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