At what temperature (in kelvin) is the rms speed of hydrogen molecules the same as oxygen molecules at 1327 ℃ ?

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At what temperature (in kelvin) is the rms speed of hydrogen molecules the same as oxygen molecules at

1327 ℃

?

ChemistryStates of MatterJEE Main

Solution:

2400 Upvotes Verified Answer

The correct answer is: 100

{v_{H}}_{2} = {v_{O}}_{2}

\sqrt{\frac{3 {R T}_{H}_{2}}{M H_{2}}} = \sqrt{\frac{3 R {T_{O}}_{2}}{M O_{2}}}

So,

\sqrt{{M_{O}}_{2} {T_{H}}_{2}} = \sqrt{{M_{H}}_{2} {T_{O}}_{2}}

32 \times {T_{H}}_{2} = 2 \times 1600

T_{H}_{2} = 2 \times \frac{1600}{32} = 100

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