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.