Gavin Howe
The Beer-Lambert Law states that absorbance is directly proportional to the concentration, path length, and intensity of incident light. However, deviations from this law can occur in various forms. These include true deviations due to high analyte concentrations, instrumental deviations caused by factors like stray light and the use of polychromatic light, and chemical deviations due to shifts in chemical equilibria. The linear relationship between absorbance and concentration described by Beer's Law is only valid under certain conditions, and when these conditions are not met, deviations can occur.
| Characteristics | Values |
|---|---|
| True deviations | High analyte concentrations that cause interactions between molecules and changes in optical properties |
| Instrumental deviations | Use of polychromatic light, improper slit width, stray light, mismatched cells, scanning speed, and low-quality instruments |
| Chemical deviations | Shifts in chemical equilibria with changing concentration, like for pH indicators |
| Causes of limitations | Stray light, non-polychromatic radiation, unequal light path lengths, unequal absorber concentration, changes in refractive index of the solution, light scattering by the sample matrix |
| Other causes | High and low analyte concentrations, solvent effects, light source imperfections, dynamic equilibria of absorbing species |
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What You'll Learn
High analyte concentrations
Beer's Law, also known as Beer-Lambert Law, states that there is a linear relationship between absorbance and concentration of an analyte. In other words, a plot of absorbance vs concentration should be a straight line with a y-intercept of zero.
However, at high analyte concentrations, Beer's Law may not hold true and deviations can occur. This is because, at higher concentrations, the individual particles of analyte are no longer independent of each other, and interactions between particles of analyte may change the analyte's absorptivity. This results in a deviation from linearity, which is observed as a nonlinear Beer's law plot.
This deviation is further influenced by the nature of the analyte and the radiation used. For instance, if the analyte is involved in an equilibrium reaction, the Beer's law plot may deviate from linearity. Additionally, if the radiation used is not monochromatic, Beer's law may not be strictly obeyed and deviations can occur.
To minimize these deviations, it is important to optimize factors such as concentration, slit width, and wavelength range used. Diluting the sample can also help bring the absorbance value into the linear portion of the curve, ensuring that the curve remains linear over the concentration region of interest.
Furthermore, when using UV-Vis spectroscopy, it is important to consider the solvent effects, as solvents can alter absorption wavelengths and intensities, leading to deviations from Beer's law.
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Instrumental factors
One of the key factors is the use of polychromatic light. Beer's Law assumes the use of monochromatic light, but real-world light sources often have small bandwidths, leading to polychromatic effects. This can cause absorbance to vary not just with concentration but also with wavelength, especially across a broad absorption peak. The use of a suitable monochromator can help mitigate this issue by allowing only a narrow range of wavelengths to pass through the sample. The range of wavelengths passed by the monochromator depends on its slit width, which should ideally be at least one-tenth of the natural bandwidth of the analyte.
Stray radiation is another significant instrumental factor. This occurs when imperfections in the wavelength selector allow light to bypass the sample and reach the detector directly. At higher concentrations of analyte, this can result in an absorbance that is smaller than expected, causing a negative deviation from Beer's Law.
Other instrumental factors include unequal light path lengths, unequal absorber concentration across the light beam, scanning speed, and light-scattering by the sample matrix, especially in turbid samples. Additionally, low-quality instruments, especially when operated near their wavelength limits, can exacerbate non-linearity at high absorbances.
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Chemical equilibria shifts
Beer's Law, also known as Beer-Lambert Law, states that absorbance is directly proportional to concentration, path length, and intensity of incident light. However, there are certain limitations to this law, and deviations can occur under certain conditions.
One such deviation is due to chemical equilibria shifts. This occurs when the analyte is involved in an equilibrium reaction. For instance, consider the weak acid, HA, which is in equilibrium with its conjugate weak base, A–. If both HA and A– absorb at the selected wavelength, Beer's law is:
> A=ε_HA*b*CHA+ε_A*b*CA
Since HA is a weak acid, the value of α_HA varies with pH. To maintain a constant α_HA, each standard solution must be buffered to the same pH. If the standards are not buffered, the calibration curve will deviate from Beer's law due to the relative values of α_HA and α_A.
