What is the concentration (in M) of a sample of the unknown dye with an absorbance of 0.25 at 542 nm?

To calculate the concentration of the unknown dye, we can use **Beer-Lambert Law**, which is expressed as:

\[
A = \varepsilon \cdot c \cdot l
\]

where:
- \( A \) is the absorbance,
- \( \varepsilon \) is the molar absorptivity (M⁻¹ cm⁻¹),
- \( c \) is the concentration of the solution (M),
- \( l \) is the path length of the cuvette (typically in cm).

You provided the absorbance (\( A = 0.25 \)), but we still need the values for \( \varepsilon \) and \( l \) to determine the concentration \( c \). If you have those, we can easily solve for \( c \):

\[
c = \frac{A}{\varepsilon \cdot l}
\]

Could you provide the molar absorptivity and the path length, or indicate if any other assumptions should be made (such as a standard cuvette with \( l = 1 \) cm)?

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Would you like more details on how this law is applied?

Here are 5 follow-up questions related to this topic:
1. What is the typical path length used in spectrophotometry experiments?
2. How can the molar absorptivity of a substance be determined experimentally?
3. How does wavelength affect absorbance and concentration determination?
4. What are the limitations of Beer-Lambert Law at high concentrations?
5. What happens when the dye absorbs light at multiple wavelengths?

**Tip:** Always make sure the absorbance value is between 0.1 and 1 for accurate concentration calculations, as extreme values can lead to errors.

Learn how to calculate the concentration of an unknown dye using Beer-Lambert Law with an absorbance of 0.25 at 542 nm. This example covers spectrophotometry basics, including the Beer-Lambert equation, molar absorptivity, and concentration determination. Ideal for undergraduate chemistry or biochemistry students.

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