At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at $1327^{\circ} C$ ?

173 K

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100 K

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400 K

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523 K

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Solution

The correct option is B $100 K$
$u_{r m s} = \sqrt{\frac{3 R T}{M}}$
According to the question, $(\sqrt{\frac{3 R T_{1}}{M_{H_{2}}}}) = (\sqrt{\frac{3 R T_{2}}{M_{O_{2}}}}) \sqrt{\frac{T_{1}}{2}} = \sqrt{\frac{1600}{32}} \Rightarrow \frac{T_{1}}{2} = \frac{1600}{32} ∴ T_{1} = 100 K .$

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Similar questions

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at

1327^{\circ} C

Q. At what temperature is the rms speed of

H_{2}

molecules the same as that of oxygen molecules at

1327^{\circ} C

At what temperature the rms speed of hydrogen molecules is same as that of oxugen molecules at 1327⁰C?

The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is $v$ . The rms speed of the hydrogen molecules at the same temperature will be

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At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at 1327∘C ?

The correct option is B 100 Kurms=√3RTM According to the question, (√3RT1MH2)=(√3RT2MO2)√T12=√160032⇒T12=160032∴T1=100 K.

At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at $1327^{\circ} C$ ?

The correct option is B $100 K$
$u_{r m s} = \sqrt{\frac{3 R T}{M}}$
According to the question, $(\sqrt{\frac{3 R T_{1}}{M_{H_{2}}}}) = (\sqrt{\frac{3 R T_{2}}{M_{O_{2}}}}) \sqrt{\frac{T_{1}}{2}} = \sqrt{\frac{1600}{32}} \Rightarrow \frac{T_{1}}{2} = \frac{1600}{32} ∴ T_{1} = 100 K .$