Name: reaction half-life in kinetics
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 42 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

Half-life of a Reaction

Durante una reazione chimica, la concentrazione del reagente diminuisce nel tempo. Il tempo necessario per ridurlo alla metà della sua quantità iniziale è chiamato emi-vita della reazione, abbreviato in t1/2. Considerate il refrigerante triclorofluorometano, che impoverisce lo strato di ozono.

Il suo tempo di residenza atmosferica è di 45 anni ed è vietato in molti Paesi. Ma quanto tempo ci vuole perché la concentrazione scenda al 50 percento? Per stimare la concentrazione di un reagente dopo un tempo trascorso, è possibile utilizzare l'emi-vita.

L'emi-vita differisce per ogni tipo di reazione. A seconda dell'ordine di reazione, è possibile derivare un'espressione generale dell'emi-vita dalle leggi di velocità integrate. Considerate la legge del tasso integrato di ordine zero.

A t1/2, la concentrazione del reagente è la metà della sua concentrazione iniziale In sostituzione di questi parametri, viene formulata un'espressione per l'emi-vita. La formula mostra che l'emi-vita di una reazione di ordine zero dipende da ed è direttamente proporzionale alla concentrazione iniziale del reagente. Man mano che la concentrazione dei reagenti diminuisce, l'emi-vita continua a diminuire.

Per una reazione del primo ordine, l'espressione della velocità integrata viene modificata sostituendo il tempo come t1/2 e la quantità di reagente come metà della sua concentrazione iniziale. Alla risoluzione, si determina che l'espressione per t1/2 è una costante. Pertanto, l'emi-vita di una reazione del primo ordine risulta essere indipendente dalla concentrazione iniziale del reagente.

Indipendentemente dalla diminuzione della concentrazione dei reagenti, l'emi-vita rimane costante. Per una reazione del secondo ordine, l'espressione della velocità integrata viene convertita in t1/2, sostituendo i parametri di tempo e concentrazione dei reagenti. Le emi-vite delle reazioni di secondo ordine dipendono inversamente dalla concentrazione iniziale dei reagenti.

Quando la concentrazione del reagente diminuisce, il valore t1/2 aumenta;questo significa che l'emi-vita continua ad allungarsi. L'emi-vita aiuta anche a stimare l'entità della costante di velocità, e offre un confronto relativo fra diverse velocità di reazione;minore è l'emi-vita, maggiore è la velocità di reazione, e viceversa. Per esempio, l'isotopo radioattivo sodio-24, con una breve emi-vita di 14, 7 ore, mostra un tasso di decadimento più rapido del cobalto-60, con un'emi-vita più lunga, di 5, 3 anni.

emivita di una reazione

Il tempo di dimezzamento di una reazione (t_1/2) è il tempo necessario affinché venga consumata la metà di una determinata quantità di reagente. In ciascuna emivita successiva, viene consumata metà della concentrazione rimanente del reagente. Ad esempio, nella decomposizione del perossido di idrogeno, durante la prima emivita (da 0.00 ore a 6.00 ore), la concentrazione di H_2O_2 diminuisce da 1.000 M a 0.500 M. Durante la seconda emivita (da 6.00 ore a 12.00 ore ), la concentrazione diminuisce da 0,500 M a 0,250 M, infine durante il terzo emivita scende da 0,250 M a 0,125 M. Quindi, durante ogni periodo successivo di 6,00 ore, la concentrazione di H_2O_2 diminuisce della metà.

Il tempo di dimezzamento di una reazione del primo ordine è indipendente dalla concentrazione del reagente. Tuttavia, l'emivita delle reazioni con altri ordini dipende dalle concentrazioni dei reagenti.

Emivita delle reazioni del primo ordine

Un'equazione che mette in relazione il tempo di dimezzamento di una reazione del primo ordine con la sua costante di velocità può essere derivata dalla sua legge di velocità integrata:

<img alt="Eq1" src="/files/ftp_upload/11378/11378_Equation_1.png" style="text-align: center; height: 135px;" />

Secondo la definizione di emivita, al tempo t_1/2, la concentrazione del reagente A è la metà della sua concentrazione iniziale. Perciò; t = t_1/2 e [A]_t = ½ [A]_0.

