Name: determining activation energy from temperature
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 34 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

Arrhenius Plots

化学反応の速度は、温度変化に非常に敏感です。この温度依存性は、アレニウス方程式を使用して数学的に説明されます。これは、速度定数、絶対温度、周波数係数、および活性化エネルギーの関係を表します。
活性化エネルギーと周波数係数は、アレニウス方程式を非指数関数形式に変換することにより、グラフィカルに決定することもできます。
両側の自然対数を使用して、線形関数の方程式が生成されます。傾き値は、ガス定数に対する活性化エネルギーの負の値に対応し、y 切片は周波数係数の自然対数に対応します。
この方程式を使用して、アレニウスプロットと呼ばれるグラフを生成できます。このグラフでは、レート定数の自然対数がケルビン単位の温度の逆関数として表されます。
実験と反応の速度論的データは、このアレニウスプロットを使用して説明および分析できます。この例では、グラフは直線になります。ケルビンで与えられる傾き値は、R上の活性化エネルギーの負の値に等しく設定されます。気体定数の値を割り当て、活性化エネルギーを解くと、93.1 kJ/molの値が得られます。
また、26.8のy切片は、周波数係数の自然対数に等しくなります。したがって、A を解くと、1 オーバー モルリティ 秒 (レート定数と同じ単位) で 4.36 × 1011 の値が得られます。
運動データが限られている場合やグラフィカルな表現が困難な場合は、アレニウス方程式の2点形式を利用して、非グラフィカルな方法で活性化エネルギーを計算できます。
このような場合、アレニウス方程式の非指数形式は、2つの異なる温度でのレート定数を含むように変更されます。
その後の式の減算と再配置により、アレニウス方程式の2点形式が得られ、2つの異なる温度で実験的に生成された速度定数から活性化エネルギーを計算するために使用されます。これらを代入すると、この反応の活性化エネルギーは145kJ/molと計算されます。

アレニウスプロット

アレニウス式は、化学反応の活性化エネルギーと速度定数kを関係付ける式です。アレニウス式は、k = Ae−Ea/RTと表されます。ここでRは気体定数であり、その値は8.314 J/mol·K、Tは絶対温度、Eaは活性化エネルギー（J/mol）、eはネイピア数(2.7183...)、Aは頻度因子と呼ばれる定数で、衝突の頻度や反応する分子の向きなどに関係します。
 アレニウス式は、実験データから反応の活性化エネルギーを計算するために使用することができます。ある反応のEaを決定する便利な方法は、2つ以上の異なる温度でkを測定することです。この方法では、一次方程式に変形したアレニウス式を使用します。
  <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />
 ln k対1/Tのプロットは、傾きが −Ea/Rに等しく、y切片が ln Aに等しい直線となります。
 以下の反応を考えると、
  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />
 この反応の活性化エネルギーは、図を参考に反応速度データを用いて、速度定数の温度による変化がわかれば求めることができます。
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">絶対温度 (K)</td>
 <td style="color: black; border: 1px solid black; text-align: center;">反応速度定数 (L/mol/s)</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">555</td>
 <td style="color: black; border: 1px solid black; text-align: center;">3.52 × 10–7</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">575</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.22 × 10–6</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">645</td>
 <td style="color: black; border: 1px solid black; text-align: center;">8.59 × 10–5</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">700</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.16 × 10–3</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">781</td>
 <td style="color: black; border: 1px solid black; text-align: center;">3.95 × 10–2</td>
 </tr>
 </tbody>
 </table>
 与えられたデータを用いると、温度の逆数（1/T）とkの自然対数（ln k）の値を導き出すことができます。
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1/T (K–1)</td>
 <td style="color: black; border: 1px solid black; text-align: center;">ln k</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">   1.80 × 10–3    </td>
 <td style="color: black; border: 1px solid black; text-align: center;">     –14.860     </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1.74 × 10–3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">–13.617</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1.55 × 10–3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">–9.362</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1.43 × 10–3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">–6.759</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1.28 × 10–3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">–3.231</td>
 </tr>
 </tbody>
 </table>
  <img alt="Image1" src="/files/ftp_upload/11380/11380_Image 1.png" style="height: 350px;" />
 導き出されたデータ点をln k vs. 1/Tでプロットすると、図のようにln kと1/Tの間に直線的な関係を示す線図が生成されます。
 活性化エネルギーに相当する直線の傾きは、2つの実験データのいずれかを用いて推定することができます。              
  <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />
 活性化エネルギーを導出する別の方法として、2つの異なる温度での速度定数を利用する方法があります。この方法では、アレニウス方程式を2点間の直線式に並べ替えます。
  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />
 式を並べ替えると、活性化エネルギーの式となります。
  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />
 任意の2つのデータを代入してさらに計算すると、活性化エネルギーの値がJ/molまたはkJ/molで得られます。
  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />
 この代替となる2点法は、グラフを用いる方法と同じ結果をもたらします。しかし、実際の実験データを扱う際には、グラフを用いる方法の方がより信頼性の高い結果を得ることができます。
 上記の文章は以下から引用しました。<a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory</a>.

アレニウス方程式は、化学反応の活性化エネルギーと速度定数kを関連付けます。アレニウス方程式では、k = Ae−Ea / RT、Rは...

Education

JoVE Core

Chemistry

化学

Chemical Kinetics

化学反応速度論

KEY TERMS AND CONCEPTS

主要用語と概念

determining activation energy from temperature

The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules.

Experimental kinetic data can be used to find the activation energy of a reaction. One practical method is to measure k at two or more temperatures. The Arrhenius equation can then be rewritten in a linear form. A plot of ln k versus 1/T gives a straight line. The slope equals −Ea/R, and the y-intercept equals ln A.

