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

K12 Standards

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IPC.7

IPC.7.E

Beer's Law

许多化学反应具有正向和逆向两个方向。随着时间推移，正向反应和逆向反应的速率会达到相等，反应物和生成物的浓度将不再发生变化。这种状态称为化学平衡。
在化学平衡状态下，各组分的浓度通过平衡常数 K 相互关联，K 是产物浓度与反应物浓度之比，每种物质的浓度均以其化学计量系数作为指数。
但是如何确定平衡浓度呢？一种方法是测量产物在通过样品前后对特定波长光的吸收强度。吸收强度的差异称为吸光度，它对应于样品中吸收光的化合物的量。
你可能记得，电子大多处于基态。当它们吸收一定能量后，会被激发到更高的能级。这种能量对应于特定波长的光。你可以通过分光光度计找到这一波长并测量吸光度，该仪器将一束光穿过样品，并测量一个或多个波长下光强度的变化。
吸光度等于衰减后光强与入射光强比值的负对数。通过绘制不同已知产物浓度的多种溶液的吸光度值，我们可观察到吸光度与浓度之间存在线性关系。这是比尔定律的一个实例。
比尔定律用以下数学公式表示，其中 A 为吸光度，ε 为摩尔衰减系数（每种化合物特有的常数），l 为光通过样品的光程长度，c 为化合物的浓度。
通过确定特定波长和光程长度下某化合物的线性函数，可以利用平衡状态下溶液的吸光度数据来确定产物的平衡浓度。由此可进一步计算反应物的平衡浓度，并求解平衡常数。在本实验中，你将配制一系列硫氰酸铁(III)溶液，并使用分光光度计测定其在不同浓度下的吸光度。

