Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 39 s
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IPC.7

IPC.7.F

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The Integrated Rate Law: The Dependence of Concentration on Time

Ein Geschwindigkeitsgesetz, das zur Bestimmung der Reaktionsgeschwindigkeit aus Reaktantenkonzentrationen und Geschwindigkeitskonstanten verwendet wird, kann in Geschwindigkeitsgesetze umgewandelt werden, die die Abhängigkeit der Reaktionsgeschwindigkeit von der Reaktantenkonzentration und -zeit demonstrieren.
Diese Geschwindigkeitsgesetze können verwendet werden, um zu untersuchen, wie langsam oder schnell ein Reaktant verbraucht wird oder wie viel Zeit erforderlich ist, um die Hälfte der Konzentration eines Reaktanten zu erreichen.
Untersuchen Sie zunächst das Gesetz der Differenzgeschwindigkeit, das die Reaktionsgeschwindigkeit als Änderung der Reaktantenkonzentration während eines bestimmten Zeitintervalls ausdrückt. Die Integration dieses Gesetzes führt zum integrierten Geschwindigkeitsgesetz, das die Reaktionsgeschwindigkeit als Beziehung zwischen der Anfangskonzentration eines Reaktanten und seiner Konzentration nach einer bestimmten Dauer ausdrückt.
Das integrierte Geschwindigkeitsgesetz ist abhängig von der Gesamtreaktionsordnung und variiert daher für jede Reaktionsart. Unabhängig von der Gesamtordnung liegen jedoch alle integrierten Geschwindigkeitsgesetze in Form einer linearen Standardgleichung mit unterschiedlichen y-, m-, x- und b-Komponenten vor und können aufgetragen werden, um eine gerade Linie zu erzeugen.
In einem integrierten Geschwindigkeitsgesetz nullter Ordnung ist [A]t die Reaktantenkonzentration zum Zeitpunkt t, k ist die Geschwindigkeitskonstante, t ist die Zeit und [A]0 ist die anfängliche Reaktantenkonzentration.
Für eine Reaktion nullter Ordnung ergibt sich aus einem Diagramm der Reaktantenkonzentration als Funktion der Zeit eine gerade Linie. Die Steigung ist der negative Wert der Geschwindigkeitskonstante, und der y-Achsenabschnitt ist die anfängliche Reaktantenkonzentration.
Bei einer Reaktion erster Ordnung ergibt der natürliche Logarithmus der Reaktantenkonzentration, aufgetragen als Funktion der Zeit, eine gerade Linie. Die Steigung entspricht dem negativen Wert der Geschwindigkeitskonstante, während der y-Achsenabschnitt den natürlichen Logarithmus der anfänglichen Reaktantenkonzentration darstellt.
Nach dem integrierten Geschwindigkeitsgesetz zweiter Ordnung ergibt ein Diagramm des Kehrwerts der Reaktantenkonzentration über der Zeit eine gerade Linie. Die Steigung entspricht der Geschwindigkeitskonstante, und der y-Achsenabschnitt stellt den Kehrwert der anfänglichen Reaktantenkonzentration dar.
Die Gesamtreihenfolge der Reaktion kann mit Hilfe experimenteller kinetischer Daten identifiziert werden, indem die verschiedenen integrierten Geschwindigkeitsgesetze aufgetragen werden. Nur der Plot mit einem linearen Graphen entspricht der korrekten Gesamtreaktionsordnung. Die anschließende Analyse ermöglicht die Bestimmung der Geschwindigkeitskonstante und der Reaktantenkonzentration zu einem bestimmten Zeitpunkt.

das integrierte geschwindigkeitsgesetz: die abhängigkeit der konzentration von der zeit

