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Homework Help: Molecule Speed

  1. Sep 27, 2006 #1
    A physics student measures molecular speeds in a laboratory apparatus and concludes that the distribution of speeds is such that:
    10% have a speed of 200 m/s
    10% gave a speed of 250m/s
    15% have a speed of 500m/s
    30% have a speed of 650m/s
    20% have a speed of 900m/s
    15% have a speed of 1300 m/s

    Calculate
    a) the average speed
    b) the rms speed
    c)the most probable speed
    Assuming that the apparatus contains and ideal gas with the molecular mass m = 50 x 10^-3 kg/mol, and the above distribution of speeds
    d) determine the temperature of the gas in the apparatus

    a) The precentages throw me off in this problem. I know that to find the average speed, I need to add up all the speeds^2 and divide by the total number of molecules.

    [(1 x 200m/s) + (1 x 250m/s) + (1.5 x 500 m/s)+ (3.0 x 650 m/s) + (2 x 900m/s) + (1.5 x 1300m/s)]/10



    b) [(1 x 200m/s)^2 + (1 x 250m/s)^2 + (1.5 x 500 m/s)^2 + (3.0 x 650 m/s)^2 + (2 x 900m/s)^2 + (1.5 x 1300m/s)^2]/10

    =1.15x 10^6 m^2/s^2


    The rms speed = sqrt(1.15x 10^6 m^2/s^2)

    c) I really don't know what the most probable speed is or how to go about calculating it please help!!

    d)I know that the rms speed = sqrt(3RT/M)

    I'm not too good at math ( if you didn't already realize by now) so I'm not sure how to set the equation to solve for T.

    T^2 = sqrt((Vrms^2(M))/3RT)

    Any help is much appreciated. Thanks in advance.
     
  2. jcsd
  3. Sep 27, 2006 #2

    HallsofIvy

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    Science Advisor

    No, not "speeds^2". This is just a standard average: add all the speeds and divide by the number. If the percentages are throwing you off, imagine that there are 100 molecules and use numbers of molecules instead:
    10 have a speed of 200 m/s
    10 gave a speed of 250m/s
    15 have a speed of 500m/s
    30 have a speed of 650m/s
    20 have a speed of 900m/s
    15 have a speed of 1300 m/s

    Or you could assume 10 molecules instead! That's exactly what you did here.


    I'm not clear on what "most probable speed" means either- I suspect they are asking which speed the greatest number of molecules have. You don't have to "calculate" that- just look at your percentage table. What speed do the greatest percentage of molecules have?

    No, not T2.
    First get rid of the square root by squareing both sides:
    (rms speed)2= 3RT/M.
    Now isolate T by multiplying both sides of the equation by M and dividing both sides by 3R:
    T= M(rms speed)2/3R.

     
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