比尔定律

吸光度与荧光
当光照射到物质上时，会被吸收、透射或反射。通常情况下，物质会与一定范围内的光波长发生相互作用，不同波长的光与分子或原子的相互作用方式各不相同。某种物质可能吸收特定波长范围的光，反射另一波长范围的光，同时透射其余波长的光。
当分子吸收光时，其能量有四种不同的去向：（1）平动，使分子改变其分子运动速度；（2）振动，使分子间距离迅速发生变化；（3）转动，使原子围绕分子中的化学键旋转；（4）电子激发，使电子跃迁至更高的能级。
<h4>能级</h4>
1913年，尼尔斯·玻尔提出了一个氢原子模型，其中电子在固定的圆形轨道（称为定态）上围绕原子核运动。每个轨道或定态所对应的能量仅以固定且离散的数值存在。只有当电子跃迁到另一个轨道时，才会吸收或释放能量。电子永远不会处于两个状态之间的中间状态。这种跃迁只有在吸收或释放的能量等于两个能级之间的能量差时才会发生。
在玻尔模型中，量子数 n 表示电子的能量。当电子处于最低可能的能量状态时，称为处于基态，即 n = 1。当电子吸收一个光子，其能量等于第一和第二能级之间的差值时，电子被激发，从基态跃迁到激发态，此时 n = 2。如果光子的能量等于第一和第三能级之间的差值，电子则跃迁到第三能级，即 n = 3，依此类推。
电子可以自发地回到基态或任何其他较低的激发态。当这种情况发生时，激发过程中获得的多余能量会以发射光子的形式释放出来。光子的能量等于这两个能级之间的能量差，并对应于不同波长的光。
<h4>吸收与发射光谱</h4>
尽管大多数物质在某一特定波长下吸收或发射的光量最大，但它们也倾向于在一系列波长范围内吸收或发射光。这一系列波长范围称为光谱。吸收光的能量通过吸收光谱进行量化和可视化，而发射光的能量则通过发射光谱进行量化和可视化。
吸收光谱和发射光谱通过分光光度计进行测量，该仪器可将光透过样品，随后测量透过光的波长和强度。分光光度计内部装有衍射光栅或棱镜，可将入射光分离为其组成波长。不同波长的光随后穿过样品，其强度被线性电荷耦合器件（CCD）检测器记录。CCD 是蚀刻在硅表面的集成电路，形成称为像素的光敏元件。CCD 收集并分类衍射光，并在特定吸收波长处读取信号。
测量样品吸光度时，通常将溶质溶解于溶剂中，并置于一种称为比色皿的容器内。随后将样品放入分光光度计中，测量透射光的强度及其光的波长，以获得吸光度光谱。正如预期，当分光光度计内放置样品时，透射光的强度低于无样品时的强度。
这是因为透射光会被样品、比色皿和溶剂吸收。在测量样品之前，必须使用“空白样”对分光光度计进行校准。空白样是指仅含有用于溶解溶质的溶剂的比色皿。通过校准，可将比色皿和溶剂所产生的总吸光度从样品测得的吸光度中扣除，从而让我们记录到仅由目标物质引起的吸光度。
通常在单一波长下测量吸光度，即最大吸收波长。然而，也可以在一系列波长下测量吸收，以获得吸收光谱。为此，将样品暴露于一系列不同波长的入射光下，并在每个波长处记录其吸收值。如果样品能够发光，则以类似方式测量发射光谱，不同之处在于入射光的波长固定在最大吸收波长处。仪器随后测量在一系列波长范围内发射光的强度。
<h4>比尔-朗伯定律</h4>
样品在最大吸收波长处的吸光度可提供有关该样品的信息，即其浓度。比尔-朗伯定律是一个将透射率与样品浓度关联起来的方程。透射率，即透射光的强度，是指通过样品的原始光的比例 I 与入射光强度 I0 的比值。
<img src="/CDNSource/lm/labs/49/49_Concepts_1.jpg" alt="透射率方程 \(T = \frac{I}{I_0}\)，光密度分析示意图。" data-altupdatedat="1754904545000" data-alt="透射方程 \( T = \frac{I}{I_0} \)；光吸收分析。" />
比尔-朗伯定律指出，溶液中某物质的光吸收度 A 与透光率的负对数相关。
<img src="/CDNSource/lm/labs/49/49_Concepts_2.jpg" alt="吸光度公式 A=-log(T)，光谱学研究中光学吸收分析的方程。" data-altupdatedat="1754904545000" data-alt="吸光度方程 A=-log(T)，光谱学与光学分析中的核心概念。" />
比尔-朗伯定律的一个替代版本指出，光吸收度， A，溶液中某物种的浓度与其呈线性正比关系， c，该物种在波长λ和光程长度 l保持不变。
<img src="/CDNSource/lm/labs/49/49_Concepts_3.jpg" alt="比尔-朗伯定律公式 A=εcl，吸收概念，光谱数据分析，物理图示。" data-altupdatedat="1754904545000" data-alt="比尔-朗伯定律公式 \(A=\varepsilon c l\)，吸收光谱分析。" />
摩尔衰减系数ε是衡量某种物质在特定波长下吸收光强度的指标。摩尔衰减系数越大，吸光度越高。光程（l）是指光通过样品所经过的距离，即比色皿的宽度。标准比色皿的光程为 1 cm。
吸光度与浓度之间的这种线性关系是一种强大的工具，可用于根据未知样品的吸光度来确定其浓度。为此，需使用已知溶质浓度梯度绘制标准曲线。对每种浓度，在其最大吸收波长 λmax 处测量吸光度。
通过绘制浓度与吸光度的关系图，可观察到符合比尔-朗伯定律的线性关系。该直线的斜率等于光程长度与摩尔衰减系数的乘积。利用此计算得到的线性函数，若已知未知样品的吸光度，则可轻松确定其浓度。
如果被分析的样品是处于平衡状态的反应，可以在该产物或反应物特有的 λmax 处测量吸光度，利用比尔定律确定该产物或反应物的平衡浓度。一旦已知浓度，即可确定其余反应物和产物的平衡浓度，进而求得平衡常数 Keq。
<h4>参考文献</h4>
<ol>
	<li style="font-size:17px">Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). 化学与化学反应性。加利福尼亚州贝尔蒙特：Brooks/Cole, Cengage Learning。</li>
	<li style="font-size:17px">Silderberg, M.S. (2009). 化学：物质的分子本质与变化。马萨诸塞州波士顿：McGraw Hill, Boston。</li>
	<li style="font-size:17px">Harris, D.C. (2015). 定量化学分析。纽约州纽约市：W.H. Freeman and Company。</li>
</ol>

吸光度与荧光  
当光照射到物质上时，可能被吸收、透射或反射。通常情况下，物质会与一定范围的……

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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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Soap Formation from Triglycerides

