Anonymous

# Derive an expression for the concentration in terms of absorbance and molar extinction coefficient?

I think I need to get from Beer Lambert's law I = Io x 10^-e.c.l

to A=e.c.l

Relevance

The transmission of light through a sample is defined as I / Io:

I / Io = 10^-e.c.l

where:

I (capital i) = intensity of transmitted light through the sample

Io (capital i subscript zero) = intensity of transmitted light in the absence of the sample

l (lower case L) = the path length of the sample through which the light passes

c = the molar concentration of the absorbing species

e = the molar absorption coefficient of the absorbing species

Absorbance of light by the sample, A, is defined as:

A = -log(I / Io)

or A = log (Io / I)

So taking logs of the first equation:

log(I / Io) = -e.c.l

-log(I / Io) = e.c.l

Substituting for -log(I / Io) gives:

A = e.c.l

You need to keep track of your units throughout all your calculations, otherwise it's easy to come unstuck when you quote your final value for e.