Question

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C; the rms speed of the molecules will be ______.

Options

• 100 m/s

• `80sqrt5` m/s

• `100sqrt5` m/s

• 80 m/s

Answer 1

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C; the rms speed of the molecules will be `underlinebb((100sqrt5)  "m""/""s")`.

Explanation:

`V_{rms} = sqrt((3RT)/M)`

`ν_1/ν_2 = sqrt(T_1/T_2) = ((273 + 127))/((273 + 237)) = sqrt(400/500) = sqrt4/5 = 2/sqrt5`

∴ `ν_2 = sqrt5/2ν_1 = sqrt5/2 xx 200 = 100sqrt5` m/s.