If for two gases of molecular weights `M_(A) and M_(B)` at temperature `T_(A) and T_(B), 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 mol
D. `V_(rms)`

Answer

D

Explanation

(i) density of a gas `(rho) =(PM)/(RT)`
Since `(M_(B))/(T_(B))=(M_(A))/(T_(A)) therefore` at the same pressure `rho_(A) =rho_(B)`
But f pressure is different then `rho_(A) ne rho_(B)`
(ii) Pressure of the gases would be equal if their densities are equal other wise not.
KE per mol `=(3)/(2)RT`
`therefore` It will be different for the two gases.
(iii) `V_(rms) =sqrt((3RT)/(M))," since "(T_(A))/(M_(A))=(T_(B))/(M_(B)), V_(rms)" of "A=V_(rms)" of "B`
Hence, (D) is the correct answer.