Chemical deviations from Beer's law can also occur due to changes in solvent effects. Solvents can alter absorption wavelengths and intensities, leading to deviations from the expected linear relationship between absorbance and concentration. Common solvents used in UV-visible spectroscopy include ethanol, hexane, and water. Solvent effects can result in bathochromic shifts, hypsochromic shifts, hyperchromic shifts, and hypochromic shifts, all of which can impact the accuracy of UV-visible spectroscopy measurements.
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Non-linearity
Firstly, non-linearity can be caused by high concentrations of the analyte. At higher concentrations, individual particles of the analyte are no longer independent of each other, and interactions between particles may alter the analyte's absorptivity. This leads to deviations from the expected linear relationship between absorbance and concentration.
Secondly, non-linearity can be caused by the use of polychromatic light. In ideal conditions, monochromatic light is used, but in reality, light sources often have small bandwidths that lead to polychromatic effects. This causes absorbance to vary not just with concentration but also with wavelength, resulting in non-linear plots.
Thirdly, non-linearity can be caused by stray radiation, which is light that reaches the detector without passing through the sample. At low analyte concentrations, stray radiation has a negligible effect. However, at higher concentrations, less light passes through the sample, and the contribution of stray radiation becomes significant, leading to a smaller absorbance than expected and a negative deviation from Beer's Law.
Additionally, non-linearity can be caused by other factors such as improper slit width, mismatched cells, scanning speed, and changes in chemical equilibria with changing concentration. These factors can influence the interaction between light and the analyte, resulting in deviations from the expected linear relationship.
To minimize non-linearity, it is important to optimize factors such as concentration, slit width, and wavelength range. By carefully controlling these variables, the deviation from linearity can be reduced, improving the accuracy of measurements and analyses.
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Stray radiation
> A=-log((P_T+P_stray)/(P_0+P_stray))
In this equation, A represents absorbance, P_T is the radiant power transmitted, P_0 is the incident radiant power, and P_stray denotes the stray radiant power.
At low analyte concentrations, the impact of stray radiation is negligible, and the absorbance remains unaffected. However, as the concentration of the analyte increases, less light passes through the sample, leading to a decrease in P_T. Consequently, P_T and P_stray become comparable in magnitude, resulting in an absorbance that is lower than expected. This deviation from the expected absorbance value constitutes a negative deviation from Beer's Law.
To address the issue of stray radiation, it is crucial to select a suitable monochromator that permits only a narrow range of wavelengths to pass through the sample. The choice of the monochromator should be guided by the specific requirements of the analyte, with the monochromator's slit width being a critical factor in minimizing the entry of stray light.
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Frequently asked questions
There are three main types of deviations: true deviations, instrumental deviations, and chemical deviations. True deviations occur due to high analyte concentrations, which cause interactions between molecules and changes in optical properties. Instrumental deviations are caused by factors like stray radiation, the use of polychromatic light, and imperfections in the measuring instrument. Chemical deviations occur due to shifts in chemical equilibria with changing concentrations, such as in pH indicators.
At higher concentrations, individual particles of the analyte are no longer independent of each other, and interactions between them may change the analyte's absorptivity. This results in deviations from the expected linear relationship between absorbance and concentration.
When using polychromatic radiation, Beer's Law is not strictly obeyed and linearity is not observed. This is because the absorber's absorption coefficient may vary over the wavelength interval of light passing through the sample, causing absorbance to vary not just with concentration but also with wavelength.
Stray radiation arises from imperfections in the wavelength selector, allowing light to reach the detector without passing through the sample. At higher concentrations of the analyte, this results in an absorbance that is smaller than expected, leading to a negative deviation from Beer's Law.
