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 reacción química, la concentración del reactivo disminuye con el tiempo. El tiempo necesario para reducirlo a la mitad de su cantidad inicial se denomina vida media de la reacción, y se abrevia como t1/2. Considere el refrigerante triclorofluorometano, que agota la capa de ozono.Su tiempo de residencia atmosférica es de 45 años y está prohibido en muchos países. Pero, cuánto tiempo tarda la concentración en bajar al 50 porciento? Para estimar la concentración de un reactivo después de un tiempo transcurrido, se puede usar la vida media.La vida media difiere para cada tipo de reacción. Dependiendo del orden de reacción, se puede derivar una expresión de semivida general a partir de las leyes de velocidad integradas. Considere la ley de velocidad integrada de orden cero.En t1/2, la concentración de reactivo es la mitad de su concentración inicial. Al sustituir estos parámetros, se formula una expresión para la vida media. La fórmula muestra que la vida media de una reacción de orden cero depende y es directamente proporcional a la concentración inicial de reactivo.A medida que disminuye la concentración de reactivo, la vida media continúa acortándose. Para una reacción de primer orden, la expresión de velocidad integrada se modifica sustituyendo el tiempo como t1/2 y la cantidad de reactivo como la mitad de su concentración inicial. Al resolver, se determina que la expresión para t1/2 es una constante.Por tanto, la vida media de una reacción de primer orden se deriva para que sea independiente de la concentración inicial de reactivo. Independientemente de la disminución de la concentración de reactivo, la vida media permanece constante. Para una reacción de segundo orden, la expresión de velocidad integrada se convierte en t1/2 sustituyendo los parámetros de tiempo y concentración de reactivo.Las vidas medias de las reacciones de segundo orden dependen inversamente de la concentración inicial de reactivo. A medida que disminuye la concentración de reactivo, aumenta el valor t1/2;es decir, la vida media continúa prolongándose. La vida media también ayuda a calcular la magnitud de la constante de velocidad.Ofrece una comparación relativa entre diferentes velocidades de reacción;cuanto más corta sea la vida media, más rápida será la velocidad de reacción y viceversa. Por ejemplo, el isótopo radiactivo sodio-24, con una vida media corta de 14, 7 horas, exhibe una tasa de desintegración más rápida que el cobalto-60, con una vida media más larga de 5, 3 años.

vida media de una reacción

La vida media o semivida de una reacción (t1/2) es el tiempo necesario para que se consuma la mitad de una cantidad determinada de reactivo. En cada semivida posterior, se consume la mitad de la concentración restante del reactivo. Por ejemplo, durante la descomposición del peróxido de hidrógeno, durante la primera semivida (de 0,00 horas a 6,00 horas), la concentración de H2O2 disminuye de 1,000 M a 0,500 M. Durante la segunda semivida (de 6,00 horas a 12,00 horas), la concentración disminuye de 0,500 M a 0,250 M, mientras que durante la tercera semivida, cae de 0,250 M a 0,125 M. Por lo tanto, durante cada período sucesivo de 6,00 horas, la concentración de H2O2 disminuye a la mitad.
 La vida media de una reacción de primer orden es independiente de la concentración del reactivo. Sin embargo, la semivida de las reacciones de otros órdenes depende de las concentraciones de los reactivos.
 Vida media de las reacciones de primer orden
 Una ecuación que relaciona la vida media de una reacción de primer orden con su constante de velocidad puede derivarse de su ley de velocidad integrada:
 <img alt="Eq1" src="/files/ftp_upload/11378/11378_Equation_1.png" style="text-align: center; height: 135px;" />
 Según la definición de semivida, en el tiempo t1/2, la concentración del reactivo A es la mitad de su concentración inicial. Por lo tanto, t = t1/2 y [A]t = ½ [A]0.
 Si se sustituyen estos términos en la ley de velocidad integrada reorganizada y se simplifica, se obtiene la ecuación de semivida:
 <img alt="Eq2" src="/files/ftp_upload/11378/11378_Equation_2.png" style="text-align: center; height: 135px;" />
 Esta ecuación de semivida describe una relación inversa esperada entre la semivida de la reacción y su constante de velocidad, k. Las reacciones más rápidas muestran constantes de velocidad más grandes y, en consecuencia, semividas más cortas, mientras que las reacciones más lentas muestran constantes de velocidad más pequeñas y semividas más largas.
 Vida media de las reacciones de segundo orden
 Siguiendo el mismo enfoque que para las reacciones de primer orden, una ecuación que relaciona la vida media de una reacción de segundo orden con su constante de velocidad y concentración inicial puede derivarse de su ley de velocidad integrada:  
 <img alt="Eq3" src="/files/ftp_upload/11378/11378_Equation_3.png" style="text-align: center; height: 75px;" />
 Al sustituir t = t1/2 y [A]t = ½[A]0, se simplifica la ley de velocidad integrada:
 <img alt="Eq4" src="/files/ftp_upload/11378/11378_Equation_4.png" style="text-align: center; height: 175px;" />
 Para una reacción de segundo orden, t1/2 es inversamente proporcional a la concentración del reactivo, y la semivida aumenta a medida que la reacción avanza porque la concentración del reactivo disminuye. A diferencia de las reacciones de primer orden, la constante de velocidad de una reacción de segundo orden no puede calcularse directamente a partir de la semivida a menos que se conozca la concentración inicial.
 Vida media de las reacciones de orden cero
 Una ecuación para la semivida de orden cero también puede derivarse de su ley de velocidad integrada:   
 <img alt="Eq5" src="/files/ftp_upload/11378/11378_Equation_5.png" style="text-align: center; height: 50px;" />
 Sustituyendo t = t1/2 y  [A]t = ½ [A]0, en la ley de velocidad integrada de orden cero se obtiene:
 <img alt="Eq6" src="/files/ftp_upload/11378/11378_Equation_6.png" style="text-align: center; height: 175px;" />
 La vida media de una reacción de orden cero es inversamente proporcional a su constante de velocidad. Sin embargo, la vida media de una reacción de orden cero aumenta a medida que aumenta la concentración inicial.
 Este texto es adaptado de<a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws"> Openstax, Química 2e, Sección 12.4: Leyes de velocidad Integrada.</a>

Vida Media de una Reacción

La vida media de una reacción (t1/2) es el tiempo necesario para que se consuma la mitad de una cantidad determinada de reactivo. En cada vida media sucesiva, la mitad de ...

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KEY TERMS AND CONCEPTS

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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

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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

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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

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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

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Reaction Half-Life in Kinetics

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