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

K12 Standards

Texas Essential Knowledge and Skills

High School

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

반응물 농도 및 속도 상수로부터 반응 속도를 결정하는 데 사용되는 속도 법칙은 반응물 농도 및 시간에 대한 반응 속도의 의존성을 나타내는 속도 법칙으로 변환될 수 있습니다. 이러한 속도 법칙을 사용하여 반응물이 얼마나 느리게 또는 얼마나 빨리 소비되는지 또는 반응물 농도의 절반에 도달하기 위해 얼마나 많은 시간이 필요한지를 연구할 수 있습니다. 먼저 반응 속도를 특정 시간 구간에서 반응물 농도의 변화로 나타내는 미분형 속도 법칙을 조사합니다.

이 법칙을 통합하면 적분형 속도 법칙을 유도하는 데 이 법칙은 반응 속도를 반응물의 초기 농도와 특정 지속시간 후의 농도 사이의 관계로 표현합니다. 적분형 속도 법칙은 전체 반응 차수에 따라 달라지며 따라서 반응 유형마다 다릅니다. 그러나 전체 차수와 관계없이 모든 적분형 속도 법칙은 고유한 y, m, x 및 b 성분을 갖는 표준 선형 방정식의 형태를 취하며 도표를 그리면 직선을 생성합니다.

0차 적분형 속도 법칙에서 _t는 시간 t에서 반응물 농도, k는 속도 상수, t는 시간, _0은 초기 반응물 농도입니다. 0차 반응의 경우 시간의 함수로써 반응물 농도의 그래프는 직선으로 됩니다. 기울기는 속도 상수의 음수 값이고 y 절편은 초기 반응물 농도입니다.

1차 반응에서 시간의 함수로 표시된 반응물 농도의 자연 로그는 직선으로 됩니다. 기울기는 속도 상수의 음수 값에 해당하는 반면 y 절편은 초기 반응물 농도의 자연 로그입니다. 2차 적분형 속도 법칙에 따라 반응물 농도 대 시간의 역 그래프는 직선으로 됩니다.

기울기는 속도 상수와 같으며 y 절편은 초기 반응물 농도의 역수를 나타냅니다. 서로 다른 적분형 속도 법칙을 구획화함으로써 실험적인 운동 데이터를 사용하여 전체 반응 차수를 확인할 수 있습니다. 선형 그래프인 경우에만 올바른 전체 반응 차수입니다.

추가 분석을 통해 주어진 시점에서 속도 상수 및 반응물 농도를 결정할 수 있습니다.

적분 속도 법칙: 시간에 따른 농도의 의존성

미분 속도 법칙이 반응물의 속도와 농도와 관련이 있는 반면, 적분 속도 법칙이라고 불리는 두 번째 형태의 속도 법칙은 반응물의 농도와 시간과 관련이 있습니다. 적분 속도 법칙은 일정 시간이 지난 후 존재하는 반응물이나 생성물의 양을 결정하거나 반응이 어느 정도 진행되는 데 필요한 시간을 추정하는 데 사용될 수 있습니다. 예를 들어, 적분 속도 법칙은 방사능이 안전한 수준으로 붕괴되기 위해 방사성 물질을 보관해야 하는 기간을 결정하는 데 도움이 됩니다.

미적분학을 사용하면 화학 반응의 미분 속도 법칙을 시간에 대해 통합하여 반응물/생성물 양과 반응 경과 시간을 연관시키는 방정식을 제공할 수 있습니다.

1차 반응

간단한 1차 반응(속도 = k[A])에 대한 속도 법칙을 통합하면 시간에 따른 반응물 농도의 변화를 설명하는 방정식이 생성됩니다.

 <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />

여기서 [A]_t는 임의의 시간 t에서의 A의 농도이고, [A]_0는 A의 초기 농도이고, k는 1차 속도 상수입니다. 수학적 편의를 위해 이 방정식은 직선 방정식(y = mx + b)의 형태를 취하는 시간에 대한 농도의 선형 의존성을 보여주는 형식으로 재배열됩니다.

 <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />

방정식은 1차 반응에 대한 t 대 ln[A]_t의 플롯이 기울기가 −k이고 y 절편이 ln[A]_0인 직선임을 나타냅니다. 일련의 속도 자료가 이런 방식으로 표시되었지만 직선이 아닌 경우 반응은 A에서 1차 반응이 아닙니다.

2차 반응

간단한 2차 반응에 대한 미분 속도 법칙은 속도 = k[A]^2이고 적분 속도 법칙은 다음과 같습니다.

<img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />

2차 적분율 법칙은 또한 직선에 대한 방정식의 형태를 취합니다. 방정식에 따르면 2차 반응에 대한 t 대 1/[A]_t의 플롯은 기울기가 k이고 y 절편이 1/[A]_0인 직선입니다. 플롯이 직선이 아닌 경우 반응은 2차 반응이 아닙니다.

0차 반응

0차 반응의 경우 미분 속도 법칙은 속도 = k입니다. 0차 반응은 반응물의 농도에 관계없이 일정한 반응 속도를 나타냅니다. 0차 동역학은 특정 특정 조건에서만 일부 반응에 대해 관찰됩니다. 이러한 동일한 반응은 특정 조건이 충족되지 않을 때 다른 동역학 거동을 나타내며, 이러한 이유로 보다 신중한 용어인 유사 0차(pseudo-zero-order)가 때때로 사용됩니다.

0차 반응에 대한 적분 속도 법칙은 y = mx + b 형식을 취하는 선형 함수이기도 합니다.

 <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />

0차 반응에 대한 [A] 대 시간 t의 플롯은 기울기가 -k이고 y 절편이 [A]_0인 직선입니다.



이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

차등 속도 법칙은 반응물의 속도 및 농도와 관련이 있지만 통합 속도 법칙이라고 하는 두 번째 형태의 속도 법칙은 ...

Education

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JoVE Core

Chemistry

화학

하나

Chemical Kinetics

화학 반응 속도론

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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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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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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JoVE Core 화학은 간결하고 이해하기 쉬운 애니메이션을 통해 일반 화학 개념을 설명합니다. 또한, 과학자가 직접 고전실험과 연구실험을 진행하는 실사 영상을 제공합니다.

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Reading Reaction Progress with Integrated Laws

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