Question

What are beer lambert equations?
List all of them correctly

Answer 1

The Beer-Lambert law, which describes the relationship between the absorbance of light by a medium and the properties of that medium, is commonly expressed in various forms. Here are the key equations related to the Beer-Lambert law:

1. **Beer-Lambert Law Equation**:
\[
A = \varepsilon \cdot c \cdot l
\]
Where:
- \( A \) = Absorbance (dimensionless)
- \( \varepsilon \) = Molar absorptivity (or molar extinction coefficient) (L·mol\(^{-1}\)·cm\(^{-1}\))
- \( c \) = Concentration of the absorbing species (mol·L\(^{-1}\))
- \( l \) = Path length of the sample (cm)

2. **Transmittance Relation**:
\[
T = \frac{I}{I_0}
\]
Where:
- \( T \) = Transmittance (dimensionless, ranging from 0 to 1)
- \( I \) = Intensity of transmitted light
- \( I_0 \) = Intensity of incident light

3. **Relationship between Absorbance and Transmittance**:
\[
A = -\log_{10}(T) = -\log_{10}\left(\frac{I}{I_0}\right)
\]
This shows how absorbance is related to the logarithm of the transmittance.

4. **Exponential Form**:
\[
I = I_0 e^{-\alpha l}
\]
Where:
- \( I \) = Intensity of transmitted light
- \( I_0 \) = Intensity of incident light
- \( \alpha \) = Absorption coefficient (cm\(^{-1}\))
- \( l \) = Path length of the sample (cm)

5. **Combining with Concentration**:
If \( \alpha \) is expressed in terms of molar absorptivity \( \varepsilon \) and concentration \( c \):
\[
\alpha = \varepsilon c
\]
Thus, the equation can also be expressed in a form dependent on concentration:
\[
I = I_0 e^{-\varepsilon c l}
\]

These equations are used widely in analytical chemistry and physics to quantify how much light is absorbed by a solution, which can help in determining concentration and other properties of the absorbing species.