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Question

At what temperature (K) would rms speed of CO2 molecule be equal to H2 at 27 C.


Solution

Since, the rms velocity is inversely proportional to the square root of the molar mass, rms velocity of CO2 will be less than H2 at the same temperature. In order for CO2 to have the same rms velocity as that of H2, then the temperature must be increased.

rmsCO2 at T K=rmsH2 at 300 K
(3RTM)CO2=(3R300M)H2
3×R×T44×103=3×R×3002×103
T=6600 K

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