The rate of diffusion of a gas is proportional to

Options

A. `(p)/(sqrt(d))`
B. `sqrt((p)/(d))`
C. `(p)/(d)`
D. `(sqrt(p))/(d)`

Answer

B

Explanation

According to Graham's law of diffusion , under the same conditions of temperature and pressure , the rates of diffusion for gaseous substances are inversely proportional to the square root of their molar masses :
`r prop (1)/(sqrt(M))` (1)
According to the ideal gas equation ,
`pV = nRT`
or `pV = (m)/(M) RT`
where `m` is mass and `M` is molar mass of the gas.
or `M = (m)/(V) .(RT)/(p)`
`= (dRT)/(p)`
where `d (=m//V)` is the density of the gas.
Thus , at constant temperature,
`M prop (d)/(p)`
Combining Eqs. (1) and (2) , we get
`r prop sqrt((p)/(d))`