Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 39 s
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The Integrated Rate Law: The Dependence of Concentration on Time

Закон скорости, используемый для вывода скорости реакции из концентраций исходных веществ и констант скорости, может быть преобразован в законы скорости, демонстрирующие зависимость скорости реакции от концентрации исходных веществ и времени. Эти законы скорости можно использовать для изучения того, насколько медленно или быстро расходуется исходное вещество или сколько времени необходимо для достижения половины концентрации исходного вещества. Для начала рассмотрим закон дифференциальной скорости, который выражает скорость реакции как изменение концентрации исходного вещества в течение определенного интервала времени.Интеграция этого закона приводит к интегрированному закону скорости, который выражает скорость реакции как отношение между начальной концентрацией исходного вещества и его концентрацией по прошествии определенного времени. Интегрированный закон скорости зависит от общего порядка реакции и, следовательно, отличается для каждого типа реакции. Однако, независимо от общего порядка, все интегрированные законы скорости принимают форму стандартного линейного уравнения с различными компонентами y, m, x и b и могут быть нанесены на график с образованием прямой линии.В интегрированном законе скорости нулевого порядка _t концентрация исходного вещества в момент времени t, k константа скорости, t время, а _0 начальная концентрация исходного вещества. Для реакции нулевого порядка график зависимости концентрации исходного вещества от времени представляет собой прямую линию. Наклон это отрицательное значение константы скорости, а точка пересечения по оси y начальная концентрация исходного вещества.В реакции первого порядка натуральный логарифм концентрации исходного вещества, построенный как функция времени, дает прямую линию. Наклон соответствует отрицательному значению константы скорости, а точка пересечения по оси игрек дает натуральный логарифм начальной концентрации исходного вещества. Согласно закону интегрированной скорости второго порядка, график зависимости концентрации исходного вещества от времени дает прямую линию.Наклон соответствует константе скорости, а точка пересечения оси игрек представляет собой обратную величину начальной концентрации исходного вещества. Общий порядок реакции можно определить с помощью экспериментальных кинетических данных, построив на графике различные законы интегрированной скорости. Только линейный график соответствует правильному общему порядку реакции.Последующий анализ позволяет определить константу скорости и концентрацию исходного вещества в любой момент времени.

Закон интегрированной скорости: зависимость концентрации от времени

В то время как закон о дифференциальных темпах относит скорость и концентрации реагенты, вторая форма закона о темпах под названием закон о комплексных темпах относит концентрации реагенты и времени. Интегрированные законы о тарировании могут использоваться для определения количества реагент или продукта, присутствуемого после определенного периода времени, или для оценки времени, необходимого для реакции на определенные действия. Например, интегрированный закон о нормах помогает определить продолжительность хранения радиоактивного материала для его распада до безопасного уровня. 
 С помощью расчетов можно интегрировать закон о дифференциальной скорости химической реакции с учетом времени, чтобы дать уравнение, связывание количества восстановителя/продукта с истекшим временем реакции. 
 Реакции первого порядка 
 Интеграция закона скорости для простой реакции первого порядка (скорость = k[A]) приводит к уравнению, описывающее изменение концентрации реагент со временем: 
  <img alt=""Eq1"" src=""/files/ftp_upload/11377/11377_Equation 1.png"" style=""height: 50px;"" />
 Здесь [A]t — концентрация A в любое время t, [A]0 — начальная концентрация A, а k — константа скорости первого порядка. Для математического удобства это уравнение переупорядочивается в формат, показывающий линейную зависимость концентрации от времени, принимающую форму прямого уравнения (y = mx + b):         
  <img alt=""Eq2"" src=""/files/ftp_upload/11377/11377_Equation 2.png"" style=""height: 50px;"" />
 Уравнение предполагает, что эпюра ln[A]t против t для реакции первого порядка является прямой линией с уклоном -k и y-отрезком ln[A]0. Если набор данных скорости вычерчивается таким образом, но не приводит к прямой линии, реакция не является первой в A. 
 Реакции второго порядка 
 Закон о дифференциальной скорости для простой реакции второго порядка — это скорость = k[A]2, а закон о интегрированной скорости: 
 <img alt=""Eq3"" src=""/files/ftp_upload/11377/11377_Equation 3.png"" style=""text-align: center; height: 70px;"" />
 Интегрированный закон ставок второго порядка также принимает форму уравнения для прямой линии. Согласно уравнению, эпюра 1/[A]t против t для реакции второго порядка представляет собой прямую линию с уклоном k и y-отсекаемый отрезком 1/[A]0. Если график не является прямой линией, то реакция не является второй. 
 Реакции нулевого порядка            
 Для реакций нулевого порядка закон о дифференциальной скорости равен Rate = k. Реакция нулевого порядка характеризуется постоянной скоростью реакции, независимо от концентрации восстановителя (восстановителя). Кинетика нулевого порядка наблюдается при некоторых реакциях только при определенных условиях. Эти же реакции демонстрируют различное кинетическое поведение, когда не выполняются конкретные условия, и по этой причине иногда используется более благоразумный термин псевдо-нулевой порядок.                            
 Интегрированный закон скорости для реакции нулевого порядка также является линейной функцией, принимая форму y = mx + b:                 
  <img alt=""Eq4"" src=""/files/ftp_upload/11377/11377_Equation 4.png"" style=""height: 50px;"" />
 Эпюра [A] в сравнении с временем t для реакции нулевого порядка представляет собой прямую линию с наклоном -k и Y-отсекаемого отрезка [A]0. 
 Этот текст был адаптирован к<a href=""https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws""> Openstax, Химия 2е изд., раздел 12.4: Законы о комплексных тарифах. </a>

В то время как закон дифференциальной скорости связывает скорость и концентрацию реагентов, вторая форма закона скорости, называемая законом интегрированной скорости, соотносит...

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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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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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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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