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Calculating most probable speed

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Diatomic carbon dioxide gas (CO2 has molar mass of 44.0 g/mol) is at a temperature of 305 K.

    Calculate the most probable speed v_mp.

    2. Relevant equations

    v_mp = sqrt(2kT/m)


    3. The attempt at a solution

    v_mp = sqrt(2 * 1.3801 * 10^-23 * 305 / 44)

    v_mp = 1.383 * 10^-11
     
  2. jcsd
  3. Nov 22, 2008 #2
    How about you write down the units of all the numerical values you substituted? It is always good practice to do this, and cancel out the units.
     
  4. Nov 22, 2008 #3
    I can see that m is not simply 44 mol. It needs to be in kg. m = M/N_A. The units for M is g/mol. What are the units for N_A, Avogadro's number?
     
  5. Nov 22, 2008 #4
    well, it's a number... :smile:

    6.023E23 particles/mole
     
  6. Nov 22, 2008 #5
    Then

    v_mp = sqrt(2 * 1.3801 * 10^-23 (m^2 * kg / (s^2 * K) * 305 K / (44 g/mol / (6.02E23 particles/mol) * kg/1000g)

    This ends up with the units being sqrt(m^2/s^2 * particles)

    Is that correct?
     
  7. Nov 22, 2008 #6
    heh, well particles isn't really a physical unit (neither is mol). So what you really have is sqrt(m^2/s^2).
     
  8. Nov 22, 2008 #7
    Got it. The answer was 339 m/s. Thanks!
     
    Last edited: Nov 22, 2008
  9. Nov 22, 2008 #8
    Looks like molecules should be moving a little faster than that. Check your math. The approach is correct, however.
     
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