Name: reading reaction progress with integrated laws
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The Integrated Rate Law: The Dependence of Concentration on Time

Uma lei de taxas é utilizada para determinar a taxa de reação das concentrações reagentes, e das constantes de taxas podem ser convertidas em leis de taxas demonstrando a dependência da taxa de reação da concentração do reagente e tempo. Estas leis de taxas podem ser utilizadas para estudar quão lenta ou rapidamente um reagente é consumido ou quanto tempo é necessário para atingir metade da concentração de um reagente. Para começar, a examinar o diferencial da lei das taxas, que exprime a taxa de reação como uma mudança em concentração do reagente durante um intervalo de tempo específico.A integração desta lei conduz à lei da taxa integrada, que exprime a taxa de reação como uma relação entre um reagente, a concentração inicial e a sua concentração após uma duração específica. A lei da taxa integrada está dependente sobre a reação de ordem global e, por conseguinte, varia para cada tipo de reação. No entanto, independentemente da ordem geral, todas as taxas integradas, as leis tomam a forma de uma equação linear padrão com distintos y, m, x, e b componentes e podem ser traçados para gerar uma linha reta.Numa ordem de zero de lei da taxa integrada, _t é o reagente de concentração na altura t, k é a taxa constante, t é o momento, e _0 é a concentração inicial do reagente. Para uma reação de ordem zero, uma malha de concentração do reagente em função do tempo gera uma linha reta. O declive é o valor negativo da constante da taxa, e a intercessão y é a concentração inicial do reagente.Numa reação de primeira ordem, o algoritmo natural de concentração do reagente traçado em função do tempo dá uma linha reta. O declive corresponde ao valor negativo da taxa constante, enquanto a intercessão y dá o logaritmo natural da concentração inicial do reagente. De acordo com a segunda ordem, a lei da taxa integrada, uma trama do inverso da concentração do reagente versus rendimentos temporais, produz uma linha reta.O declive equivale à taxa constante, e a intercessão y representa o inverso da concentração inicial do reagente. A reação global pode ser identificada usando dados experimentais cinéticos através de plotagem das diferentes leis de taxas integradas. Apenas a parcela com um gráfico linear corresponde à ordem correta da reação global.Análise posterior permite determinar a constante de taxa e a concentração do reagente em qualquer momento.

a lei da velocidade integrada: a dependência da concentração em relação ao tempo

Enquanto que a lei de velocidade diferencial relaciona a velocidade e as concentrações de reagentes, uma segunda forma de lei de velocidade chamada lei de velocidade integrada relaciona concentrações de reagentes e tempo. As leis de velocidades integradas podem ser usadas para determinar a quantidade de reagentes ou produtos presentes após um período de tempo ou para estimar o tempo necessário para que uma reação prossiga até certo ponto. Por exemplo, uma lei de velocidade integrada ajuda a determinar o período de tempo durante o qual uma matéria radioativa deve ser armazenada para que a sua radioatividade decaia para um nível seguro.
Usando cálculo, a lei da velocidade diferencial para uma reação química pode ser integrada em relação ao tempo para dar uma equação que relaciona a quantidade de reagente/produto ao tempo decorrido da reação.
Reações de Primeira Ordem
A integração da lei de velocidade para uma reação simples de primeira ordem (velocidade = k[A]) resulta em uma equação que descreve a variação da concentração de reagentes com o tempo:
 <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />
Aqui, [A]t é a concentração de A a qualquer momento t, [A]0 é a concentração inicial de A, e k é a constante de velocidade de primeira ordem. Para conveniência matemática, esta equação é rearranjada para um formato que mostra uma dependência linear da concentração no tempo que assume a forma de uma equação de linha recta (y = mx + b): :        
 <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />
A equação sugere que um gráfico de ln[A]t versus t para uma reação de primeira ordem é uma linha recta com um declive de −k e uma intercepção y de ln[A]0. Se um conjunto de dados de velocidade for representado desta forma, mas não resultar em uma linha recta, a reação não é de primeira ordem em A.
Reações de Segunda Ordem
A lei de velocidade diferencial para uma reação simples de segunda ordem é velocidade = k[A]2, e a lei de velocidade integrada é:
<img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />
A lei de velocidade integrada de segunda ordem também assume a forma da equação para uma linha recta. De acordo com a equação, um gráfico de 1/[A]t versus t para uma reação de segunda ordem é uma linha recta com um declive de e uma intercepção y de 1/[A]0. Se o gráfico não for uma linha recta, então a reação não é de segunda ordem.
Reações de Ordem Zero           
Para reações de ordem zero, a lei de velocidade diferencial é velocidade = k. Uma reação de ordem zero apresenta uma velocidade de reação constante, independentemente da concentração do(s) seu(s) reagente(s). A cinética de ordem zero é observada para algumas reações apenas em determinadas condições específicas. Essas mesmas reações apresentam diferentes comportamentos cinéticos quando as condições específicas não são atendidas e, por isso, o termo pseudo-ordem zero mais prudente é às vezes usado.                            
A lei de velocidade integrada para uma reação de ordem zero é também uma função linear, sob a forma de y = mx + b:                 
 <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />
Um gráfico de [A] versus tempo t para uma reação de ordem zero é uma linha recta com um declive de −k e uma intercepção y de [A]0.
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>

A Lei da Velocidade Integrada: A Dependência da Concentração em Relação ao Tempo

Enquanto a lei de taxa diferencial relaciona a taxa e as concentrações de reagentes, uma segunda forma de lei de taxa chamada lei de taxa 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

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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...

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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.

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Reading Reaction Progress with Integrated Laws

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