AP Chemistry 3.13 Beer-Lambert Law Study Notes - New Syllabus Effective fall 2024
AP Chemistry 3.13 Beer-Lambert Law Study Notes- New syllabus
AP Chemistry 3.13 Beer-Lambert Law Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.
LEARNING OBJECTIVE
Explain the amount of light absorbed by a solution of molecules or ions in relationship to the concentration, path length, and molar absorptivity.
Key Concepts:
- Beer-Lambert Law
3.13.A.1 The Beer-Lambert Law: A = εbc:
1. A = εbc:
i. Absorbance (A): This is a measure of how much light the solution absorbs. Absorbance doesn’t have units since it is the logarithmic scale of light intensity.
ii. Molar Absorptivity (ε):
It’s also known as the molar absorption coefficient. It’s the measure of how much a substance absorbs light at a certain wavelength. It’s a specific value for every chemical species and depends on the wavelength of light. Units are typically L·mol⁻¹·cm⁻¹. The greater ε is, the better it absorbs light at that wavelength.
iii. Path Length (b):
This is the distance that the light travels through the solution, usually measured in centimeters (cm). As long as the light passes through a thicker or longer path, then it will have more opportunity to interact with the absorbing species, and the absorbance will be higher.
iv. Concentration (c):
This is the concentration of the absorbing species in the solution. The higher the concentration, the more particles there are to absorb light, and thus the higher the absorbance.
How It Works:
When light travels through a solution, some of the light is absorbed by the chemical species in the solution. The amount of absorption depends on:
How strongly the species absorbs light (ε).
Amount of solution light has to travel through (b).
Number of absorbing species that exist (c).
Thus, in the Beer-Lambert law, absorption is directly proportional to the concentration and path length. For example, absorbance increases with a rise in either the concentration of the absorbed substance or path length. Conversely, with a fall in any value, absorption lowers.
Example:
If you have a solution of a dye, it can calculate how much light a dye absorbs (absorbance, A) using the Beer-Lambert law: the more a dye absorbs at a certain wave length (ε), how thick the solution is (b), and how much dye is in the solution (c).
This law is applied in spectroscopy. For example, you can determine the concentration of a substance in a solution using absorbance measurements.
2. Used in spectroscopy:
Here is how it takes place in any typical spectroscopy experiment:
a. Light Source: This is a source of light applied through the analyte-containing solution.
b. Wavelength selection: the light passed or filtered is such that its wavelength corresponds to which the solution will absorb strongly, this because a given solution will absorb the wavelength of the different wavelengths
c. Measure Absorbance: how much the solution absorbed that particular amount of light-its absorbance or A.
d. Beer-Lambert’s Law: One can determine concentration c of substance if the suitable measured absorbance A, and known molar absorptivity ε for this substance at specified wavelength and also path length b are available
Formula Summary :
Where:
- A is the absorbance (measured by the spectrometer),
- ε is the molar absorptivity (a constant specific to the substance and wavelength),
- b is the path length (how far the light travels through the sample),
- c is the concentration of the substance.
By rearranging the equation, you can solve for c (concentration):
3. Limitations:
i. Non-linear Behavior at High Concentrations:
At high concentrations, the Beer-Lambert law no longer applies since absorbance is no longer linear with concentration. This is due to molecular interactions wherein the solute molecules interact with each other. At high concentrations, this light would scatter or absorb light in a way that is not directly proportional to concentration.
Explanation: Too much concentration results in a so thick solution where light is badly scattered or even absorbed in manner complicated that laws of reflection will fail to work.
ii. Deviation from Ideal Behaviour :
The Beer-Lambert law assumes that the solution is homogeneous and that the solute molecules do not interact with each other in ways that affect absorption. However, at high concentrations, solute-solute interactions (like aggregation, dimerization, or changes in the molecular environment) can occur, leading to deviations.
iii. Limited Range of Path Length (b):
The law assumes the light path length is constant. In practice, if the solution is too concentrated or the path length is too long, too much light will be absorbed or scattered, so the spectrometer may not measure the absorbance accurately. This can cause errors.
iv. Stray Light and Instrumental Limitations:
At very high absorbances, other factors, such as stray light, come into play; this is light that is not transmitted through the sample but does reach the detector. Such an effect is insignificant at low concentrations, where the absorbance falls within the range of typical linearity.
v. Wavelength Dependence:
It works best at low concentrations where the sample is absorbing light at a specific wavelength, or at least within a very narrow range of wavelengths. The absorption will shift or broaden at higher concentrations and thus deviate from ideal behavior.
Why It Works Best at Low Concentrations:
In low concentration, the interaction between the molecules in the solution is minimal; hence, the absorption of light is directly proportional to concentration.
The path length and molar absorptivity values are also more valid in this range because the solution is optically clear, without significant scattering or complex absorption effects.
Solutions to the Problem:
Samples are diluted to bring the concentration into the linear range of the Beer-Lambert law where the relationship between absorbance and concentration is highly accurate to surmount the limitation at high concentrations.
In practical terms, if a solution’s absorbance is too high, it might be necessary to reduce the concentration of the sample or to use a shorter path length in order to keep the measurement within a linear range.
3.13.A.2 Absorbance Proportional to Concentration at Optimum Wavelength:
1. Constant Path Length & Wavelength:
i. Constant Path Length (b):
a. Why it matters: The Beer-Lambert law indicates that the absorbance (A) is directly proportional to the path length (b). As the path length varies, then the amount of light absorbed does too, leading to errors in your concentration calculation.
b. In application:
When working with a spectrophotometer, the path length of the cuvette is set to a given distance, usually 1 cm. If the path length of your cuvette is some other distance (0.5 cm or 2 cm for instance), you have to factor that into your calculation, or your result may be wrong.
