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A solution of a dye has an absorbance of 1.2 at its λmax of 450 nm. After diluti...

Jun 17, 2024

A solution of a dye has an absorbance of 1.2 at its λmax of 450 nm. After diluting the solution by a factor of 5, the absorbance is measured to be 0.24. Verify if the dilution was performed correctly and calculate the concentration of the original solution if the molar absorptivity is 25000 L/(mol·cm) and the path length is 1 cm.

Answer

The dilution was performed correctly, and the concentration of the original solution is 0.048 M.

Solution

Use Beer's Law:

A = \epsilon \cdot c \cdot l

, where

A

is absorbance,

\epsilon

is molar absorptivity,

c

is concentration, and

l

is path length

Calculate the concentration of the diluted solution:

c_{\text{diluted}} = \frac{A_{\text{diluted}}}{\epsilon \cdot l} = \frac{0.24}{25000 \cdot 1} = 9.6 \times 10^{-6} \text{ M}

Verify the dilution factor:

c_{\text{original}} = c_{\text{diluted}} \times \text{dilution factor} = 9.6 \times 10^{-6} \times 5 = 4.8 \times 10^{-5} \text{ M}

Calculate the concentration of the original solution:

c_{\text{original}} = \frac{A_{\text{original}}}{\epsilon \cdot l} = \frac{1.2}{25000 \cdot 1} = 4.8 \times 10^{-5} \text{ M}

Key Concept

Beer's Law

Explanation

Beer's Law relates the absorbance of a solution to its concentration, molar absorptivity, and path length. By using this law, we can verify the dilution and calculate the concentration of the original solution.