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Explain molar absorptivity to a dumb physicist.

  1. Apr 16, 2007 #1
    OK chem-wizards...

    I'm looking at a paper which states

    "....the integrated absorptivity of the stretching vibrations of a water molecule is 4.89 cm micro mol^-1"

    (I'm transcribing a 'mu' character as micro in the above. If mu doesn't stand for micro, then let me know!)

    OK, so some questions:

    1) Is the paper quoting an integrated 'molar absorptivity'?

    2) The integration is over the frequency axis, but is this frequency in wave-numbers?

    3) Is this defn. for molar absorptivity correct?

    Molar Absorptivity,? = A/ c l

    ( where A= absorbance, c = sample concentration in moles/liter
    & l = length of light path through the cuvette in cm.)

    taken from http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/UV-Vis/uvspec.htm

    4) According to this Wikipedia article, absorbance is calculated as a base 10 logarithm of I/I0. Is that defn. universally used?


    5) I can't understand the units. If A=absorption and alpha = absorption coefficient and L=sample length, then A=alpha L, so that means that alpha is in units of inverse length.

    If e=absorptivity, and c is the concentration in mols per liter and e=A/cL=alpha/c, then e is in units of mols^-1 liters ^-1 cm^-1. Thus, I'd expect the integrated absorptivity to be in mols^-1 liters^ -1 cm ^-2, given that the integral is over wavenumbers which have units of cm^-1.

    6) Basically what I want is to convert the number in the paper into a value for the absorption coefficient.

    Thanks in advance for any help!
  2. jcsd
  3. Apr 16, 2007 #2
    Oh, I should add, this is from an IR experiment.
  4. Apr 17, 2007 #3


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    The absorbance, A, is the exponent that is seen in the Beer-Lambert equation.

    [tex]I = I_0 ~e^{-\kappa x} = I_0 ~e^{-A} [/tex]

    The extinction coefficient, K , is often proportional to the concentration of the solution over a wide range of values, allowing us to write [itex]\kappa=M \alpha [/itex], where M is the molar concentration in Mol/Liter and [itex]\alpha[/itex] is what is usually called the molar absortivity.

    Since A is dimensionless, [itex]\alpha[/itex] has units of cm2/mol (ignoring a multiplier of 100 or 1000 depending on actual units used) and the integrated molar absorptivity [itex] \int { \alpha dk} [/itex], where [itex]k=2\pi/\lambda[/itex] has units of cm/mol.
    Last edited: Apr 17, 2007
  5. Apr 17, 2007 #4
    Thanks! I will take a good look at this later.
  6. May 2, 2007 #5
    Again, thanks. I finally got back to looking at this tonight and your explanation was enough for me to make the correct conversions in the paper I'm writing.
  7. Apr 27, 2009 #6

    Can anyone tell me what is the molar absorptivity at the irradiating wavelength for the 2,4,6-trichlorophenol? I use wavelength 293nm to detect the concentration of this chemical in a UV-Vis Spectrophotometer. Thank you.

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