If for two gases of molecular weights `M_(A)` and `M_(B)` at temperature `T_(A)` and `T_(B)`, respectively, `T_(A)M_(B)=T_(B)M_(A)`, then which property has the same magnitude for 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 gases would be equal if their densities are equal otherwise not.
(iii) `KE` per mol `=(3)/(2)RT`
`:.` It will be different of the two gas.
(iv) `V_(rms)=sqrt((3RT)/(M))`, since `(T_(A))/(M_(A))=(T_(B))/(M_(B)),`
`V_(rms)`of `A=V_(rms)` of `B`