Beer-Lamberts Law Homework: Understanding Boltzmann Constant Unit

[nordmoon]

Homework Statement

I am trying to understand a formula on a paper. On page 3138-3139 they express the Beer-Lamberts law in which they replace the concentration n with an equation involving the volume ratio ( I am guessing its the molarfraction of the investigated species). What I would like to know is the unit of Boltzmann constant kb to make this happen. I don't see how the units can fit.

Homework Equations

$$\frac{cp}{kT}$$

where c is the volume part (volume ratio) of the absorbing gas in the gas mixture, T is the temperature of the gas, k is the Boltzmann constant (unit?), p is pressure in [atm].

The Attempt at a Solution

This equation should fit to Beer law,

exp( - alpha(v)*n*l ) = exp (- tau )

where tau is unitless and alpha(v) is specific absorption coefficient per
absorbing particle and is caluclated with help of Hitran by alpha(v) = S(T)*g(v-vo) [ unit: 1/(molecule cm-2) ] and l is path length of radiation through the absorbing medium [ unit: cm ].

It's the unit of n I am trying to determine, and thus Boltzmann constant.

According to above it should be [molecules cm-3] so that tau becomes unitless.

What I know the unit if Kb is 0.659 cm-1 K-1. And there is the [ atm ] from the pressure I am missing and [ molecules ]. If c is a fraction this is unitless, so I don't see how this can go together.

This has been taken from this paper: http://iopscience.iop.org.ludwig.lub.lu.se/0022-3727/35/23/315/pdf/0022-3727_35_23_315.pdf

"Experimental verification of gas spectra calculated for high temperatures using the
HITRAN/HITEMP database"

My goal is to plot the transmission as function of % of the species.

 

[Borek]

You are aware of the fact that paper you linked to is available only to those that can log in?

 

[nordmoon]

You are aware of the fact that paper you linked to is available only to those that can log in?

Well, yes. That is why I have written everything in detail. However if you have access to the university as student or teacher you should be able to log in and read it.

I noticed that the unit is [ cm -2 atm -1 ] for the linestrength S. In hitran this is [ cm-1 / ( molecules cm-2 ) ] and absorption coefficient is [ cm-1].

I don't see the connection.