Triglycerides are lipids made of a glycerol backbone linked to three fatty acids. They are common in vegetable oils and animal fats. Plant lipids are the basis of vegetable oils, while animal lipids are used as lard or general sources of fats. A fatty acid has a long carbon chain, usually between 12 and 20 carbons, with a weak organic acid at one end. Some fatty acids contain double bonds. These are unsaturated fats. The double bond usually gives the chain a bent, cis shape. As a result,...

synthesis of luminol

Luminol Chemiluminescence in Forensics

Luminol chemiluminescence shows how a chemical reaction can produce light and help with blood detection. Chemical reactions may be endothermic or exothermic, depending on whether they absorb or release heat as reactants become products. The enthalpy of a reaction is the energy difference between reactants and products, or ΔH. A positive ΔH means the reaction is endothermic. A negative ΔH means it is exothermic. Many reactions do not happen in a single step. They can pass through intermediates...

esterification

Ester Formation and Everyday Fragrances

Esters are organic compounds with a carbonyl group attached to an oxygen that connects to another alkyl or aryl group. Their general formula is RCOOR'. They are often made by reacting a carboxylic acid with an alcohol in an esterification reaction. In this process, the hydroxyl group of the acid is replaced by an alkyl or aryl group. Many simple esters have familiar fruit and flower smells because their structures are small and less complex. Formic acid and methanol can combine to form methyl...

identification of unknown aldehydes and ketones

identification-of-unknown-aldehydes-and-ketones

Carbonyl Tests for Aldehydes and Ketones

Aldehydes and ketones are carbonyl compounds, which means they contain a C=O functional group. A ketone has two alkyl or aryl groups attached to the carbonyl carbon. Acetone is the simplest ketone, with two methyl groups. An aldehyde is similar, but it has at least one hydrogen attached to the carbonyl carbon. Formaldehyde is the simplest aldehyde, and acetaldehyde has one hydrogen and one methyl group. The carbonyl carbon in both aldehydes and ketones is electrophilic because the oxygen atom...

uv-vis spectroscopy of dyes

How Dyes Absorb Visible Light

Dyes absorb visible light because their molecular structure lets them interact with specific wavelengths. When light hits a substance, some light is absorbed and the rest is reflected or transmitted. The color we see depends on the wavelength that is reflected. A blue substance reflects blue light, around 430 to 480 nm, and absorbs the complementary orange region, around 590 to 630 nm. Compounds that do not absorb in the visible range appear colorless to the human eye. Light also has energy and...

identifying alcohols

Alcohol Tests for Primary, Secondary, and Tertiary

Alcohol tests can help sort alcohols by structure and reactivity. Alcohols are organic molecules with a hydroxyl group attached to an alkyl or aryl group, written as ROH. If the carbon with the hydroxyl group has one R group, the alcohol is primary. If it has two R groups, it is secondary. If it has three R groups, it is tertiary. Alcohols can also be aromatic when they contain a benzene ring. Phenol is the simplest aromatic alcohol. To identify an alcohol, chemists can use its chemical...

chemistry

Comprehensive, curriculum-focused videos for both instructors and students in introductory chemistry lab courses.

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Explore how spectrophotometers measure absorbance spectra, how blank calibration works, and how Beer-Lambert Law is used to find concentration and equilibrium values.

Absorbance Spectra and Beer-Lambert Analysis | JoVE K12

Louisiana Student Standards for Science

motion-and-stability-forces-and-interactions

Motion And Stability: Forces And Interactions

HS-PS2-6

通过这段 7 分钟的教师指南，准备教授 比尔定律。涵盖 JoVE Lab Manual 上 Chemistry 实验的关键准备步骤。

Chemistry 中的 比尔定律 教师准备 - 4.7K+ 观看次数 | JoVE Lab Manual

在这段 17 分钟的学生实验流程视频中，逐步学习 比尔定律 的操作步骤。属于 JoVE Lab Manual 上的 Chemistry 系列。

Chemistry 中的 比尔定律 学生实验流程 - 40K+ 观看次数 | JoVE Lab Manual

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

The Born-Haber Cycle

Lattice Energy&#xA0;

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a ...

trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

lewis-structures-of-molecular-compounds-and-polyatomic-ions

Lewis Structures of Molecular Compounds and Polyatomic Ions

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 ...

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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