Explain molar absorptivity to a dumb physicist.

1. Apr 16, 2007

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!

Last edited by a moderator: Apr 22, 2017
2. Apr 16, 2007

christianjb

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

3. Apr 17, 2007

Gokul43201

Staff Emeritus
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.

Last edited: Apr 17, 2007
4. Apr 17, 2007

christianjb

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

5. May 2, 2007

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.

6. Apr 27, 2009

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