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.

Question

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.

Accepted Answer

∻Answer∻ ⚹ The dilution was performed correctly, and the concentration of the original solution is 0.048 M. ⚹ ∻Solution∻ ‖ a ⋮ 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. ‖ ‖ b ⋮ Calculate the concentration of the diluted solution: $c_{ ext{diluted}} = \frac{A_{ ext{diluted}}}{\epsilon \cdot l} = \frac{0.24}{25000 \cdot 1} = 9.6 imes 10^{-6} ext{ M}$. ‖ ‖ c ⋮ Verify the dilution factor: $c_{ ext{original}} = c_{ ext{diluted}} imes ext{dilution factor} = 9.6 imes 10^{-6} imes 5 = 4.8 imes 10^{-5} ext{ M}$. ‖ ‖ d ⋮ Calculate the concentration of the original solution: $c_{ ext{original}} = \frac{A_{ ext{original}}}{\epsilon \cdot l} = \frac{1.2}{25000 \cdot 1} = 4.8 imes 10^{-5} ext{ M}$. ‖ ∻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. ⚹◊What is the relationship between absorbance, molar absorptivity, path length, and concentration in Beer-Lambert Law?⍭ Generate me a similar question◊

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