Question

You have isolated an unknown colored compound (MW = 200,000 g/mol) with a concentration of 5 mg/mL. After you add 2 mL of your unknown to 8 mL of buffer, you obtain an absorption spectrum of your colored compound. You record an Absorbance value of 0.57 at its lambda max, 460 nm. The light path is 1 cm.

1. Calculate the molar concentration (M) of your diluted sample. Show your work.

       B. Calculate the extinction coefficient (M^-1cm^-1) of your diluted colored compound. Show your work.

Answer 1

A) In order to calculate the molar concentration of the diluted sample, we first have to calculate the molar concentration of the original sample. This can be calculate using:

Where n is the number of moles (given by the quotient between the mass of compound and it molar mass, M_R) and V(L) is the volume in units of liters. We have, originally, a solution with 5 mg (0.005 g) per mL (0.001 L),. It's molar concentration can be caluclated as:

We can now use the dilution formula to calculate the concentration of the diluted solution:

Where the subscripts 1 and 2 represent values before and after dilution. For our solution, we can calculate (notice that the final volume is the sum of the 2 mL of original solution and 8 mL of buffer):

B) We can now calulate the molar absorptivity (represented by the greek letter epsilon), using the Lambert-Beer equation:

Whera A is absorbance, l the optical path length and c the concentration. We can re-arrange and calculate the absorptivity: