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

Kimyasal bir reaksiyon sırasında, reaktan konsantrasyonu zamanla azalır. İlk miktarının yarısına indirgemek için geçen süre, reaksiyonun yarı ömrü olarak adlandırılır ve t1/2 olarak kısaltılır. Ozon tabakasını delen soğutucu trikloroflorometanı düşünün.Atmosferde kalma süresi 45 yıldır ve birçok ülkede yasaklanmıştır. Fakat konsantrasyonun 50'ye düşmesi ne kadar sürer? Geçen bir sürenin ardından bir reaktanın konsantrasyonunu tahmin etmek için yarı ömür kullanılabilir.Yarı ömür, her reaksiyon türü için farklıdır. Reaksiyon sırasına bağlı olarak, genel bir yarı ömür ifadesi, entegre hız yasasından türetilebilir. Sıfır dereceli entegre hız yasasını düşünün.T1/2'de, reaktan konsantrasyonu, başlangıç konsantrasyonunun yarısıdır. Bu parametrelerin yerine koyarak yarı ömür hesaplaması için bir ifade formüle edilir. Formül, sıfır dereceli bir reaksiyon için yarı ömrünün, başlangıçtaki reaktan konsantrasyonuna bağlı ve doğrudan orantılı olduğunu gösterir.Reaktan konsantrasyonu düştükçe, yarı ömür kısalmaya devam eder. Birinci dereceden bir reaksiyon için, entegre hız ifadesi, zamanın t1/2 olarak ve reaktan miktarının başlangıç konsantrasyonunun yarısı olarak ikame edilmesiyle modifiye edilir. Çözerken, t1/2 ifadesi sabit olarak belirlenir.Bu nedenle, birinci dereceden bir reaksiyonun yarı ömrü, başlangıçtaki reaktan konsantrasyonundan bağımsız olarak elde edilir. Reaktant konsantrasyonundaki düşüşe bakılmaksızın, yarı ömür sabit kalır. İkinci dereceden bir reaksiyon için, entegre hız ifadesi, zaman ve reaktan konsantrasyon parametreleri yerleştirilerek tl/2'ye dönüştürülür.İkinci derece reaksiyonların yarı ömürleri, başlangıçtaki reaktan konsantrasyonu ile ters orantılıdır. Reaktan konsantrasyonu azaldıkça t1/2 değeri artar;yani yarı ömür uzamaya devam eder. Yarı ömür ayrıca hız sabitinin büyüklüğünün tahmin edilmesine yardımcı olur.Farklı reaksiyon hızları arasında göreceli bir karşılaştırma sunar;yarılanma ömrü ne kadar kısa olursa, reaksiyon hızı o kadar hızlı olur ve bunun tersi de geçerlidir. Örneğin, 14, 7 saatlik kısa bir yarı ömre sahip radyoaktif izotop sodyum-24, 5, 3 yıllık daha uzun yarı ömürle kobalt-60'tan daha hızlı bir bozunma hızı sergiler.

bir reaksiyonun yarı Ömr

Bir reaksiyonun yarı ömrü (t1/2), belirli bir reaktant miktarının yarısının tüketilmesi için gereken süredir. Sonraki her bir yarılanma ömründe, reaktantın kalan konsantrasyonunun yarısı tüketilir. Örneğin, hidrojen peroksitin ayrışması sırasında, ilk yarılanma ömrü boyunca (0.00 saatten 6.00 saate kadar), H2O2 konsantrasyonu 1,000 M'den 0,500 M'ye kadar. İkinci yarılanma ömrü sırasında (6.00 saatten 12.00 saate), konsantrasyon 0,500 M'den 0,250 M'ye düşerken, üçüncü yarılanma ömrü boyunca 0,250 M'den 0,125 M'ye düşmektedir. Birbirini izleyen 6.00 saatlik periyotta H2O2 konsantrasyonu yarı yarıya azalır.
 
 Birinci dereceden bir reaksiyonun yarı ömrü, reaktan konsantrasyonundan bağımsızdır. Bununla birlikte, diğer dereceli reaksiyonların yarı ömürleri, reaktanların konsantrasyonlarına bağlıdır.
 
