Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
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Chemistry and Physics

IPC.7

IPC.7.F

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

The Integrated Rate Law: The Dependence of Concentration on Time

Una ley de velocidad utilizada para determinar la velocidad de reacción a partir de las concentraciones de reactivo y las constantes de velocidad se puede convertir en leyes de velocidad que demuestren la dependencia de la velocidad de reacción en la concentración y el tiempo del reactivo. Estas leyes de velocidad se pueden usar para estudiar qué tan lento o rápido se consume un reactivo o cuánto tiempo se requiere para alcanzar la mitad de la concentración de un reactivo. Para empezar, examine la ley de velocidad diferencial, que expresa la velocidad de reacción como un cambio en la concentración de reactivo durante un intervalo de tiempo específico.La integración de esta ley conduce a la ley de velocidad integrada, que expresa la velocidad de reacción como una relación entre la concentración inicial de un reactivo y su concentración después de una duración específica. La ley de velocidad integrada depende del orden de reacción general y, por lo tanto, varía para cada tipo de reacción. Sin embargo, independientemente del orden general, todas las leyes de velocidad integradas toman la forma de una ecuación lineal estándar con componentes distintos y, m, x y b, y que pueden trazarse para generar una línea recta.En una ley de velocidad integrada de orden cero, _t es la concentración de reactivo en el tiempo t, k es la constante de velocidad, t es el tiempo y _0 es la concentración inicial de reactivo. Para una reacción de orden cero, una gráfica de la concentración de reactivo en función del tiempo genera una línea recta. La pendiente es el valor negativo de la constante de velocidad y la intersección con el eje y es la concentración inicial de reactivo.En una reacción de primer orden, el logaritmo natural de la concentración de reactivo representado en función del tiempo da una línea recta. La pendiente corresponde al valor negativo de la constante de velocidad, mientras que la intersección con el eje y da el logaritmo natural de la concentración inicial de reactivo. De acuerdo con la ley de velocidad integrada de segundo orden, un gráfico de la inversa de la concentración de reactivo en función del tiempo produce una línea recta.La pendiente equivale a la constante de velocidad y la intersección con el eje y representa la inversa de la concentración inicial de reactivo. El orden de reacción general se puede identificar utilizando datos cinéticos experimentales trazando las diferentes leyes de velocidad integradas. Solo el gráfico con un gráfico lineal corresponde al orden de reacción general correcto.El análisis posterior permite determinar la constante de velocidad y la concentración del reactivo en un momento dado.

las leyes de velocidad integrada: dependencia entre la concentración y el tiempo

Mientras que la ley de velocidad diferencial relaciona la velocidad y las concentraciones de los reactivos, una segunda forma de ley de velocidad llamada ley de velocidad integrada relaciona las concentraciones de los reactivos y el tiempo. Las leyes de velocidad integrada se pueden utilizar para determinar la cantidad de reactivo o producto presente después de un período de tiempo o para estimar el tiempo necesario para que una reacción proceda en cierta medida. Por ejemplo, una ley de velocidad integrada ayuda a determinar el tiempo que debe almacenarse un material radiactivo para que su radiactividad decaiga hasta un nivel seguro.
 Usando el cálculo, la ley de velocidad diferencial para una reacción química puede ser integrada con respecto al tiempo para obtener una ecuación que relacione la cantidad de reactivo/producto con el tiempo transcurrido de la reacción.
 Reacciones de primer orden
 La integración de la ley de velocidad para una reacción simple de primer orden (velocidad = k[A]) resulta en una ecuación que describe la variación en la concentración de los reactivos con el tiempo:
  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />
 Aquí, [A]t es la concentración de A en cualquier momento t, [A]0 es la concentración inicial de A, y k es la constante de velocidad de primer orden. Para mayor comodidad matemática, esta ecuación se reorganiza a un formato que muestra una dependencia lineal entre la concentración y el tiempo que toma la forma de una ecuación de linea recta (y =mx +b):         
  <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />
 La ecuación sugiere que un gráfico de ln[A]t versus t para una reacción de primer orden es una línea recta con una pendiente de −k y una intercepción y de ln[A]0. Si un conjunto de datos de velocidad se grafican de esta manera pero no dan como resultado una línea recta, la reacción no es de primer orden en A.
 Reacciones de segundo orden
 La ley de velocidad diferencial para una reacción de segundo orden simple es, velocidad = k[A]2, y la ley de velocidad integrada es:
 <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />
 La ley de velocidad integrada de segundo orden también toma la forma de la ecuación para una línea recta. Según la ecuación, un gráfico de 1/[A]t versus t para una reacción de segundo orden es una línea recta con una pendiente de k y una intersección y de 1/[A]0. Si el gráfico no es una línea recta, la reacción no es de segundo orden.
 Reacciones de orden cero           
 Para las reacciones de orden cero, la ley de velocidad diferencial es, velocidad = k. Una reacción de orden cero muestra una velocidad de reacción constante, independientemente de la concentración de sus reactivos. La cinética de orden cero se observa para algunas reacciones sólo en determinadas condiciones específicas. Estas mismas reacciones muestran diferentes comportamientos cinéticos cuando no se cumplen las condiciones específicas, y por esta razón, a veces se utiliza el término pseudo-orden cero más prudente.                            
 La ley de velocidad integrada para una reacción de orden cero también es una función lineal, tomando la forma de y =mx + b:                 
  <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />
 Un gráfico de [A] frente al tiempo t para una reacción de orden cero es una línea recta con una pendiente de −k y una intercepción y de [A]0.
 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 Velocidades Integradas.</a>

Las Leyes de Velocidad Integrada: Dependencia entre la Concentración y el Tiempo

Mientras que la ley de velocidad diferencial relaciona la tasa y las concentraciones de reactivos, una segunda forma de ley de tasa llamada ley de tasa integrada se relaciona ...

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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 form relates the concentration of A at time t to the initial concentration [A]0 and the first-order rate constant k. The equation can be rearranged into the straight-line form y = mx + b. That means a plot of ln[A]t versus t should be linear. The slope is −k, and the y-intercept is ln[A]0. If the data do not make a straight line, the reaction is not first order in A.

Second-order reactions follow a different pattern. For a simple second-order reaction, the differential rate law is rate = k[A]2. Its integrated rate law also gives a straight-line relationship. A plot of 1/[A]t versus time t should be linear, with slope k and y-intercept 1/[A]0. If the plot is not straight, the reaction is not second order.

Zero-order reactions behave differently again. For these reactions, the rate is rate = k, so the reaction rate stays constant even when reactant concentration changes. Some reactions show zero-order kinetics only under certain conditions, so the term pseudo-zero-order is sometimes used. The integrated rate law is also linear here. A plot of [A] versus time t is a straight line with slope −k and y-intercept [A]0.

Reading Reaction Progress with Integrated Laws

reading-reaction-progress-with-integrated-laws

reaction rate

Measuring Reaction Rates

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the integrated rate law: the dependence of concentration on time

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

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catalysis

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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 integrated rate laws connect concentration and time for first-order, second-order, and zero-order reactions, including straight-line plots and slopes.

Reading Reaction Progress with Integrated Laws | JoVE K12

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Reading Reaction Progress with Integrated Laws

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