Question

Blue dye can be decolorized by treatment with bleach. The kinetics of the reaction can be studied by testing the absorbance of the solution over time.

At the start of an experiment, the blue dye had a concentration of 9.05 x 10-6 M and an absorbance of 0.70 at the observed maximum wavelength.
The path length of the cell is 1.00 cm.

Part 1 (1 point)
What is the molar absorptivity of the blue dye? cm-¹M-1


Part 2 (1 point)

What will the concentration of the blue dye be when the absorbance falls to 0.43? M

Answer 1

The molar absorptivity of the blue dye is calculated as 77348 cm⁻¹M⁻¹ using Beer's Law, and the concentration of the dye when the absorbance drops to 0.43 is found to be 5.56 × 10⁻⁶ M.

Calculating Molar Absorptivity and Concentration

To calculate the molar absorptivity of the blue dye using Beer's Law, we can use the formula A = εc&l; where A is absorbance, ε is the molar absorptivity, c is the concentration, and l is the path length.

Given the initial concentration (c) of the blue dye as 9.05 ×
`10^{-6` M, the absorbance (A) as 0.70, and the path length (l) as 1.00 cm, we can rearrange Beer's Law to solve for the molar absorptivity (ε):

ε = A / (c&l;).

By substituting the known values we get:

ε = 0.70 / (9.05 ×
`10^{-6` M × 1.00 cm) = 77348
`cm^(-1)M^{-1.`

For Part 2, to calculate the new concentration when the absorbance falls to 0.43, we use the same formula A = εc&l; and solve for c with our known ε value:

c = A / (ε&l;).

c = 0.43 / (77348
`cm^(-1)M^{-1` × 1.00 cm) = 5.56 ×
`10^{-6` M.

We find that the concentration of the blue dye when the absorbance is 0.43 is 5.56 ×
`10^{-6` M.