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

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The Integrated Rate Law: The Dependence of Concentration on Time

Prawo szybkości używane do określania szybkości reakcji na podstawie stężeń reagentów i stałych szybkości można przekształcić w prawa szybkości pokazujące zależność szybkości reakcji od stężenia i czasu reagenta.
Te prawa szybkości można wykorzystać do badania, jak wolno lub szybko reagent jest zużywany lub ile czasu jest potrzebne, aby osiągnąć połowę stężenia reagenta.
Na początek zbadaj prawo szybkości różnicowej, które wyraża szybkość reakcji jako zmianę stężenia reagenta w określonym przedziale czasu. Integracja tego prawa prowadzi do prawa zintegrowanej szybkości, które wyraża szybkość reakcji jako relację między początkowym stężeniem reagenta a jego stężeniem po określonym czasie.
Zintegrowane prawo szybkości zależy od ogólnej kolejności reakcji, a zatem różni się dla każdego typu reakcji. Jednak niezależnie od ogólnej kolejności, wszystkie zintegrowane prawa szybkości mają postać standardowego równania liniowego z różnymi składnikami y, m, x i b i można je wykreślić w celu wygenerowania linii prostej.
W zintegrowanym prawie szybkości zerowego rzędu, [A] t jest stężeniem reagenta w czasie t, k jest stałą szybkości, t jest czasem, a [A]0 jest początkowym stężeniem reagenta.
W przypadku reakcji zerowego rzędu wykres stężenia reagenta w funkcji czasu generuje linię prostą. Nachylenie jest ujemną wartością stałej szybkości, a punkt przecięcia z osią y jest początkowym stężeniem reagenta.
W reakcji pierwszego rzędu logarytm naturalny stężenia reagenta wykreślony w funkcji czasu daje linię prostą. Nachylenie odpowiada ujemnej wartości stałej szybkości, podczas gdy punkt przecięcia z osią y daje logarytm naturalny początkowego stężenia reagenta.
Zgodnie z prawem zintegrowanej szybkości drugiego rzędu, wykres odwrotności stężenia reagenta w funkcji czasu daje linię prostą. Nachylenie jest równe stałej szybkości, a punkt przecięcia z osią y reprezentuje odwrotność początkowego stężenia reagenta.
Ogólną kolejność reakcji można określić za pomocą eksperymentalnych danych kinetycznych, wykreślając różne zintegrowane prawa szybkości. Tylko wykres z wykresem liniowym odpowiada prawidłowej ogólnej kolejności reakcji. Późniejsza analiza pozwala określić stałą szybkości i stężenie reagentów w dowolnym momencie.

zintegrowane prawo stopy procentowej: zależność koncentracji od czasu

Podczas gdy prawo różnicy szybkości łączy szybkość i stężenia reagentów, druga forma prawa szybkości, zwana zintegrowanym prawem szybkości, łączy stężenia reagentów i czas. Zintegrowane prawa szybkości można zastosować do określenia ilości reagenta lub produktu obecnego po pewnym czasie lub do oszacowania czasu potrzebnego do zajścia reakcji w określonym zakresie. Na przykład zintegrowane prawo dotyczące stawek pomaga określić, jak długo należy przechowywać materiał radioaktywny, aby jego radioaktywność spadła do bezpiecznego poziomu.

Za pomocą rachunku różniczkowego można zintegrować prawo różnicowej szybkości reakcji chemicznej ze względu na czas, uzyskując równanie odnoszące ilość reagenta/produktu do czasu, jaki upłynął od reakcji.

<h4>Reakcje pierwszego rzędu</h4>

Całkowanie prawa szybkości prostej reakcji pierwszego rzędu (szybkość = k[A]) daje równanie opisujące zmianę stężenia reagenta w czasie:

 <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;">

Tutaj [A]t jest stężeniem A w dowolnym momencie t, [A]0 jest początkowym stężeniem A, a k jest stałą szybkości pierwszego rzędu. Dla wygody matematycznej równanie to przekształcono do formatu przedstawiającego liniową zależność stężenia od czasu, który przyjmuje postać równania liniowego (y = mx + b):

 <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;">

Równanie sugeruje, że wykres ln[A]t w funkcji t dla reakcji pierwszego rzędu jest linią prostą o nachyleniu −k i punkcie przecięcia z y wynoszącym ln[A]0. Jeżeli w ten sposób wykreślono zbiór danych dotyczących szybkości, lecz nie otrzymano linii prostej, reakcja w A nie jest pierwszego rzędu.

<h4>Reakcje drugiego rzędu</h4>

Różnicowe prawo szybkości dla prostej reakcji drugiego rzędu to szybkość = k[A]2, a zintegrowane prawo szybkości to:

<img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;">

Zintegrowane prawo stopy procentowej drugiego rzędu ma również postać równania linii prostej. Zgodnie z równaniem wykres 1/[A]t w funkcji t dla reakcji drugiego rzędu jest linią prostą o nachyleniu k i punkcie przecięcia y równym 1/[A]0. Jeżeli wykres nie jest linią prostą, wówczas reakcja nie jest drugiego rzędu.

<h4>Reakcje zerowego rzędu</h4>

W przypadku reakcji zerowego rzędu prawem szybkości różnicowej jest szybkość = k. Reakcja zerowego rzędu wykazuje stałą szybkość reakcji, niezależnie od stężenia jej reagentów. Kinetykę zerowego rzędu obserwuje się w przypadku niektórych reakcji tylko w określonych warunkach. Te same reakcje wykazują różne zachowania kinetyczne, gdy nie są spełnione określone warunki, i z tego powodu czasami używany jest bardziej ostrożny termin pseudo-rząd zerowy.

Zintegrowane prawo szybkości dla reakcji zerowego rzędu jest również funkcją liniową, przyjmującą postać y = mx + b:

 <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;">

Wykres [A] w funkcji czasu t dla reakcji zerowego rzędu jest linią prostą o nachyleniu −k i punkcie przecięcia y wynoszącym [A]0.

Zintegrowane prawo stopy procentowej: zależność koncentracji od czasu

Podczas gdy prawo różnicowej stawki odnosi się do szybkości i stężeń reagentów, druga forma prawa stawek, zwana ustawą o zintegrowanej stawce, odnosi się ...

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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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