If you would like to test your skills working with the Beer-Lambert Law then you might like to look at the Spectrophotometry tests at: Maths4Biosciences.com.
Some students struggle to understand the relationship between the Beer-Lambert Law and a straight line, and working out the units of the extinction coefficient (ε).
The Beer-Lambert Law states:
So, what connection between this and a straight line, and what are the units of the extinction coefficient?
The units of the extinction coefficient
In my opinion, the extinction coefficient has some of the craziest units out there.
Absorbance (A) has no units so the units of the extinction coefficient (ε) are determined by how the concentration (c) and path length (l) are being measured. That is, the units of the extinction coefficient must cancel out the units of the concentration and path length so that the absorbance can have no units!
A worked example.
ε = 1 / ([mM] . [cm])
ε = [mM]-1 . [cm]-1
So, the units are mM-1 . cm-1
This can be checked by putting it all back together:
A = ([mM]-1 . [cm]-1) . [mM] . [cm]
So, the mM and the cm cancel each other out, leaving no units for absorbance A.
A straight line
The Beer-Lambert Law:
The equation for a straight line is:
If you plot concentration, against absorbance, then x = concentration and y = absorbance. Plus, from the Beer-Lambert Law, we know that if the concentration is zero, then absorbance must be zero.
From above, if concentration = 0, then absorbance = 0, hence c must be zero
(* note, this c is the y-intercept and not the concentration)
With (and rearranging):
A = (ε . l) . c
y = m . x
You may also find the following two videos useful.