Two dyes X,Y have concentration ratio cX/cY=0.25 and are measured in identical cuvettes. Their absorbance ratio AX/AY=0.5. Find the ratio of molar extinction coefficients εX/εY.
Beer–Lambert law gives A=εcℓ. Identical cuvettes have equal path length, so AX/AY=(εX/εY)(cX/cY). Thus εX/εY=.5/.25=2. Neither the absolute concentrations nor path length is needed after taking the ratio.
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