The Beer-Lambert Law Calculator is used in spectroscopy and analytical chemistry to determine the concentration of a solution based on its light absorption properties.
This law, also known as Beer’s Law or the Beer-Lambert-Bouguer Law, establishes a linear relationship between the absorbance of a solution and its concentration. The calculator applies this principle to provide quick and accurate results for various applications in chemistry, biology, and material science.
Beer-Lambert Law Calculator
| Parameter | Example 1 | Example 2 | Example 3 | Example 4 |
|---|---|---|---|---|
| Absorbance (A) | 0.5 | ? | 1.2 | 0.75 |
| Molar Absorptivity (ε) (L mol^-1 cm^-1) | 1000 | 2500 | 3000 | ? |
| Path Length (b) (cm) | 1.0 | 2.0 | ? | 1.5 |
| Concentration (c) (mol L^-1) | ? | 0.001 | 0.0002 | 0.0005 |
| Calculated Value | c = 0.0005 | A = 5.0 | b = 2.0 | ε = 1000 |
| Conversion Equation | c = A / (εb) | A = εbc | b = A / (εc) | ε = A / (bc) |
Beer-Lambert Law Formula
The Beer-Lambert Law is expressed by the equation:
A = εbc
Where:
- A is the absorbance (dimensionless)
- ε (epsilon) is the molar absorptivity or extinction coefficient (L mol^-1 cm^-1)
- b is the path length of the sample (cm)
- c is the concentration of the compound in solution (mol L^-1)
This formula encapsulates the fundamental relationship between light absorption and the properties of the absorbing medium. It’s important to note that this law assumes ideal conditions, such as monochromatic light and dilute solutions.
For example, a solution of copper sulfate with a molar absorptivity of 15 L mol^-1 cm^-1 at 810 nm. If we measure its absorbance in a 1 cm cuvette and obtain a value of 0.75, we can calculate the concentration:
c = A / (ε b) = 0.75 / (15 L mol^-1 cm^-1 1 cm) = 0.05 mol L^-1
How do you calculate beer’s Lambert law?
Calculating Beer’s Lambert law involves a step-by-step process that depends on which variable you’re trying to determine.
- Measure the absorbance (A) of the solution using a spectrophotometer.
- Determine the path length (b) of the sample cell or cuvette.
- Look up or measure the molar absorptivity (ε) for the substance at the wavelength used.
- Apply the formula: c = A / (ε * b)
Let’s say we’re analyzing a solution of potassium permanganate:
- Measured absorbance (A) = 0.85
- Path length (b) = 1.0 cm
- Molar absorptivity (ε) of KMnO4 at 525 nm = 2460 L mol^-1 cm^-1
Plugging these values into the formula:
c = 0.85 / (2460 L mol^-1 cm^-1 1.0 cm) = *3.46 × 10^-4 mol L^-1
This calculation gives us the concentration of potassium permanganate in the solution.
How to calculate expected absorbance?
To determine the expected absorbance:
- Gather the known parameters: concentration (c), path length (b), and molar absorptivity (ε).
- Apply the Beer-Lambert equation: A = εbc
If we’re preparing a solution of nickel(II) chloride:
- Concentration (c) = 0.02 mol L^-1
- Path length (b) = 1.0 cm
- Molar absorptivity (ε) at 720 nm = 2.5 L mol^-1 cm^-1
Expected absorbance = (2.5 L mol^-1 cm^-1) (1.0 cm) (0.02 mol L^-1) = 0.05
Which is the correct equation for Lambert Beer law?
The correct equation for the Lambert-Beer law is:
A = εbc
This equation is universally accepted and applies to a wide range of scenarios in spectroscopy.
Transmittance form: T = 10^-εbc or T = e^-εbc
Where T is the transmittance, related to absorbance by A = -log(T)
Intensity form: I = I0 10^-εbc
Where I is the intensity of light after passing through the sample, and I0 is the *initial intensity
Concentration form: c = A / (εb)
Rearranged to solve for concentration directly
Each of these forms is correct and can be derived from the others. The choice of which to use depends on the specific problem at hand and the available data.
How to calculate molar absorptivity?
Molar absorptivity (ε) is a fundamental property of a substance that indicates how strongly it absorbs light at a given wavelength.
To calculate molar absorptivity:
Prepare solutions of known concentrations of the substance.
Measure the absorbance of each solution at the desired wavelength.
Plot absorbance vs. concentration to create a calibration curve.
Calculate the slope of this line, which represents ε * b.
Divide the slope by the path length (b) to obtain ε.
Let’s calculate the molar absorptivity of a dye:
Prepare solutions with concentrations: 1 × 10^-5, 2 × 10^-5, 3 × 10^-5, and 4 × 10^-5 mol L^-1
Measure absorbances: 0.202, 0.404, 0.606, and 0.808 respectively
Plot these points and calculate the slope: 20,200 L mol^-1
If the path length was 1 cm, then ε = 20,200 L mol^-1 cm^-1
This method allows for accurate determination of molar absorptivity, which is crucial for applying the Beer-Lambert law in quantitative analysis.
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