# 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