Questions: In the spectrophotometry lab experiment, you constructed a calibration curve to determine the concentration of an unknown dye using the Beer-Lambert law. A=εℓc Based on the experiment, select the CORRECT statement below: The calibration curve was used to determine the molar absorptivity, ε, which was the slope of the line. The calibration curve was used to obtain the x-axis which is the concentration of the unknown dye. The calibration curve was used to obtain the y-axis, which is the concentration of the unknown dye. The Beer-Lambert law can be used directly without generating a calibration curve for determining the concentration of an unknown dye.

In the spectrophotometry lab experiment, you constructed a calibration curve to determine the concentration of an unknown dye using the Beer-Lambert law.
A=εℓc

Based on the experiment, select the CORRECT statement below:
The calibration curve was used to determine the molar absorptivity, ε, which was the slope of the line.
The calibration curve was used to obtain the x-axis which is the concentration of the unknown dye.
The calibration curve was used to obtain the y-axis, which is the concentration of the unknown dye.
The Beer-Lambert law can be used directly without generating a calibration curve for determining the concentration of an unknown dye.

Transcript text: In the spectrophotometry lab experiment, you constructed a calibration curve to determine the concentration of an unknown dye using the Beer-Lambert law. \[ A=\varepsilon \ell c \] Based on the experiment, select the CORRECT statement below: The calibration curve was used to determine the molar absorptivity, $\varepsilon$, which was the slope of the line. The calibration curve was used to obtain the $x$-axis which is the concentration of the unknown dye. The calibration curve was used to obtain the $y$-axis, which is the concentration of the unknown dye. The Beer-Lambert law can be used directly without generating a calibration curve for determining the concentration of an unknown dye.

Solution

Solution Steps

Step 1: Understanding the Beer-Lambert Law

The Beer-Lambert law is given by: \[ A = \varepsilon \ell c \] where:

$A$ is the absorbance,
$\varepsilon$ is the molar absorptivity,
$\ell$ is the path length of the sample cell,
$c$ is the concentration of the solution.

Step 2: Role of the Calibration Curve

In a spectrophotometry lab experiment, a calibration curve is constructed by measuring the absorbance of standard solutions with known concentrations. The calibration curve typically plots absorbance ($A$) on the $y$-axis against concentration ($c$) on the $x$-axis.

Step 3: Determining the Slope of the Calibration Curve

The slope of the calibration curve represents the product $\varepsilon \ell$. Since $\ell$ (path length) is usually constant and known, the slope can be used to determine the molar absorptivity $\varepsilon$.

Step 4: Analyzing the Statements

The first statement is correct: The calibration curve was used to determine the molar absorptivity, $\varepsilon$, which was the slope of the line.
The second statement is incorrect: The $x$-axis of the calibration curve is the concentration of the standard solutions, not the unknown dye.
The third statement is incorrect: The $y$-axis of the calibration curve is the absorbance, not the concentration of the unknown dye.
The fourth statement is incorrect: The Beer-Lambert law requires a calibration curve to determine the molar absorptivity $\varepsilon$ for accurate concentration determination of an unknown dye.