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Question: The root mean square velocity at STP for the gases \(H_{2},N_{2}\)and HBr are in the order...

The root mean square velocity at STP for the gases H2,N2H_{2},N_{2}and HBr are in the order

A

H2>N2<O2<HBrH_{2} > N_{2} < O_{2} < HBr

B

HBr<O2<N2<H2HBr < O_{2} < N_{2} < H_{2}

C

H2<N2=O2<HBrH_{2} < N_{2} = O_{2} < HBr

D

HBr<O2<H2<N2HBr < O_{2} < H_{2} < N_{2}

Answer

HBr<O2<N2<H2HBr < O_{2} < N_{2} < H_{2}

Explanation

Solution

: We know,

PV=13mnu2=13Mu2PV = \frac{1}{3}mnu^{2} = \frac{1}{3}Mu^{2}

Or u=3PV/Mu = \sqrt{3PV/M}

At STPU∝1mSTPU \propto \sqrt{\frac{1}{m}}

and molecular masses of H2,N2,O2H_{2},N_{2},O_{2}and HBr are 2, 28, 32 and 81.