Prove that at a certain pressure, the rate of diffusion of a gas is proportional to the square root of the absolute temperature of the gas.

Explanation

The rate of diffusion of a gas at constant pressure `(r) prop` root mean square velocity of the gas `(c_(rms))`
`therefore r prop c_(rms) or, rprop sqrt((3RT)/(M))" "[because c_(rms)=sqrt((3RT)/(M)]`
At a constant pressure, if `r_(1) and r_(2)` be the rates of diffusion of a particular gas at temperatures `T_(1) and T_(2)`,
respectively, then `r_(1) prop sqrt((3RT_(1))/(M)) and r_(2) propsqrt((3RT_(2))/(M))` ltBrgt `therefore r_1/r_(2)=sqrt((T_(1))/(T_(2))) or, rpropsqrt(T)`
So, at constant pressure, the rate of diffusion of a gas is proportional to the square root of the absolute temperature of the gas.