A gas bulb of 1 mL capacity contains `2.0 xx 10^(21)` molecules of nitrogen exerting a pressure of `7.57 xx 10^(3)Nm^(-2)`. The root mean square speed of the gas molecules is

Options

A. `274 ms^(-1)`
B. `494 ms^(- 1)`
C. `690 ms^(-1)`
D. `988 ms^(-1)`

Answer

B

Explanation

Number of moles of gas = `(2.0 xx 10^(21))/(6.02 xx 10^(23)) ` mol = `3.32 xx 10^(-3)` mol
From , pV =n RT , `T = (pV)/(nR) = (7.57 xx 10^(3) xx 10^(-3))/(3.32 xx 10^(-3) xx 8.314) = 274.25` K
`because` Root mean square speed , `v_(rms) = sqrt((3RT)/(M)) = sqrt((3 xx 8.314 xx 274.25)/(28 xx 10^(-3))) = 494.26 ms^(-1)`