Explain molar absorptivity to a dumb physicist.

[christianjb]

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?

http://en.wikipedia.org/wiki/Absorbance

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!

 

[christianjb]

Oh, I should add, this is from an IR experiment.

 

[Gokul43201]

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

I = I_0 ~e^{-\kappa x} = I_0 ~e^{-A}

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

Since A is dimensionless, \alpha has units of cm²/mol (ignoring a multiplier of 100 or 1000 depending on actual units used) and the integrated molar absorptivity \int { \alpha dk}, where k=2\pi/\lambda has units of cm/mol.

 

[christianjb]

Thanks! I will take a good look at this later.

 

[christianjb]

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.

 

[ratormo]

Hi,

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.

Cheers
Collin