Name: absorbance spectra and beer-lambert analysis
Uploaded: 2020-03-26T07:22:26.000Z
Duration: 2 min 53 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.E

Beer's Law

Many chemical reactions progress in two directions, forward and reverse. Over time, the forward and reverse reactions will occur at the same rate, and the concentration of the reactants and products will no longer change. This is known as chemical equilibrium.
At chemical equilibrium, the concentrations of each component are related to each other by the equilibrium constant, K, which is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.
But how do you determine equilibrium concentrations? One method measures the intensity of a wavelength of light that the product absorbs before and after it passes through a sample. The intensity difference is called absorbance, and it corresponds to the amount of the absorbing compound in the sample.
You might remember that electrons mostly occupy the ground state. When they absorb a certain amount of energy, they are excited to a higher energy level. That energy corresponds to a specific wavelength of light. You can find this wavelength and measure absorbance with a spectrophotometer, which directs a beam of light through the sample and measures the change in intensity at one or more wavelengths.
The absorbance is equal to the negative log of the intensity of the attenuated light over the intensity of the incident light. By plotting the absorbance values of multiple solutions with different known product concentrations, we observe a linear relationship between absorbance and concentration. This is an example of Beer&#39;s Law.
Beer&#39;s Law is expressed mathematically by this equation, where A is the absorbance, epsilon is the molar attenuation coefficient, a constant that varies for each compound, l is the path length of light through the sample, and c is the concentration of the compound.
By identifying the linear function for a given compound at a specific wavelength and path length, you can use the absorbance data of a solution at equilibrium to determine the product&#39;s equilibrium concentration. From there, you can calculate the equilibrium concentrations of the reactants and solve for the equilibrium constant. In this lab, you will prepare solutions of iron(III) isothiocyanate and use a spectrophotometer to determine its absorbance at various concentrations.

