The molar absorptivity of a red-colored dye molecule in water is 1997.0 L mol-1

Question

The molar absorptivity of a red-colored dye molecule in water is 1997.0 L mol-1 cm-1 at 470 nm. This dye is neutral and has a partition coefficient of 2.0 for a system of neutral water and benzene.

If you combine 25.0 mL of the 0.1 mM dye-containing (aqueous) solution and 25.0 mL of benzene, and perform an extraction. What is the concentration of the red-colored dye in aqueous solution? What is the absorption of aqueous solution at 470 nm? In the situation described in part (b), what fraction of dye is the benzene layer? How many moles of red-colored dye are in the benzene layer?

Could someone please EXPLAIN each step? Thanks!

Explanation / Answer

(a) with partition coefficient of red dye molecule = 2.0 in water and benzene

let x be the amount lost in benzene after extraction

then,

2.0 = [(0.1 - x)/25]/(x/25)

0.08x = 0.004 - 0.04x

x = 0.004/0.12 = 0.033 mM

concentration of red-colored dye in aqueous solution = 0.067 mM

(b) fraction of dye in the benzene layer = 0.033 x 100/0.1 = 33%

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