Name: reaction half-life in kinetics
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 42 s
Channel: JoVE

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Half-life of a Reaction

Podczas reakcji chemicznej stężenie reagenta spada z czasem. Czas potrzebny do zredukowania go do połowy początkowej ilości nazywa się okresem półtrwania reakcji, w skrócie t1/2.
Weźmy pod uwagę czynnik chłodniczy trichlorofluorometan, który zubaża warstwę ozonową. Jego czas przebywania w atmosferze wynosi 45 lat i jest zakazany w wielu krajach. Ale jak długo potrzeba, aby stężenie spadło do 50%? Aby oszacować stężenie reagenta po upływie czasu, można użyć okresu półtrwania.
Okres półtrwania różni się w zależności od typu reakcji. W zależności od kolejności reakcji, ogólny okres półtrwania może być wyprowadzony ze zintegrowanych praw szybkości. 
Weźmy pod uwagę ustawę o zintegrowanej stopie procentowej zerowego rzędu. Przy t1/2 stężenie reagenta wynosi połowę jego początkowego stężenia. Po podstawieniu tych parametrów formułuje się wyrażenie na okres półtrwania.
Wzór pokazuje, że okres półtrwania dla reakcji zerowego rzędu jest zależny i wprost proporcjonalny do początkowego stężenia reagenta. Wraz ze spadkiem stężenia reagenta okres półtrwania nadal się skraca.
W przypadku reakcji pierwszego rzędu zintegrowane wyrażenie szybkości jest modyfikowane przez podstawienie czasu jako t1/2, a ilości reagenta jako połowy jego początkowego stężenia. Podczas rozwiązywania wyrażenie dla t1/2 jest określane jako stała.
W związku z tym określa się okres półtrwania reakcji pierwszego rzędu jako niezależny od początkowego stężenia reagenta. Niezależnie od spadku stężenia reagenta, okres półtrwania pozostaje stały. 
W przypadku reakcji drugiego rzędu zintegrowane wyrażenie szybkości jest przekształcane na t1/2 poprzez podstawienie parametrów czasu i stężenia reagenta. 
Okresy półtrwania reakcji drugiego rzędu są odwrotnie proporcjonalne do początkowego stężenia reagenta. Wraz ze spadkiem stężenia reagenta wzrasta wartość t1/2; co oznacza, okres półtrwania nadal się wydłuża.
Okres półtrwania pomaga również oszacować wielkość stałej szybkości. Oferuje względne porównanie różnych szybkości reakcji; Im krótszy okres półtrwania, tym szybsza szybkość reakcji i odwrotnie. 
Na przykład radioaktywny izotop sodu-24, o krótkim okresie połowicznego rozpadu wynoszącym 14,7 godziny, wykazuje szybsze tempo rozpadu niż kobalt-60, z dłuższym okresem połowicznego rozpadu wynoszącym 5,3 roku

okres półtrwania reakcji

Okres półtrwania reakcji (t1/2) to czas wymagany do zużycia połowy danej ilości reagenta. W każdym kolejnym okresie półtrwania zużywana jest połowa pozostałego stężenia reagenta. Przykładowo podczas rozkładu nadtlenku wodoru, w pierwszym okresie półtrwania (od 0,00 do 6,00 godzin) stężenie H2O2 spada z 1,000 M do 0,500 M. Podczas drugiego okresu półtrwania (od 6,00 do 12,00 godzin) stężenie zmniejsza się od 0,500 M do 0,250 M, natomiast w trzecim okresie półtrwania spada z 0,250 M do 0,125 M. Stąd w każdym kolejnym okresie 6,00 godzin stężenie H2O2 zmniejsza się o połowę.

Okres półtrwania reakcji pierwszego rzędu nie zależy od stężenia reagenta. Jednakże okresy półtrwania reakcji innych rzędów zależą od stężeń reagentów.