beer's law

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range of wavelengths of light, each one interacting with the molecules or atoms differently. A substance may absorb a specific range of wavelengths, reflect another range of wavelengths, and transmit the other wavelengths of light.
When a molecule absorbs light, the energy is used in four different ways: (1) translation, which causes the molecule to change its molecular velocity; (2) vibration, which causes the distance between the molecules to change rapidly; (3) rotation, which causes the atoms to rotate around the bonds in a molecule; and (4) electron excitement, which causes electrons to transition to higher energy levels.
<h4>Energy Levels</h4>
In 1913, Niels Bohr proposed a model for the hydrogen atom in which electrons travel around the nucleus in fixed, circular orbits, called stationary states. The energy associated with each orbit, or stationary state, exists only at fixed, discrete energies. Only when an electron moves to another orbit is energy absorbed or emitted. The electron is never in-between states. This change only occurs if the absorbed or emitted energy equals the difference between the two energy states.
In Bohr&#8217;s model, the quantum number n represents the electron&#8217;s energy. When an electron occupies the lowest possible energy state, it is said to occupy the ground state, which is n = 1. When an electron absorbs a photon, whose energy equals the difference between the first and second states, the electron becomes excited and transitions from the ground state to the excited state, where n = 2. If the energy of the photon equals the difference between the first and third states, the electron transitions to the third state, or n = 3, and so on.
Electrons can spontaneously return to the ground state or any other lower, excited state. When this happens, the excess energy that was gained from excitation is released in the form of an emitted photon. The energy of the photon is equal to the difference between the two energy states and corresponds to different wavelengths of light.
<h4>Absorption and Emission Spectra</h4>
While most substances absorb or emit the maximum amount of light at one wavelength, they also tend to absorb or emit light at a range of wavelengths. This range of wavelengths is called a spectrum. The energy of the absorbed light is quantified and visualized using an absorption spectrum, while the energy of the emitted light is quantified and visualized using an emission spectrum.
Absorption and emission spectra are measured using a spectrophotometer, which is a device that transmits light through a sample and then measures both the wavelength and intensity of light that passes through it. Inside the spectrophotometer is either a diffraction grating or a prism, which separates incoming light into its component wavelengths. The different wavelengths are then transmitted through the sample, and the intensity is recorded on a linear charge-coupled device (CCD) detector. The CCD is an integrated circuit etched onto a silicon surface that forms light-sensitive elements called pixels. The CCD collects and sorts the diffracted light and reads it back at an absorption wavelength.
When measuring the absorbance of a sample, the solute is usually dissolved in a solvent and placed in a container known as a cuvette. Then, the sample is placed inside the spectrophotometer, and the intensity of the transmitted light is measured along with the wavelengths of light to obtain an absorbance spectra. As expected, the intensity of the transmitted light is lower than when there is no sample present inside the spectrophotometer.
This is because the transmitted light is absorbed by the sample, the cuvette, and the solvent. Before measuring samples, the spectrophotometer must be calibrated with a &#8216;blank&#8217;. A blank is a cuvette that only contains the solvent that is used to dissolve the solute. The spectrophotometer is calibrated so that the total absorbance due to the cuvette and solvent is subtracted from the sample&#8217;s measured absorbance. This allows us to record the absorbance that is only attributed to the species of interest.
The absorbance is often measured at one wavelength, the maximum absorbance wavelength. However, the absorption can also be measured at a range of wavelengths to acquire the absorption spectrum. For this, the sample is exposed to a range of wavelengths of incident light, and the absorption is recorded at each wavelength. If the sample emits light, the emission spectrum is measured similarly, except the incident wavelength is fixed at the wavelength of maximum absorbance. The instrument then measures the intensity of emitted light over a range of wavelengths.
<h4>Beer-Lambert Law</h4>
The absorbance of a sample at the wavelength of maximum absorbance provides information about the sample, namely its concentration. The Beer-Lambert Law is an equation that relates transmittance to sample concentration. The transmittance, or intensity of transmitted light, is the fraction of original light that passes through the sample, I, divided by the intensity of the incident light, I0.
<img src="/CDNSource/lm/labs/49/49_Concepts_1.jpg" alt="Transmittance equation \(T = \frac{I}{I_0}\), diagram for optical density analysis." data-altupdatedat="1754904545000" data-alt="Transmission equation \( T = \frac{I}{I_0} \); optical absorption analysis." />
The Beer-Lambert Law states that the optical absorbance, A, of a species in solution is related to the negative log of the transmittance.
<img src="/CDNSource/lm/labs/49/49_Concepts_2.jpg" alt="Absorbance formula A=-log(T), equation for optical absorption analysis in spectroscopy studies." data-altupdatedat="1754904545000" data-alt="Absorbance equation A=-log(T), key concept in spectroscopy and optical analysis." />
An alternative version of the Beer-Lambert Law states that the optical absorbance, A, of a species in solution is linearly proportional to the concentration, c, of that species when the wavelength, &#955;, and pathlength, l, are held constant.
<img src="/CDNSource/lm/labs/49/49_Concepts_3.jpg" alt="Beer-Lambert Law equation, A=&#949;cl, absorption concept, spectroscopic data analysis, physics diagram." data-altupdatedat="1754904545000" data-alt="Beer-Lambert law equation \(A=\varepsilon c l\), absorption spectroscopy analysis." />
The molar attenuation coefficient, &#949;, is a measure of how strongly a species absorbs light at a given wavelength. The greater the molar attenuation coefficient, the greater the absorbance. The pathlength, l, is the distance that the light travels through the sample, which is the width of the cuvette. Standard cuvettes have a pathlength of 1 cm.
This linear relationship between absorbance and concentration is a powerful tool that is used to determine the concentration of an unknown sample based on its absorbance. To do this, a standard curve is generated using a gradient of known concentrations of the solute. The absorbance at the peak absorbance wavelength, &#955;max, is measured for each concentration.
By plotting concentration versus absorbance, a linear relationship is observed that corresponds to the Beer-Lambert equation. The slope of this line is equal to the product of the pathlength and the molar attenuation coefficient. Using this calculated linear function, if the absorbance of the unknown sample is known, the concentration can easily be determined.
If the sample being analyzed is a reaction at equilibrium, Beer&#8217;s Law can be used to determine the equilibrium concentration of a product or reactant if the absorbance is measured at &#955;max specific to that product or reactant. Once the concentration is known, you can determine the equilibrium concentrations of the remaining reactants and products and then solve for the equilibrium constant Keq.
<h4>References</h4>
<ol>
	<li style="font-size:17px">Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). Chemistry and Chemical Reactivity. Belmont, CA: Brooks/Cole, Cengage Learning.</li>
	<li style="font-size:17px">Silderberg, M.S. (2009). Chemistry: The Molecular Nature of Matter and Change. Boston, MA: McGraw Hill, Boston.</li>
	<li style="font-size:17px">Harris, D.C. (2015). Quantitative Chemical Analysis. New York, NY: W.H. Freeman and Company.</li>
</ol>

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range ...

