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Question
A fresh air is composed of nitrogen N2 (78%) and oxygen O2 (21%). Find the rms speed of N2 and O2 at 20°C.
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Solution
Absolute temperature T = 20°C + 273 = 293 K
Gas constant R = 8.32 J mol−1 K−1
For, Nitrogen (N2),
Molar mass (M) = 28 g per mol = 28 × 10−3 kg/mol
∴ vrms = `sqrt((3"RT")/"M") = sqrt((3 xx 8.32 xx 293)/(28 xx 10^-3)) = sqrt(7313.28/(28 xx 10^-3))`
`("v"_"rms")_("N"_2)` = 511 ms−1
For, Oxygen (O2),
Molar mass (M) = 32 g per mol = 32 × 10−3 kg/mol
∴ vrms = `sqrt((3"RT")/"M") = sqrt((3 xx 8.32 xx 293)/(32 xx 10^-3)) = sqrt(7313.28/(32 xx 10^-3))`
`("v"_"rms")_("O"_2)` = 478 ms−1
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