If two gases of moleuclar weight `M_(1) and M_(2)` at temperature `T_(1) and T_(2), T_(1)M_(2)=T_(2)M_(1)`, then which property has the same magnitude of both the gases?

Options

A. density
B. pressure
C. `KE` per mole
D. `V_(rms)`

Answer

D

Explanation

(i) density of a gas `(rho) =(PM)/(RT)`
Since `(M_(B))/(T_(B))=(M_(A))/(T_(A))`
`:.` at the same pressure `rho_(A)=rho_(B)`
But if pressure is different, then `rho_(A)!=rho_(B)`
(ii) Pressure of the gas would be equal if their densities are equal otherwise not
(iii) `KE` per mol `=(3)/(2)RT`
`:.` It will be different for the two gases
(iv) `V_(rms)=sqrt((3RT)/(M))`, since `(T_(A))/(M_(A))=(T_(B))/(M_(B))`
`V_(rms)` of `A=V` of`B`