# The transmittance for a sample of a solution, measured at #590nm# in a #1.5-cm# cuvette, was #76.2%#. What is the corresponding absorbance?

##### 1 Answer

Absorbance as it relates to transmittance is given by a logarithmic relationship, just as loudness is related to sound intensity in that manner.

#A = log(1/T)# where

#T# is the transmittance. Why must this be#1/T# since#0 < T < 1# ?

So we know the absorbance to be:

#color(blue)(A) = log(1/0.762) = color(blue)(0.118)#

Knowing the concentration, we can use Beer's law at low concentrations to see a linear relationship:

#A = epsilonbc# where:

#epsilon# is themolar absorptivityin#"L"/("mol"cdot"cm")# .#b# is thepath length, standardized to be#"1 cm"# in many labs.#c# is theconcentrationin#"mol/L"# .

Thus, the **molar absorptivity** would be:

#color(blue)(epsilon) = A/(bc)#

#= 0.118/("1 cm" cdot "0.0802 mol/L")#

#= color(blue)("1.472 L/mol"cdot"cm")# which is fairly low.

It makes physical sense because **the absorbance was quite low**, even though the concentration was also low.

If the absorptivity was already known to be

#color(blue)(c) = A/(epsilonb)#

#= 0.118/("1000 L/mol"cdot"cm" cdot "1 cm")#

#= color(blue)(1.181 xx 10^(-4) "M")#

If the molar absorptivity was this high (which is quite large), and the absorbance was still so low, it would only be because there was a **low concentration of particles** to absorb the incoming excitation light source.