The mass of O $_{2}$ molecules is 16 times that of H $_{2}$ molecules. The rms velocity of O $_{2}$ molecules at room temperature is C $_{r m s}$ . The rms velocity of H $_{2}$ molecules at the same temperature will be :

16 C_{r m s}

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4 C_{r m s}

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\frac{C_{r m s}}{4}

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\frac{C_{r m s}}{16}

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Solution

The correct option is B $4 C_{r m s}$
According to the kinetic theory of gases

$C_{r m s} = \sqrt{\frac{3 R T}{M}}$

at constant temperature

$C_{r m s} α \sqrt{\frac{1}{M}}$

$\frac{C_{r m s o f H_{2}}}{C_{r m s o f O_{2}}} = \sqrt{\frac{M_{O_{2}}}{M_{H_{2}}}}$ eq(1)

$M_{O_{2}} = 16 \times M_{H_{2}}$

$\frac{M_{O_{2}}}{M_{H_{2}}} = 16$

substitute values back in eq(1)

$\frac{C_{r m s o f H_{2}}}{C_{r m s o f O_{2}}} = 4$

$C_{r m s o f H_{2}} = 4 \times C_{r m s}$

answer is B.

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The mass of O2 molecules is 16 times that of H2 molecules. The rms velocity of O2 molecules at room temperature is Crms. The rms velocity of H2 molecules at the same temperature will be :

The correct option is B 4CrmsAccording to the kinetic theory of gasesCrms=√3RTMat constant temperatureCrmsα√1MCrmsofH2CrmsofO2=√MO2MH2 eq(1)MO2=16×MH2MO2MH2=16substitute values back in eq(1)CrmsofH2CrmsofO2=4CrmsofH2=4×Crmsanswer is B.

The mass of O $_{2}$ molecules is 16 times that of H $_{2}$ molecules. The rms velocity of O $_{2}$ molecules at room temperature is C $_{r m s}$ . The rms velocity of H $_{2}$ molecules at the same temperature will be :