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

K12 Standards

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Chemistry and Physics

IPC.7

IPC.7.F

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The Integrated Rate Law: The Dependence of Concentration on Time

Een snelheidswet die wordt gebruikt om de reactiesnelheid uit reactantconcentraties en snelheidsconstanten te bepalen, kan worden omgezet in snelheidswetten die de afhankelijkheid van reactiesnelheid van reactantconcentratie en tijd aantonen. Deze snelheidswetten kunnen worden gebruikt om te bestuderen hoe langzaam of snel een reactant wordt verbruikt of hoeveel tijd nodig is om de helft van de concentratie van een reactant te bereiken. Bekijk om te beginnen de wet van de differentiële snelheid, die de reactiesnelheid uitdrukt als een verandering in reactantconcentratie gedurende een specifiek tijdsinterval.Integratie van deze wet leidt tot de geïntegreerde snelheidswet, die de reactiesnelheid uitdrukt als een relatie tussen de beginconcentratie van een reactant en zijn concentratie na een bepaalde duur. De geïntegreerde snelheidswet is afhankelijk van de algehele reactie-orde en verschilt daarom voor elk reactietype. Ongeacht de algehele orde nemen alle geïntegreerde snelheidswetten echter de vorm aan van een standaard lineaire vergelijking met verschillende y-m-x-en b-componenten en kunnen ze worden uitgezet om een rechte lijn te genereren.In een geïntegreerde snelheidswet van de nulde orde is _t de reactantconcentratie op het tijdstip t, k is de snelheidsconstante, t is de tijd en _0 is de aanvankelijke reactantconcentratie. Voor een nulde-orde-reactie genereert een grafiek van de reactantconcentratie als functie van de tijd een rechte lijn. De helling is de negatieve waarde van de snelheidsconstante en het y-snijpunt is de aanvankelijke reactantconcentratie.In een eerste-orde-reactie geeft de natuurlijke log van reactantconcentratie uitgezet als functie van de tijd een rechte lijn. De helling komt overeen met de negatieve waarde van de snelheidsconstante, terwijl het y-snijpunt de natuurlijke log van de aanvankelijke reactantconcentratie geeft. Volgens de geïntegreerde snelheidswet van de tweede orde levert een plot van de inverse van de reactantconcentratie tegen de tijd een rechte lijn op.De helling is gelijk aan de snelheidsconstante en het y-snijpunt vertegenwoordigt de inverse van de aanvankelijke reactantconcentratie. De algehele orde van de reactie kan worden geïdentificeerd met behulp van experimentele kinetische gegevens door de verschillende geïntegreerde snelheidswetten te plotten. Alleen de plot met een lineaire grafiek komt overeen met de juiste algehele reactie-orde.Daaropvolgende analyse maakt het mogelijk om op elk moment de snelheidsconstante en de reactantconcentratie te bepalen.

de geïntegreerde snelheidswet: de afhankelijkheid van concentratie van tijd

Terwijl de differentiële snelheidswet de snelheid en concentraties van reactanten in verband brengt, heeft een tweede vorm van snelheidswet, de geïntegreerde snelheidswet genaamd, betrekking op concentraties van reactanten en tijd. Geïntegreerde snelheidswetten kunnen worden gebruikt om de hoeveelheid reactant of product die na een bepaalde tijd aanwezig is te bepalen of om de tijd te schatten die nodig is om een reactie tot op zekere hoogte te laten verlopen. Een geïntegreerde snelheidswet helpt bijvoorbeeld bij het bepalen van de tijdsduur die een radioactief materiaal moet worden opgeslagen voordat de radioactiviteit tot een veilig niveau vervalt. Met behulp van calculus kan de differentiële snelheidswet voor een chemische reactie worden geïntegreerd met betrekking tot de tijd om een vergelijking te geven die de hoeveelheid reactant/product relateert aan de verstreken tijd van de reactie. Eerste orde reacties Integratie van de snelheidswet voor een eenvoudige eerste-orde reactie (snelheid = k[A]) resulteert in een vergelijking die de variatie in de concentratie van reactanten in de tijd beschrijft:  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;"> Hier is [A]t de concentratie van A op elk moment t, [A]0 is de initiële concentratie van A en k is de snelheidsconstante van de eerste orde. Voor wiskundig gemak is deze vergelijking herschikt naar een formaat dat een lineaire afhankelijkheid van de concentratie van de tijd laat zien en dat de vorm aanneemt van een lineaire vergelijking (y = mx + b):          <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;"> De vergelijking suggereert dat een grafiek van ln[A]t versus t voor een eerste-orde reactie een rechte lijn is met een helling van −k en een y-snijpunt van ln[A]0. Als een reeks snelheidsgegevens op deze manier wordt uitgezet maar niet in een rechte lijn resulteert, is de reactie niet van de eerste orde in A. Tweede orde reacties De differentiële snelheidswet voor een eenvoudige reactie van de tweede orde is snelheid = k[A]2, en de geïntegreerde snelheidswet is: <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;"> De geïntegreerde snelheidswet van de tweede orde neemt ook de vorm aan van de vergelijking voor een rechte lijn. Volgens de vergelijking is een grafiek van 1/[A]t versus t voor een reactie van de tweede orde een rechte lijn met een helling van k en een y-snijpunt van 1/[A]0. Als de plot geen rechte lijn is, is de reactie niet van de tweede orde. Nul-orde-reacties            Voor reacties van de nulde orde is de differentiële snelheidswet snelheid = k. Een nulde-orde reactie vertoont een constante reactiesnelheid, ongeacht de concentratie van de reactant(en). Kinetiek van de nulde orde wordt voor sommige reacties alleen onder bepaalde specifieke omstandigheden waargenomen. Deze zelfde reacties vertonen verschillend kinetisch gedrag wanneer niet aan de specifieke voorwaarden wordt voldaan, en om deze reden wordt soms de voorzichtigere term pseudo-nulorde gebruikt.                             De geïntegreerde snelheidswet voor een reactie van de nulde orde is ook een lineaire functie, in de vorm van y = mx + b:                   <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;"> Een grafiek van [A] versus tijd t voor een reactie van de nulde orde is een rechte lijn met een helling van −k en een y-snijpunt van [A]0.

De geïntegreerde snelheidswet: de afhankelijkheid van concentratie van tijd

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates ...

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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...

determining order of reaction

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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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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...

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

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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 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.D

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Reading Reaction Progress with Integrated Laws

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