Determining the Concentration of a Solution: Beer's Law
Background
To characterize the ability of solutions to absorb light, we use two physical quantities: transmittance T and absorbance A. Transmittance is defined as
where
$I$ = the number of transmitted photons (the intensity) per unit time with the absorbing species present
$I_0$ = the number of transmitted photons per unit time with the absorbing species absent
Transmittance multiplied by 100 gives the percentage of the photons that can pass through a solution. It is rather difficult to work with the number of photons, so "absorbance" is used instead. Absorbance is defined as follows:
It is important to keep in mind that absorption depends on wavelength, and therefore is color specific. That is, the ability of a substance to absorb light is different for photons with different wavelengths.
The wavelength dependence of absorbance is expressed by Beer's Law:
$A = \epsilon l c$
where
$A$ = absorbance
$\epsilon$ = absorptivity coefficient ($M^{-1}cm^{-1}$)
$l$ = path length that light travels through the solution (cm)
$c$ = molar concentration of the absorbing species (M)
Note: Equation 1 can also be written as "A = a b c" where a and b correspond to $\epsilon$ and $l$, respectively.
