1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    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.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Molecule Speed
Loading...