Question

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?

• A. density
• B. pressure
• C. K.E. per mole
• D. μrms

Answer 1

The correct option is D

μrms

Density of a gas $\left(d\right)=\frac{PM}{RT}$

Since, $\frac{M_B}{T_B}=\frac{M_A}{T_A}$

$\therefore$ At the same presure, $d_A=d_B$.

But, if pressure is diffrent, then $d_A\ne d_B$.

Pressure of the Gases would be equal if their densities are equal otherwise not.

$K.Epermole=\frac{3}{2}RT$

(\therefore \) It will be diffrent for the two Gases.

$\mu rms=\sqrt{\frac{3RT}{M}}$, Since, $\frac{T_A}{M_A}=\frac{T_B}{M_B}=\mu rmsofA=\mu rmsofB.$