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absorbance spectra and beer-lambert analysis

Absorbance spectra and the Beer-Lambert Law show how light can be used to study molecules in solution. When light hits a substance, it may be absorbed, transmitted, or reflected. A substance often interacts with a range of wavelengths, and each wavelength can affect the molecules or atoms in a different way.

When a molecule absorbs light, that energy can be used for translation, vibration, rotation, or electron excitement. Electron excitement is especially important in spectroscopy because it moves an electron to a higher energy level. In Niels Bohr’s model, electrons in the hydrogen atom move in fixed circular orbits called stationary states, and each state has a discrete energy. An electron can move only when it absorbs or emits energy equal to the difference between two states.

The lowest energy state is the ground state, or n = 1. If a photon has the right energy, the electron can move to a higher state such as n = 2 or n = 3. When the electron returns to a lower state, it releases the extra energy as an emitted photon. The photon energy matches the energy gap between the two states and corresponds to specific wavelengths of light.

Most substances absorb or emit most strongly at one wavelength, but they usually interact with a range of wavelengths. That range is called a spectrum. An absorption spectrum shows how much light a sample absorbs at different wavelengths, and an emission spectrum shows the light a sample gives off. These spectra are measured with a spectrophotometer, which sends light through a sample and records the wavelength and intensity of the light that passes through.

Inside the spectrophotometer, a diffraction grating or a prism separates incoming light into its component wavelengths. The light then passes through the sample, and a linear charge-coupled device, or CCD, detector records the intensity. A CCD is an integrated circuit on silicon that contains light-sensitive pixels. It collects and sorts the diffracted light and reads it back at an absorption wavelength.

For absorbance measurements, the solute is usually dissolved in a solvent and placed in a cuvette, which is the container used in the instrument. The sample is then placed in the spectrophotometer, and the intensity of transmitted light is measured along with wavelength to produce an absorbance spectrum. The transmitted light is lower than when no sample is present because light is absorbed by the sample, the cuvette, and the solvent. Before samples are measured, the spectrophotometer is calibrated with a blank, which is a cuvette that contains only the solvent. This step removes the absorbance from the cuvette and solvent so the reading reflects only the species of interest.

Absorbance is often measured at the wavelength of maximum absorbance, but it can also be recorded across a range of wavelengths. For emission spectra, the incident wavelength is fixed at the wavelength of maximum absorbance, and the instrument measures emitted light over a range of wavelengths. The Beer-Lambert Law then connects absorbance to sample concentration. Transmittance is the fraction of light that passes through the sample, I divided by I0, and absorbance is related to the negative log of transmittance.

A second form of the Beer-Lambert Law shows that absorbance is directly proportional to concentration when wavelength and pathlength stay constant. The molar attenuation coefficient, ε, describes how strongly a species absorbs light at a given wavelength. The pathlength, l, is the distance the light travels through the sample, which is the width of the cuvette. Standard cuvettes have a 1 cm pathlength. This linear relationship makes it possible to find the concentration of an unknown sample from its absorbance.

To do that, a standard curve is made with known concentrations of the solute. The absorbance at λ max is measured for each standard, and the results are plotted as concentration versus absorbance. The line that appears matches the Beer-Lambert equation, and its slope equals the product of the pathlength and the molar attenuation coefficient. Once that line is known, the concentration of an unknown sample can be calculated from its absorbance.

Beer’s Law can also be used for reactions at equilibrium. If absorbance is measured at the λ max of a specific product or reactant, the equilibrium concentration of that species can be found. The concentrations of the other reactants and products can then be determined, and the equilibrium constant K eq can be solved.

Absorbance Spectra and Beer-Lambert Analysis

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To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Dr&#xFC;de called the ...

Model basic atomic structure and relate an element's atomic structure to its bonding, reactivity, and placement on the Periodic Table.

IPC.7.A

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

Use patterns within the Periodic Table to predict the relative physical and chemical properties of elements.

IPC.7.B

Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Absorbance Spectra and Beer-Lambert Analysis

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