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!

Clausius mossotti equation

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data

    http://img809.imageshack.us/img809/5676/unavngivetk.png [Broken]

    Additional table info:

    The molarmass ##M_{air}## is ##29 * 10^{-3} g/mol = 29*\frac{10^{-3}}{1000} kg/mol##
    The mass density ## \rho_{air} ## is ##1.3 kg/m^{3}##
    The dielectric constant ## K_{air}## is 1.00059

    My teacher told me to consider the air as 1 molecule.

    2. Relevant equations

    http://img94.imageshack.us/img94/1667/unavngivet2w.png [Broken]

    3. The attempt at a solution

    Here is my approach:

    Basically it is only N we need which is molecules per volume:

    [tex] N = \frac{Molecules}{V} = \frac{N_a n}{V} = \frac{m}{M_{air}} \frac{N_a}{V} = \frac{\rho_{air}V}{M_{air}} \frac{N_a}{V} = \frac{\rho_{air}N_a}{M_{air}} [/tex]

    [tex] \alpha = \frac{3 \varepsilon_0 M_{air}}{\rho_{air}N_a} \frac{K_{air}-1}{K_{air}+1} [/tex]

    Inserting the values:


    [tex]\frac{3(8.854*10^{-12})(29*\frac{10^{-3}}{1000})}{1.3(6.022*10^{23})} * \frac{1.00059 - 1}{1.00059 + 1} = 2.902 * 10^{-43}[/tex]

    The answer in the back of my book says it is supposed to be: ##\alpha = 9.7 * 10^{-41}##

    Can any of you guys spot where I did wrong? (The table values were some I got from my teacher and if my approach is right, then he might have wrote them wrong)
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 22, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    A quick Google check on the molar mass of air will show an error in this value.

    You used
    [tex] \alpha = \frac{3 \varepsilon_0 M_{air}}{\rho_{air}N_a} \frac{K_{air}-1}{K_{air}+1} [/tex]

    but the denominator of ##K_{air}+1 ## does not agree with the form of the Claussius-Mossotti equation that you quoted.


    Also, does your answer for ##\alpha## correspond to a molecule or an atom?
     
    Last edited: Nov 22, 2012
  4. Nov 22, 2012 #3
    All three things you pointed out gave me the right answer. Thank you ^^
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Clausius mossotti equation
  1. This equation? (Replies: 1)

Loading...