The number of molecules in a litre of a gas at temperature of `27^(@)C` and a pressure of `10^(6)` dyne `cm^(-2)`

Options

A. `2.4xx10^(20)`
B. `2.4xx10^(21)`
C. `2.4xx10^(22)`
D. `2.4xx10^(23)`

Answer

C

Explanation

The number of molecules (n) in a volume (V) at pressure p and temperature T is given by `n=(pV)/(KT)`
Hence, `p=10^(6)"dyne"cm^(-2),V=1000cm^(3),`
T= 273 + 27 = 300K
K = `1.38xx10^(-6)` ergs per molecule per K.
`thereforen=((10^(6))(1000))/(1.38xx10^(-16)xx300)~~2.4xx10^(22)`