Während das Differentialgeschwindigkeitsgesetz die Geschwindigkeit und Konzentrationen der Reaktanten in Beziehung setzt, setzt eine zweite Form des Geschwindigkeitsgesetzes, das integrierte Geschwindigkeitsgesetz, die Konzentrationen der Reaktanten und die Zeit in Beziehung. Integrierte Geschwindigkeitsgesetze können verwendet werden, um die Menge an Reaktanten oder Produkten zu bestimmen, die nach einem bestimmten Zeitraum vorhanden sind, oder um die Zeit abzuschätzen, die erforderlich ist, damit eine Reaktion bis zu einem bestimmten Grad abläuft. Beispielsweise hilft ein integriertes Geschwindigkeitsgesetz bei der Bestimmung der Zeitspanne, die ein radioaktives Material gelagert werden muss, damit seine Radioaktivität auf ein sicheres Maß abfällt. Mithilfe der Analysis kann das Differentialgeschwindigkeitsgesetz für eine chemische Reaktion über die Zeit integriert werden, um eine Gleichung zu erhalten, die die Reaktanten-/Produktmenge mit der verstrichenen Zeit der Reaktion in Beziehung setzt. Reaktionen erster Ordnung Die Integration des Geschwindigkeitsgesetzes für eine einfache Reaktion erster Ordnung (Geschwindigkeit = k[A]) führt zu einer Gleichung, die die zeitliche Variation der Reaktantenkonzentration beschreibt:  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;"> Dabei ist [A]t die Konzentration von A zu jedem Zeitpunkt t, [A]0 die Anfangskonzentration von A und k die Geschwindigkeitskonstante erster Ordnung. Aus mathematischen Gründen wird diese Gleichung in ein Format umgestellt, das eine lineare Abhängigkeit der Konzentration von der Zeit zeigt und die Form einer geraden Gleichung (y = mx + b) annimmt:          <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;"> Die Gleichung legt nahe, dass eine Auftragung von ln[A]t gegen t für eine Reaktion erster Ordnung eine gerade Linie mit einer Steigung von −k und einem y-Achsenabschnitt von ln[A]0 ist. Wenn ein Satz von Geschwindigkeitsdaten auf diese Weise aufgetragen wird, aber keine gerade Linie ergibt, ist die Reaktion in A nicht erster Ordnung. Reaktionen zweiter Ordnung Das Differentialgeschwindigkeitsgesetz für eine einfache Reaktion zweiter Ordnung lautet rate = k[A]2, und das integrierte Geschwindigkeitsgesetz lautet: <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;"> Das integrierte Geschwindigkeitsgesetz zweiter Ordnung hat ebenfalls die Form der Geradengleichung. Gemäß der Gleichung ist eine Auftragung von 1/[A]t gegen t für eine Reaktion zweiter Ordnung eine gerade Linie mit einer Steigung von k und einem y-Achsenabschnitt von 1/[A]0. Wenn das Diagramm keine gerade Linie ist, ist die Reaktion nicht zweiter Ordnung. Reaktionen nullter Ordnung            Für Reaktionen nullter Ordnung lautet das Differentialgeschwindigkeitsgesetz rate = k. Eine Reaktion nullter Ordnung weist eine konstante Reaktionsgeschwindigkeit auf, unabhängig von der Konzentration ihrer Reaktanten. Kinetiken nullter Ordnung werden für einige Reaktionen nur unter bestimmten spezifischen Bedingungen beobachtet. Dieselben Reaktionen zeigen ein unterschiedliches kinetisches Verhalten, wenn die spezifischen Bedingungen nicht erfüllt sind. Aus diesem Grund wird manchmal der vorsichtigere Begriff Pseudo-Null-Ordnung verwendet.                             Das integrierte Geschwindigkeitsgesetz für eine Reaktion nullter Ordnung ist ebenfalls eine lineare Funktion und hat die Form y = mx + b:                   <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;"> Eine Auftragung von [A] gegen die Zeit t für eine Reaktion nullter Ordnung ist eine gerade Linie mit einer Steigung von −k und einem y-Achsenabschnitt von [A]0. Dieser Text ist adaptiert von <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

Das integrierte Geschwindigkeitsgesetz: Die Abhängigkeit der Konzentration von der Zeit

Während das differentielle Geschwindigkeitsgesetz die Geschwindigkeit und die Konzentrationen von Reaktanten in Beziehung setzt, bezieht sich eine zweite Form des Geschwindigkeitsgesetzes, das integrierte Geschwindigkeitsgesetz, auf ...

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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

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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...

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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

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 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...

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arrhenius plots

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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...

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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...

rate-determining steps

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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 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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IPC.7.B

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IPC.7.D

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IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Reading Reaction Progress with Integrated Laws

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