<h4>Okres półtrwania reakcji pierwszego rzędu</h4>

Równanie odnoszące okres półtrwania reakcji pierwszego rzędu do jej stałej szybkości można wyprowadzić ze zintegrowanego prawa szybkości:

<img alt="Eq1" src="/files/ftp_upload/11378/11378_Equation_1.png" style="text-align: center; height: 135px;">

Zgodnie z definicją okresu półtrwania, w chwili t1/2 stężenie reagenta A wynosi połowę jego stężenia początkowego. Dlatego; t = t1/2 i [A]t = ½ [A]0.

Podstawienie tych terminów do przeorganizowanego zintegrowanego prawa stopy procentowej i uproszczenie daje równanie okresu półtrwania:

<img alt="Eq2" src="/files/ftp_upload/11378/11378_Equation_2.png" style="text-align: center; height: 135px;">


To równanie okresu półtrwania opisuje oczekiwaną odwrotną zależność między okresem półtrwania reakcji a jej stałą szybkości, k. Szybsze reakcje wykazują większe stałe szybkości i odpowiednio krótsze okresy półtrwania, podczas gdy wolniejsze reakcje wykazują mniejsze stałe szybkości i dłuższe okresy półtrwania.

<h4>Okres półtrwania reakcji drugiego rzędu</h4>

Stosując to samo podejście, co w przypadku reakcji pierwszego rzędu, równanie odnoszące okres półtrwania reakcji drugiego rzędu do jej stałej szybkości i początkowego stężenia można wyprowadzić ze zintegrowanego prawa szybkości:

<img alt="Eq3" src="/files/ftp_upload/11378/11378_Equation_3.png" style="text-align: center; height: 75px;">

Podstawiając t = t1/2 i [A]t = ½[A]0, zintegrowane prawo stopy procentowej zostaje uproszczone:

<img alt="Eq4" src="/files/ftp_upload/11378/11378_Equation_4.png" style="text-align: center; height: 175px;">

W przypadku reakcji drugiego rzędu t1/2 jest odwrotnie proporcjonalne do stężenia reagenta, a okres półtrwania wzrasta w miarę postępu reakcji, ponieważ stężenie reagenta maleje. W przeciwieństwie do reakcji pierwszego rzędu, stałej szybkości reakcji drugiego rzędu nie można obliczyć bezpośrednio z okresu półtrwania, chyba że znane jest początkowe stężenie.

<h4>Okres półtrwania reakcji zerowego rzędu</h4>

Równanie na okres półtrwania rzędu zerowego można również wyprowadzić ze zintegrowanego prawa szybkości:

<img alt="Eq5" src="/files/ftp_upload/11378/11378_Equation_5.png" style="text-align: center; height: 50px;">

Podstawiając t = t1/2 i [A]t = ½ [A]0, w zintegrowanym prawie stopy zerowej otrzymujemy:

<img alt="Eq6" src="/files/ftp_upload/11378/11378_Equation_6.png" style="text-align: center; height: 175px;">

Okres półtrwania reakcji zerowego rzędu jest odwrotnie proporcjonalny do stałej szybkości. Jednakże okres półtrwania reakcji zerowego rzędu wzrasta wraz ze wzrostem początkowego stężenia.

Okres półtrwania reakcji

Okres półtrwania reakcji (t1/2) to czas potrzebny do spożycia połowy danej ilości reagenta. W każdym kolejnym okresie półtrwania, połowa ...

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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 concentration. An equation for this half-life comes from the integrated rate law and shows an inverse relationship with the rate constant, k. Faster reactions have larger rate constants and shorter half-lives. Slower reactions have smaller rate constants and longer half-lives.

Second-order reactions follow a different pattern. Their half-life depends on both the rate constant and the initial concentration. As the reaction continues and the reactant concentration falls, the half-life gets longer. Unlike a first-order reaction, the rate constant for a second-order reaction cannot be found directly from the half-life unless the initial concentration is known.

Zero-order reactions have their own half-life relationship as well. Their half-life is inversely proportional to the rate constant. It also increases when the initial concentration is higher. These different formulas show that reaction order changes how half-life behaves during a reaction.

Reaction Half-Life in Kinetics

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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...

half-life of a reaction

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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key terms and concepts

Learn how reaction half-life changes in first-, second-, and zero-order reactions, with a hydrogen peroxide example and key rate law relationships.

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Reaction Half-Life in Kinetics

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