Sostituendo questi termini nella legge sui tassi integrati riorganizzata e semplificando si ottiene l'equazione per l'emivita:

<img alt="Eq2" src="/files/ftp_upload/11378/11378_Equation_2.png" style="text-align: center; height: 135px;" />

Questa equazione del tempo di dimezzamento descrive una relazione inversa prevista tra il tempo di dimezzamento della reazione e la sua costante di velocità, k. Le reazioni più veloci mostrano costanti di velocità più grandi e emivite corrispondentemente più brevi, mentre le reazioni più lente mostrano costanti di velocità più piccole e emivite più lunghe.

Emivita delle reazioni del secondo ordine

Seguendo lo stesso approccio delle reazioni del primo ordine, un'equazione che mette in relazione il tempo di dimezzamento di una reazione del secondo ordine con la sua costante di velocità e la sua concentrazione iniziale può essere derivata dalla sua legge di velocità integrata:

<img alt="Eq3" src="/files/ftp_upload/11378/11378_Equation_3.png" style="text-align: center; height: 75px;" />

Sostituendo t = t_1/2 e [A]_t = ½[A]_0, la legge tariffaria integrata si semplifica:

<img alt="Eq4" src="/files/ftp_upload/11378/11378_Equation_4.png" style="text-align: center; height: 175px;" />

Per una reazione del secondo ordine, t_1/2 è inversamente proporzionale alla concentrazione del reagente e l'emivita aumenta man mano che la reazione procede perché la concentrazione del reagente diminuisce. A differenza delle reazioni del primo ordine, la costante di velocità di una reazione del secondo ordine non può essere calcolata direttamente dal tempo di dimezzamento a meno che non sia nota la concentrazione iniziale.

Emivita delle reazioni di ordine zero

Un'equazione per l'emivita di ordine zero può anche essere derivata dalla sua legge sulla velocità integrata:

<img alt="Eq5" src="/files/ftp_upload/11378/11378_Equation_5.png" style="text-align: center; height: 50px;" />

Sostituendo t = t_1/2 e [A]_t = ½ [A]_0, nella legge sui tassi integrati di ordine zero si ottiene:

<img alt="Eq6" src="/files/ftp_upload/11378/11378_Equation_6.png" style="text-align: center; height: 175px;" />

Il tempo di dimezzamento di una reazione di ordine zero è inversamente proporzionale alla sua costante di velocità. Tuttavia, l'emivita di una reazione di ordine zero aumenta all'aumentare della concentrazione iniziale.

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

Emivita di una reazione

L'emivita di una reazione (t1/2) è il tempo necessario per consumare la metà di una data quantità di reagente. In ogni emivita successiva, metà di ...

Education

Didattica

JoVE Core

Chemistry

Chimica

Chemical Kinetics

Cinetica Chimica

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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 concentration. An equation for this half-life comes from the integrated rate law and shows an inverse relationship with the rate constant, k. Faster reactions have larger rate constants and shorter half-lives. Slower reactions have smaller rate constants and longer half-lives.

Second-order reactions follow a different pattern. Their half-life depends on both the rate constant and the initial concentration. As the reaction continues and the reactant concentration falls, the half-life gets longer. Unlike a first-order reaction, the rate constant for a second-order reaction cannot be found directly from the half-life unless the initial concentration is known.

Zero-order reactions have their own half-life relationship as well. Their half-life is inversely proportional to the rate constant. It also increases when the initial concentration is higher. These different formulas show that reaction order changes how half-life behaves during a reaction.

Reaction Half-Life in Kinetics

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 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

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...

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 reaction half-life changes in first-, second-, and zero-order reactions, with a hydrogen peroxide example and key rate law relationships.

Reaction Half-Life in Kinetics | JoVE K12

chemistry

JoVE Core: Chimica illustra concetti chiave di chimica attraverso video animazioni concise e di immediata comprensione. Inoltre, i video della sezione "scienziati in azione" mostrano procedure metodologiche realizzate da ricercatori provenienti dai migliori laboratori internazionali.

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

Alabama Course of Study Science

Matter and Its Interactions: Energy

9-12.C.3.3.d

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

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-5.

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 ...

Balmer Series

The Bohr Model
Niels Bohr proposed a model for the hydrogen atom in 1913 that described discrete energy states are associated with a fixed electron orbit ...

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 ...

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:

Reaction Half-Life in Kinetics

Description

Transcript

Tags

More videos by Standards