A gas bulb of `1 L` capacity contains `2.0xx10^(11)` molecules of nitrogen exerting a pressure of `7.57xx10^(3)Nm^(-2)`. Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square is `0.82`, calculate the most probable speed for these molecules at this temperature.

A gas bulb of `1 L` capacity contains `2.0xx10^(11)` molecules of nitr

1.	A gas bulb of `1 L` capacity contains `2.0xx10^(11)` molecules of nitrogen exerting a pressure of `7.57xx10^(3)Nm^(-2)`. Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square is `0.82`, calculate the most probable speed for these molecules at this temperature.
Answer» Given `P =7.57 xx 10^(3) Nm^(-2), V = 1 litre = 10^(-3) m^(3)` `R = 8.314 J, n = (2 xx 10^(21))/(6.023 xx 10^(23)` mole Using `PV =nRT` `7.57 xx 10^(3) xx 10^(-3) = (2 xx 10^(21))/(6.023 xx 10^(23)) xx 8.314 xx T` `T =274.2 K` `:. u_(rms) = sqrt(((3RT)/(M))) =sqrt(((3 xx 8.314 xx 274.2)/(28 xx 10^(-3)))` (M in kg) `= 494.22 m sec^(-1)` Now `u_(MP)/(u_(rms))=0.82` `u_(MP) = 405.26 m sec^(-1)` .

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