Here `P = 10 mm` of mercury of `= 1 cm` of mercury
`= 1 xx 13.6 xx 980 = 1.33 xx 10^(4) dynes//cm^(2)`
Thus, we have
`KE = (3)/(2) xx 1.33 xx 10^(4) xx 1 = 1.99 xx 10^(4) ergs`
As mean kinetic energy per molecule is `4 xx 10^(-14) ergs`,
the number of molecule will be
`(1.99 xx 10^(4))/(4 xx 10^(-14)) = 4.9 xx 10^(17) ~~ 5 xx 10^(17)` molecules