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 uma reação química, a concentração do reagente decresce com o tempo. O tempo necessário para reduzi-lo a metade da sua quantidade inicial é chamada a meia-vida da reação, abreviada como t1/2. Considere o refrigerante triclorofluorometano, o que esgota a camada de ozono.Na sua residência atmosférica, o tempo é de 45 anos e é proibido em muitos países. Mas quanto tempo é que demora para a concentração para cair para 50%para estimar uma concentração do reagente após um período de tempo decorrido, a meia-vida pode ser usada. A meia-vida difere para cada tipo de reação.Consoante a ordem de reação, uma expressão geral de meia-vida pode ser derivado das leis de taxas integradas. Considere a ordem zero da lei da taxa integrada. Em t1/2, a concentração do reagente é metade de sua concentração inicial.Em substituição destes parâmetros, uma expressão para a meia-vida é formulada. A fórmula mostra que a meia-vida para uma reação de ordem zero está dependente e é diretamente proporcional à concentração inicial do reagente. Como o reagente na concentração decresce, a meia-vida continua para ficar mais curta.Para uma reação de primeira ordem, a expressão da taxa integrada é modificado substituindo o tempo como t1/2 e a quantidade de reagente como metade de sua concentração inicial. Ao resolver, a expressão para t1/2 está determinado a ser uma constante. Assim, a meia-vida de uma reação de primeira ordem é derivada para ser independente da concentração inicial do reagente inicial.Independentemente do decréscimo da concentração do reagente, a meia-vida permanece constante. Para uma reação de segunda ordem, a expressão da taxa integrada é convertida em t1/2 substituindo o tempo e parâmetros de concentração do reagente As meias-vidas das reações de segunda ordem estão inversamente dependentes da concentração inicial do reagente. Como o reagente na concentração decresce, o valor t1/2 aumenta;significado, a meia-vida continua a durar mais tempo.A meia-vida também ajuda a estimar a magnitude da taxa constante. Oferece uma comparação relativa entre diferentes reações mais curtas;a meia-vida mais curta, quanto mais rápida for a reação e vice-versa. Por exemplo, o isótopo radioativo sódio-24, com uma meia-vida curta de 14, 7 horas, apresenta uma taxa de decadência mais rápida que a taxa de cobalto-60, com uma meia-vida de 5, 3 anos.

meia-vida de uma reação

A meia-vida de uma reação (t1/2) é o tempo necessário para que metade de uma determinada quantidade de reagente seja consumida. Em cada meia-vida seguinte, metade da concentração remanescente do reagente é consumida. Por exemplo, durante a decomposição do peróxido de hidrogénio, durante a primeira meia-vida (de 0,00 horas a 6,00 horas), a concentração de H2O2 diminui de 1,000 M para 0,500 M. Durante a segunda meia-vida (de 6,00 horas a 12,00 horas), a concentração diminui de 0,500 M para 0,250 M, enquanto que durante a terceira meia-vida, cai de 0,250 M para 0,125 M. Portanto, durante cada período sucessivo de 6,00 horas, a concentração de H2O2 diminui pela metade.
A meia-vida de uma reação de primeira ordem é independente da concentração do reagente. No entanto, a meia-vida de reações com outras ordens depende das concentrações dos reagentes.
Meia-vida de Reações de Primeira Ordem
Uma equação que relaciona a meia-vida de uma reação de primeira ordem com a sua constante de velocidade pode ser derivada da sua lei de velocidade integrada:
<img alt="Eq1" src="/files/ftp_upload/11378/11378_Equation_1.png" style="text-align: center; height: 135px;" />
De acordo com a definição de meia-vida, no tempo t1/2, a concentração do reagente A é metade da sua concentração inicial. Por isso; t = t1/2  e [A]t = ½ [A]0.
Substituir e simplificar estes termos na lei de velocidade integrada reorganizada fornece a equação para a meia-vida:
<img alt="Eq2" src="/files/ftp_upload/11378/11378_Equation_2.png" style="text-align: center; height: 135px;" />
Esta equação de meia-vida descreve uma relação inversa esperada entre a meia-vida da reação e a sua constante de velocidade, k. As reações mais rápidas apresentam constantes de velocidade maiores e meias-vidas correspondentemente mais curtas, enquanto que as reações mais lentas apresentam constantes de velocidade menores e meias-vidas mais longas.
Meia-vida de Reações de Segunda Ordem
Seguindo a mesma abordagem das reações de primeira ordem, uma equação que relaciona a meia-vida de uma reação de segunda ordem com a sua constante de velocidade e concentração inicial pode ser derivada da sua lei de velocidade integrada: 
<img alt="Eq3" src="/files/ftp_upload/11378/11378_Equation_3.png" style="text-align: center; height: 75px;" />
Ao substituir t = t1/2  e [A]t = ½[A]0, a lei de velocidade integrada é simplificada:
<img alt="Eq4" src="/files/ftp_upload/11378/11378_Equation_4.png" style="text-align: center; height: 175px;" />
Para uma reação de segunda ordem, t1/2 é inversamente proporcional à concentração do reagente, e a meia-vida aumenta à medida que a reação avança porque a concentração do reagente diminui. Ao contrário das reações de primeira ordem, a constante de velocidade de uma reação de segunda ordem não pode ser calculada diretamente a partir da meia-vida, a menos que a concentração inicial seja conhecida.
Meia-vida de Reações de Ordem Zero
Uma equação para meia-vida de ordem zero também pode ser derivada da sua lei de velocidade integrada:  
<img alt="Eq5" src="/files/ftp_upload/11378/11378_Equation_5.png" style="text-align: center; height: 50px;" />
Substituindo t = t1/2  e  [A]t = ½ [A]0, na lei de velocidade integrada de ordem zero obtemos:
<img alt="Eq6" src="/files/ftp_upload/11378/11378_Equation_6.png" style="text-align: center; height: 175px;" />
A meia-vida para uma reação de ordem zero é inversamente proporcional à sua constante de velocidade. No entanto, a meia-vida de uma reação de ordem zero aumenta à medida que a concentração inicial aumenta.
Este texto é adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

Meia-vida de uma Reação

A meia-vida de uma reação (t1/2) é o tempo necessário para que metade de uma determinada quantidade de reagente seja consumida. Em cada meia-vida sucessiva, metade de ...

Education

JoVE Core

Chemistry

Química

Chemical Kinetics

Cinética Química

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

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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

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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

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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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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

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Matter and its Interactions

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Chemical Reactions

3.2.9-12.D

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Reaction Half-Life in Kinetics

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