 Birinci Dereceden Tepkimelerin Yarı Ömrü
 
 Birinci dereceden bir reaksiyonun yarı ömrünü hız sabitiyle ilişkilendiren bir denklem, entegre hız yasasından türetilebilir:
 
 <img alt="Eq1" src="/files/ftp_upload/11378/11378_Equation_1.png" style="text-align: center; height: 135px;" />
 
 Yarı ömür tanımına göre t1/2 zamanında, reaktan A'nın konsantrasyonu, başlangıç konsantrasyonunun yarısıdır. Bu nedenle; t=t1/2  ve [A]t =½[A]0.
 
 Bu terimleri yeniden düzenlenmiş entegre hız yasasına dönüştürmek ve basitleştirmek, yarı ömür denklemini verir:
 
 <img alt="Eq2" src="/files/ftp_upload/11378/11378_Equation_2.png" style="text-align: center; height: 135px;" />
 
 Bu yarı ömür denklemi, reaksiyonun yarı ömrü ile hız sabiti k arasında beklenen ters ilişkiyi açıklar. Daha hızlı reaksiyonlar daha büyük hız sabitleri ve buna bağlı olarak daha kısa yarı ömürler sergilerken, daha yavaş reaksiyonlar daha küçük hız sabitleri ve daha uzun yarı ömürler sergiler.
 
 İkinci Derece Tepkimelerin Yarı Ömrü
 
 Birinci dereceden reaksiyonlarla aynı yaklaşımı izleyerek, ikinci dereceden reaksiyonun yarı ömrünü hız sabiti ve başlangıç konsantrasyonuyla ilişkilendiren bir denklem, entegre hız yasasından türetilebilir: 
 
 <img alt="Eq3" src="/files/ftp_upload/11378/11378_Equation_3.png" style="text-align: center; height: 75px;" />
 
 t=t1/2  ve [A]t = ½[A]0, entegre hız yasası basitleştirildi:
 
 <img alt = "Eq4" src = "/ files / ftp_upload / 11378 / 11378_Equation_4.png" style = "text-align: center; height: 175px;" />
 
 İkinci dereceden bir reaksiyon için t1/2, reaktantın konsantrasyonu ile ters orantılıdır ve yarı ömür, reaksiyon ilerledikçe artar çünkü reaktan konsantrasyonu azalır. Birinci dereceden reaksiyonlardan farklı olarak, ikinci dereceden reaksiyonun hız sabiti, ilk konsantrasyon bilinmedikçe doğrudan yarı ömürden hesaplanamaz.
 
 Sıfır Dereceli Reaksiyonların Yarı Ömrü
 
 Sıfır dereceli yarı ömür için bir denklem, entegre hız yasasından da türetilebilir:   
 
 <img alt = "Eq5" src = "/ files / ftp_upload / 11378 / 11378_Equation_5.png" style = "text-align: center; height: 50px;" />
 
 t=t1/2   ve   [A]t=½[A]0, sıfır derece entegre hız yasasında şunu verir:
 
 <img alt = "Eq6" src = "/ files / ftp_upload / 11378 / 11378_Equation_6.png" style = "text-align: center; height: 175px;" /> 
 
 Sıfır dereceli bir reaksiyonun yarı ömrü, hız sabitiyle ters orantılıdır. Bununla birlikte, sıfır dereceli bir reaksiyonun yarı ömrü, başlangıçtaki konsantrasyon arttıkça artar.
 
 Bu metin bu kaynaktan uyarlanmıştır<a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

Bir Reaksiyonun Yarı Ömr

Bir reaksiyonun yarı ömrü (t1/2), belirli bir reaktan miktarının yarısının tüketilmesi için gereken süredir. Sonraki her yarı ömürde, yarısı ...

Education

JoVE Core

Chemistry

Kimya

Chemical Kinetics

Kimyasal Kinetik

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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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...

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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...

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catalysis

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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

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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

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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Virginia  Standards of Learning

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CH.7

CH.7.e

Alabama Course of Study Science

Matter and Its Interactions: Energy

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Florida Department of Education

SC.912.P.12

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New York State Science Learning Standards

HS. Chemical Reactions

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IPC.7.D

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Reaction Half-Life in Kinetics

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