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I need help with spectrophotometry ( The Beer-Lambert Law )

  1. Mar 16, 2010 #1
    I'm doing a science project about the antioxidant activity of red wines from my country. This days, I was going through the theoretical part ( the basics of spectrophotometry, photometric analysis ect. ) and I'm currently at the Beer-Lambert Law. I'm would like to know the whole mathematical path that is used so that starting from this two equations: A = 2 - log10 %T and A = [tex]\epsilon[/tex]bc,

    where:
    A is absorbance, ( no units )
    T is transmittance, ( no units )
    [tex]\epsilon[/tex] is molar absorbtivity, ( L mol-1cm-1 )
    b is the length of the sample ( path length of the cuvette ) ( cm ) and
    c is the concentration of the compound in solution ( mol L-1 )

    the equation %T = e -[tex]\epsilon[/tex]bc is deduced.

    note: the molar absorbtivity is represented by the letter epsilon from the Greek alphabet and it's not superscripted as it looks like.

    Thanks in advance
     
  2. jcsd
  3. Mar 16, 2010 #2

    Char. Limit

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    Gold Member

    Well, let's see...

    Start by putting the two equations equal to each other...

    [tex]2-log_{10}(T)=\epsilon b c[/tex]

    Add log_10(t) to both sides...

    [tex]2=\epsilon b c + log_{10}(T)[/tex]

    Subtract epsilon b c from both sides...

    [tex]2- \epsilon b c = log_{10}(T)[/tex]

    And raise both sides to the power of 10.

    [tex]T=10^2 * 10^{-\epsilon b c}[/tex]

    I got a different answer than that... I'm not sure if that's right.
     
  4. Mar 16, 2010 #3
    I started just like you ( putting the two equations equal to each other ) but I think that e, from the equation %T = e-[tex]\epsilon[/tex]bc stands for the so called Neper's number ( e = 2,72 ) and after using the rule that:

    logab = logcb / logca

    and several trasnformations I got stuck here:

    loge%T = 2loge10 - [tex]\epsilon[/tex]bc loge10
     
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