If comparing multiple samples, the same path length ensures each sample absorbs light in the same way, allowing your measurements to be consistent.
c. Constant Wavelength (λ):
Why it matters: Each substance absorbs light at unique wavelengths. Molar absorptivity (ε) is both substance and wavelength dependent. In other words, if the wavelength changes, so may the molar absorptivity of the substance, thus the concentration calculations may be inaccurate.
In practice
Selection of the correct wavelength: To achieve the best possible outcome, you will want to choose a wavelength at which the substance has a high absorption peak, known as its λ max. If you are measuring at a wavelength outside of this peak, absorbance could be too low, and you may not obtain a reliable measure of concentration.
Consistency across measurements: If you’re trying to compare several samples or replicate measurements, you must make sure that the same wavelength is used for all. If you vary the wavelength, then you could change the absorptivity values, making it difficult to compare absorbance directly.
Why This Matters:
a. Unambiguous Concentration Measurement: Since the path length, as well as the wavelength, is held constant, variations in absorbance are dependent on variations in the concentration of the species responsible for absorption and nothing else.
b. Less Error: Variations in either of these parameters can lead to some error in absorbance and give less reliable determinations about concentrations.
c. Replicates in Experiment: When you carry out more than one experiment or you compare different samples, constancy in both variables ensures that you are measuring absorbance under the same conditions each time, which is very fundamental to good conclusions.
2. Absorbance = Concentration:
Why Absorbance and Concentration Are Directly Proportional:
The Beer-Lambert law states that the relationship between absorbance and concentration is expressed as:
Where:
- A is absorbance.
- ε is the molar absorptivity (a constant that depends on the substance and the wavelength of light).
- b is the path length (how far light travels through the solution).
- c is the concentration of the absorbing species.
At constant ε and b, the equation simplifies to:
This means that, as the concentration of the absorbing substance increases, the absorbance increases proportionally, and vice versa.
Important Points Regarding This Relationship:
i. Proportionality:
If you double the concentration of the absorbing substance keeping everything else constant (same path length, same wavelength), then the absorbance will also double.
It makes the Beer-Lambert law a good law to find the unknown concentration of a substance through its absorbance value measurement.
ii. Linear Range:
In other words, this direct proportionality exists until a certain concentration value. If the concentration level is too high, then it may follow a nonlinear pattern because the absorption sites may reach saturation or scattering may take place, as mentioned before.
iii. Constant Conditions:
For the direct relationship to be valid, experimental conditions need to be consistent:
Path length (b) should be the same.
Wavelength for measuring should be selected at a point where the substance absorbs light appropriately.
Other environmental factors like temperature should be kept constant, as this avoids the introduction of other variables which may influence the absorbance.
3. Optimum Wavelength:
What is the Optimum Wavelength?
The optimum wavelength would be the wavelength at which the substance of interest would absorb light most efficiently. This usually comes from the absorption spectrum of the substance being considered. In this wavelength, the maximum molar absorptivity (ε) is achieved, and at this point, the substance absorbs light strongly, which makes the sensitivity and accuracy of the measurement high.
Why is the Optimum Wavelength Important?
a. Maximize Absorbance:
The optimum wavelength is defined as the wavelength for which the absorption band is at its peak. This means that the substance is absorbing the maximum possible amount of light, so the signal would be much stronger, that is, higher absorbance and, therefore, the concentration measurement will be more accurate and reliable.
– If the wavelength is one at which the substance absorbs to a lesser degree, the danger is that it will result in very low reading for absorbance, and accurate concentration would not be easily achievable.
b. Improves Sensitivity:
This ability to detect even slight changes in the concentration of the substance is called sensitivity. This is because even slight differences in concentration will yield observable changes in absorbance at the optimum wavelength.
For example, if the substance has a sharp, well-defined peak in its absorption spectrum, selecting that peak ensures that the instrument is sensitive enough to detect very small quantities of the substance, making the measurement sensitive.
c. Reduces Interference:
If there are other substances present that have absorption properties in the solution, selecting an appropriate wavelength for the analyte reduces interference. Ideally you want to choose a wavelength where substance of interest absorbs very high but other substances are not absorbing much. That way, you get a clean, specific signal.
If you choose a wavelength where other parts of your sample absorb light like your analyte does, you might get overlapping bands and distortion of your measurements.
d. Accuracy Guaranteed:
You get the highest accuracy for the determination of concentrations by choosing the best wavelength since **ε** is at its maximum, and the relationship between the absorbance and concentration becomes most reliable.
While measuring at a wavelength far from the absorption peak is not within the limits where ε is low, even tiny changes in concentration could lead to smaller changes in absorbance and thereby lower the accuracy of your measurements.
How to Choose the Optimum Wavelength?
Absorption Spectrum :
You can obtain an absorption spectrum for the compound by measuring absorbance over a range of wavelengths. The optimal wavelength is generally the one where the absorbance is highest, often called the λ max for that compound.
For instance, when measuring a dye in solution, the absorption spectrum might show a peak that is at or around 450 nm. That would be the optimum wavelength to use for the most accurate and sensitive measurements.
Calibration Curve:
You may plot a calibration curve by using a known series of standards-a set of solutions with known concentrations-and plotting absorbance against concentration. The best linearity of absorbance versus concentration is obtained at the point where you’ll get your optimum wavelength, generally at the maximum absorbance of the substance.
Beer-Lambert Law (OLD Content)
- The Beer-Lambert law relates the absorption of light by a solution to three variables according to the equation
- We can determine the concentration (molarity) of a sample by looking at the absorbance
Factors Affecting Calculations
- Dilution (left water)→ measured absorbance is too low
- Dirtiness (Ex: left fingerprints) or path of light is obstructed (ex: frosted wall)→ less light would pass thru solution and be detected = more light absorbed