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 the molar absorptivity in#"L"/("mol"cdot"cm")# .#b# is the path length, standardized to be#"1 cm"# in many labs.#c# is the concentration in#"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.
