# Calculate Transmission & Concentration Using Beer-Lambert Law

• nordmoon
In summary, the Beer-Lambert law states that the ratio of transmitted light to incident light is equal to the exponential of the product of the absorption coefficient and the path length. However, when using a broadband light source, the absorption coefficient is wavelength dependent, making it difficult to determine the concentration of the species being investigated. This is because the detector measures a summation of the individual wavelengths within the passband, each with its own extinction coefficient. Therefore, to extract concentration information, the density and cross section of the materials used must be taken into account, as they are not wavelength dependent.
nordmoon
Let say that you use a LED and direct it through a gas. You measure the 'light' transmitted through the gas and the 'light' entering the gas to obtain the transmission.

Since the Beer–Lambert law is wavelength dependent and the LED is broadband within the region of a for example C02 band, how can you determine the transmission of this wavelength integrated light with the ultimute goal of determine the concentration of the species investigated? Beer–Lambert law states that

I/I0 = exp(kv*l) = exp(sigma*N*l)where kv (absorption coefficient) is wavelength dependent. You have calculated kv per wavelength, but since the light measured is broadband how can you 'simulate' the transmission with known kv? Sigma is the absorption cross section.

I guess the problem is that the light 'contains many wavelength (and not just one)' and that the Beer law is for one wavelength since the absorption coefficient is wavelength dependent. So how can you extract the concentration information in such arrangement? The detector sees a passband of wavelengths and each wavelength has its own extinction coefficient. Thismeans that the detector sees a summation of the effect of each individual wavelength within the passband.

I hope I made any sense.

Last edited:
Hi,
concentration information can be obtained from the density and cross section [of the materials used]..these are not wavelength dependent.

Thank you for your question. The Beer-Lambert law is indeed wavelength dependent, and in order to accurately determine the transmission and concentration of a gas using this law, we need to take into account the broadband nature of the LED light source.

One approach to solving this problem would be to use a spectrometer to measure the intensity of light at different wavelengths within the LED's emission spectrum. This would allow us to obtain a more accurate absorption coefficient (kv) for each individual wavelength. We could then use this information to calculate the overall transmission of the LED light through the gas by integrating the contributions from each individual wavelength.

However, this method may not be practical or feasible in some cases. Another approach would be to use a reference gas with a known concentration of the species being investigated, and measure the transmission of the LED light through this reference gas. This would provide us with a baseline for the transmission of the LED light through the gas, and we could then use this information to calculate the concentration of the species in the unknown gas sample.

In summary, the key to accurately determining the concentration of a species using the Beer-Lambert law in this setup is to take into account the broadband nature of the LED light source and to either use a spectrometer or a reference gas to obtain a more accurate absorption coefficient. I hope this helps clarify the issue. Thank you.

## 1. What is the Beer-Lambert Law?

The Beer-Lambert Law, also known as the Beer-Lambert-Bouguer Law, is a mathematical equation that relates the concentration of a chemical solution to the amount of light absorbed by the solution. It states that the absorbance of light is directly proportional to the concentration and path length of the solution.

## 2. How is concentration calculated using the Beer-Lambert Law?

The concentration of a solution can be calculated using the Beer-Lambert Law by measuring the absorbance of the solution at a specific wavelength and using the known molar absorptivity coefficient and path length. The equation is C = A/εl, where C is the concentration, A is the absorbance, ε is the molar absorptivity coefficient, and l is the path length in centimeters.

## 3. What is the relationship between absorbance and concentration in the Beer-Lambert Law?

The Beer-Lambert Law states that the absorbance of a solution is directly proportional to the concentration of the solution. This means that as the concentration increases, so does the absorbance, and vice versa. This relationship is linear, meaning that a doubling of concentration will result in a doubling of absorbance.

## 4. Can the Beer-Lambert Law be used for all types of solutions?

The Beer-Lambert Law is typically used for dilute solutions, where the concentration is less than 0.01 M. For concentrated solutions or solutions with strong interactions between molecules, the law may not be accurate. Additionally, the law assumes that the path length is constant and that the solution is homogeneous, which may not always be the case.

## 5. How can the Beer-Lambert Law be applied in real-world situations?

The Beer-Lambert Law is widely used in spectrophotometry to determine the concentration of unknown solutions. It is also used in various industries, such as pharmaceuticals, environmental monitoring, and food and beverage production, to measure the concentration of substances in solutions. Additionally, the law can be used in research to study the kinetics of chemical reactions and to monitor the progress of reactions over time.

• Chemistry
Replies
5
Views
2K
• Chemistry
Replies
7
Views
2K
• Atomic and Condensed Matter
Replies
2
Views
3K
• Other Physics Topics
Replies
3
Views
846
• Introductory Physics Homework Help
Replies
10
Views
5K
• Optics
Replies
1
Views
1K
• Thermodynamics
Replies
152
Views
6K
• Optics
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K