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At 400 K, the root mean square (rms) spe...

At `400 K`, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is.

Text Solution

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The correct Answer is:
4
`mu = sqrt((3RT)/(M)) " and " alpha = sqrt((2RT)/(M))`
`mu_(x) = sqrt((3RT_(x))/(M_(x))) " and " alpha_(y) = sqrt((2RT_(y))/(M_(y)))`
Since `mu_(x) = alpha_(y)`
`:. (3RT_(x))/(M_(x)) = (2RT_(x))/(M_(y))`
or `M_(y) = (2T_(y))/(T_(x)) xx M_(x) = 2//3 xx (60)/(400) xx 40 = 4`
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Knowledge Check

  • The root mean square speed of gas molecules

    A
    is same for all gases at the same temperature
    B
    depends on the mass of the gas molecule and its temperature
    C
    is independent of the density and pressure of the gas
    D
    depends only on the temperature and volume of the gas

  • The root mean square speed of the molecules of a gas is

    A
    independent of its pressure but directly proportional to its Kelvin temperature
    B
    directly proportional to two square root of both its pressure and its Kelvin temperature
    C
    indepdent of its pressure but directly proportional to the square root of its Kelvin temperature.
    D
    directly proportional to its pressure and its Kelvin temperature.