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Molecular Speeds - Vrms, Vavg, Vmps

If for two ga...

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

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B

pressure

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C

K.E. per mole

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D

μrms

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Solution

The correct option is D
μrms

Density of a gas $(d) = \frac{P M}{R T}$

Since, $\frac{M_{B}}{T_{B}} = \frac{M_{A}}{T_{A}}$

$∴$ At the same presure, $d_{A} = d_{B}$ .

But, if pressure is diffrent, then $d_{A} \neq d_{B}$ .

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

$K . E p e r m o l e = \frac{3}{2} R T$

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

$μ r m s = \sqrt{\frac{3 R T}{M}}$ , Since, $\frac{T_{A}}{M_{A}} = \frac{T_{B}}{M_{B}} = μ r m s o f A = μ r m s o f B .$

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