Suppose you measure the absorbance of a yellow dye solution in a 1.00 cm cuvette (b=1.00 cm).

The absorbance of the solution at 427 nm is 0.30 . If the molar absorptivity of yellow dye at 427 nm is 27400 M–1cm–1, what is the concentration of the solution in M? 


To calculate the concentration of the solution using the given data, we can use **Beer-Lambert's Law**, which is:

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

Where:
- \( A \) is the absorbance (0.30),
- \( \varepsilon \) is the molar absorptivity (27,400 M\(^\text{-1}\)cm\(^\text{-1}\)),
- \( b \) is the path length (1.00 cm),
- \( c \) is the concentration in molarity (M).

We can rearrange this formula to solve for the concentration \( c \):

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

Now we plug in the values:

\[
c = \frac{0.30}{27400 \, \text{M}^{-1} \, \text{cm}^{-1} \cdot 1.00 \, \text{cm}}
\]

Let me calculate that for you.The concentration of the yellow dye solution is approximately \( 1.09 \times 10^{-5} \, \text{M} \).

Would you like more details or have any questions about the calculation? Here are five related questions:

1. What happens to the concentration if the absorbance increases?
2. How does the molar absorptivity affect the sensitivity of absorbance measurements?
3. Can Beer-Lambert’s law be applied for highly concentrated solutions?
4. What are the limitations of the Beer-Lambert law?
5. How would you measure the absorbance of a different wavelength for the same dye?

**Tip:** For very dilute solutions, absorbance values might be too small to measure accurately, so ensuring a sufficiently concentrated sample is key.

Suppose you measure the absorbance of a yellow dye solution in a 1.00 cm cuvette (b=1.00 cm). The absorbance of the solution at 427 nm is 0.30. If the molar absorptivity of yellow dye at 427 nm is 27,400 M–1cm–1, what is the concentration of the solution in M?

Learn how to calculate the concentration of a yellow dye solution using Beer-Lambert's law. This example provides a step-by-step solution for a 1.00 cm cuvette with an absorbance of 0.30 at 427 nm, and a molar absorptivity of 27,400 M–1cm–1.

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