# Homemade spectrophotometer to exemplify Beer-Lamberts law

I have built a 12-band spectrophotometer, and i'm currently keen on proving Beer-Lamberts law through a small practical example.

The solution that I'm going to test with my spectrophotometer, is orange juice that I thin with water. I naturally know I0 and I1, I.e. the absorption, and the path length that the light has to travel. Meaning that I have 2 unknowns, respectively the concentration and the molar absorptivity.

I am aware that I can figure out the molar absorptivity by doing multiple assays at different concentrations, plot them into a coordinate system and find the slope between the coordinates, which will be equal to epsilon*pathlength.

Unfortunately, I don't know how I find the molarity concentration of the orange juice that I intend investigate. I do however have the weight and the amount. Will that be sufficient to calculate the concentration molarity?

The molar absorptivity is a proportionality constant. You do not know what is the compound responsible by the color. So, this constant will not be in L/mol.cm but will be in terms of the concentration units. For example, if you use the mass to express the concentration (g/L) the constant will be express in this unit L/g.cm. With this system, you can estimate concentrations and so on. To known the molar absorptivity you must know the concentration in mol/L and it is not possible with this experiment.

• Thank you very much for your answer. What would you suggest that I do instead? I only have access to "home-chemicals", and my spectrophotometer measures intensities from 450 nm to 860nm with roughly 50nm intervals between each of the 12 bands. Nov 16, 2018 at 0:45
• I know that carotenoid is responsible for the yellow color, but i don't know the molecule structure and exactly what kind of carotenoid that is in oranges. Nov 16, 2018 at 0:47
• Why you need the value in mol?
– Koba
Nov 16, 2018 at 21:02
• To know the molar absorptivity you need the pure compound to produce a solution with a known concentration. Why are you using orange juice? What is your objective?
– Koba
Nov 16, 2018 at 21:10
• Exactly, if you plot the absorbance versus concentration (g/ml) you prove the linearity of your equipment. In this case, your epsilon will be in L.g-1.cm-1 instead L.mol-1.cm-1 but it doesn't matter. If you want you can buy some copper sulphate used in flower shops, purify by crystallization and obtain a constant in molar units for this case...
– Koba
Nov 17, 2018 at 0:04