For example, a reaction with known rate constants at 555 K, 575 K, 645 K, 700 K, and 781 K can be analyzed this way. The rate constants are 3.52 × 10−7, 1.22 × 10−6, 8.59 × 10−5, 1.16 × 10−3, and 3.95 × 10−2 L/mol/s, respectively. These values can be converted to 1/T and ln k. The resulting data set can then be plotted to show the linear relationship between ln k and 1/T.

The slope of the line gives the activation energy. It can be estimated from any two experimental data pairs on the graph. Another option is the two-point form of the Arrhenius equation. This rearranged equation uses rate constants at two temperatures to calculate Ea directly. Both methods give the same result. In practice, the graphical method is often more reliable when working with real experimental data.

Determining Activation Energy from Temperature

determining-activation-energy-from-temperature

reaction rate

Measuring Reaction Rates

Measuring reaction rates shows how fast reactants are used up or products are formed over time. The rate of reaction is the change in the amount of a reactant or product per unit time. Because of that, scientists measure how a property changes as the reaction proceeds and connect that change to reactant or product amounts. For reactions that make or use a gas, the rate can be followed by changes in volume or pressure. A rate expression is the mathematical way to write how concentration changes...

measuring reaction rates

Tracking Reaction Kinetics with Light and Pressure

Reaction kinetics can be tracked with polarimetry, spectrometry, and pressure measurements. These methods let scientists follow a reaction without disturbing the sample. They also help determine how reactant or product concentrations change over time. Polarimetry is used for optically active substances. These substances rotate the plane of polarized light, which is called optical rotation. The effect comes from molecular structure. Normal monochromatic light is unpolarized, but after it passes...

concentration and rate law

Reaction Order from Concentration

Reaction order from concentration shows how reactant amounts affect reaction rate. Rate laws, also called differential rate laws or rate equations, are mathematical expressions that connect reaction rate with the concentrations of reactants. For a generic reaction a A + b B → products, the rate law can be written using the reactant concentrations [A] and [B] and a rate constant k. In a rate law, k is the rate constant for one specific reaction at one specific temperature. The exponents m and n...

determining order of reaction

Finding Rate Law from Initial Rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change. One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and,...

the integrated rate law: the dependence of concentration on time

the-integrated-rate-law-the-dependence-of-concentration-on-time

Reading Reaction Progress with Integrated Laws

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level. These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated...

half-life of a reaction

Reaction Half-Life in Kinetics

Reaction half-life is the time needed for half of a reactant to be consumed. After each half-life, half of the remaining reactant is used up. A hydrogen peroxide decomposition example shows this pattern clearly. The concentration drops from 1.000 M to 0.500 M in the first 6.00 hours, then to 0.250 M in the next 6.00 hours, and then to 0.125 M in the third period. Each later 6.00-hour interval removes half of what is left. For first-order reactions, the half-life does not depend on the reactant...

temperature dependence on reaction rate

Collision Theory and Reaction Speed

Collision theory explains why reaction speed depends on how particles collide. Atoms, molecules, or ions must come close together before they can react. The theory says the reaction rate depends on the collision rate, the orientation of the colliding species, and whether the collision has enough energy for bonds to change. A gas-phase reaction between carbon monoxide and oxygen shows why orientation matters. The molecules can collide in more than one way. If the oxygen side of carbon monoxide...

arrhenius plots

The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules. Experimental kinetic data can be used to find the activation...

reaction mechanisms

Elementary Steps in Reaction Mechanisms

Chemical reactions can happen in steps, and a balanced equation does not show the full path at the molecular level. A reaction mechanism, also called a reaction path, gives the step-by-step process that explains how reactants become products. The decomposition of ozone is one example of a reaction that can be described by a sequence of steps. Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and when they are added together, they give the balanced...

rate-determining steps

Reaction Bottlenecks in Chemical Kinetics

Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate. The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same...

catalysis

Catalyst Action in Reaction Rates

Catalysts change the rate of a chemical reaction by giving it a faster path. A catalyst increases reaction rate without being consumed during the process. Its effect is often explained with reaction mechanisms and energy diagrams. For an endothermic reaction, the reactants and products start and end at the same energies in both cases. The uncatalyzed path is a one-step mechanism with one transition state. The catalyzed path follows a different mechanism with two transition states and a lower...

enzymes

Enzyme Action and Inhibition

Enzymes are biological catalysts that speed up many reactions in living organisms. They help control cellular metabolism by lowering the activation energy needed for biochemical reactions. When activation energy drops, reaction rates can increase. Enzyme problems can also lead to serious disease. A genetic abnormality that causes G6PD, or glucose-6-phosphate dehydrogenase, deficiency can disrupt the pathway that supplies NADPH to cells. In red blood cells, this can reduce glutathione and...

key terms and concepts

Learn how the Arrhenius equation uses temperature and rate constants to find activation energy with a graph or a two-point calculation.

Determining Activation Energy from Temperature | JoVE K12

chemistry

JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Matter and its Interactions

PS.Chm.5.1

Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.D

3.2.9-12.E

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Virginia  Standards of Learning

HIgh School

CH.7

CH.7.e

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-4

HS-PS1-5

Florida Department of Education

SC.912.P.12

SC.912.P.12.12

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

C-PS1-4

C-PS1-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-5.

Georgia Standards of Excellence

SC4.

Collision and Transition State Theory

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 ...

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 ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

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

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

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

Determining Activation Energy from Temperature

Description

Transcript

Tags

More videos by Standards