Name: finding rate law from initial rates
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 53 s
Channel: JoVE

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IPC.7.F

Determining Order of Reaction

Für eine chemische Reaktion drückt das Geschwindigkeitsgesetz das Verhältnis zwischen der Reaktionsgeschwindigkeit und der Reaktantenkonzentration aus. Die Exponenten der Reaktantenkonzentrationen beeinflussen die Reaktionsgeschwindigkeit individuell und werden als Reaktionsordnungen bezeichnet.
Die Reaktionsreihenfolge wird experimentell bestimmt, indem die Methode der Anfangsgeschwindigkeiten angewendet wird, bei der eine chemische Reaktion mehrmals mit unterschiedlichen Reaktantenkonzentrationen wiederholt wird, um die anfänglichen Reaktionsgeschwindigkeiten zu messen.
Eine Erhöhung der Reaktantenkonzentration, die eine linear-proportionale Erhöhung der Reaktionsgeschwindigkeit erzeugt, kennzeichnet eine Reaktion erster Ordnung. Wenn die Verdopplung der Reaktantenkonzentration die Anfangsrate vervierfacht, wird eine Reaktion zweiter Ordnung beobachtet.
Wenn jedoch die Änderung der Reaktantenkonzentrationen die anfänglichen Geschwindigkeitswerte nicht beeinflusst, wird eine Reaktion nullter Ordnung beobachtet.
Wenn die erhaltenen Daten der Anfangsgeschwindigkeiten eine nicht erkennbare Beziehung zwischen der Änderung der anfänglichen Reaktantenkonzentration und der entsprechenden Rate darstellen, wird ein Verhältnis der Geschwindigkeitsgesetze berechnet.
Hierbei werden zwei beliebige Konzentrationswerte des Reaktanten und deren entsprechende Reaktionsgeschwindigkeiten verwendet, um die Reaktionsreihenfolge zu bestimmen.
Aber was ist mit Reaktionen mit mehreren Reaktanten? Zunächst wird mit der Methode der Anfangsgeschwindigkeiten die Reaktionsreihenfolge jedes Reaktanten einzeln bestimmt.
Als nächstes werden die einzelnen Reaktionsordnungen als Exponenten zu ihren jeweiligen Reaktantenkonzentrationen ausgedrückt, um das Geschwindigkeitsgesetz zu formulieren. Schließlich bestimmt die Summe der einzelnen Exponenten aus dem Geschwindigkeitsgesetz die Gesamtreaktionsordnung.
Während die Reaktionsreihenfolge die Abhängigkeit der Reaktionsgeschwindigkeit von der Reaktantenkonzentration darstellt, wird ein direktes Maß für die relative Reaktionsgeschwindigkeit durch die Geschwindigkeitskonstante angezeigt.
Die Geschwindigkeitskonstante k ist der Proportionalitätskoeffizient, der die Reaktionsgeschwindigkeit mit dem Produkt der Reaktantenkonzentrationen in Beziehung setzt.
Die Einheit einer Geschwindigkeitskonstante hängt von der Gesamtreaktionsordnung ab und kann bestimmt werden, indem das Geschwindigkeitsgesetz neu angeordnet wird, um die Geschwindigkeitskonstante aufzulösen. Für eine Reaktion nullter Ordnung hat k die Einheitsmolarität pro Sekunde. Die Einheit für eine Reaktion erster Ordnung ist 1/s und für eine Reaktion zweiter Ordnung 1/M·s.
Eine große Geschwindigkeitskonstante deutet auf eine schnelle Reaktion hin. Umgekehrt deutet eine kleinere Geschwindigkeitskonstante auf eine langsame Reaktion hin. Ein Wert von Null bedeutet, dass keine chemische Reaktion stattgefunden hat.

bestimmung der reaktionsreihenfolge

Geschwindigkeitsgesetze beschreiben den Zusammenhang zwischen der Geschwindigkeit einer chemischen Reaktion und der Konzentration ihrer Reaktanten. In einem Geschwindigkeitsgesetz werden die Geschwindigkeitskonstante k und die Reaktionsordnungen experimentell bestimmt, indem beobachtet wird, wie sich die Reaktionsgeschwindigkeit ändert, wenn sich die Konzentrationen der Reaktanten ändern. Ein üblicher experimenteller Ansatz zur Bestimmung von Geschwindigkeitsgesetzen ist die Methode der Anfangsgeschwindigkeiten. Bei dieser Methode werden Reaktionsgeschwindigkeiten für mehrere experimentelle Versuche gemessen, die mit unterschiedlichen anfänglichen Reaktantenkonzentrationen durchgeführt werden. Der Vergleich der gemessenen Geschwindigkeiten dieser Versuche ermöglicht die Bestimmung der Reaktionsordnungen und anschließend der Geschwindigkeitskonstanten, die zusammen zur Formulierung eines Geschwindigkeitsgesetzes verwendet werden. Die Geschwindigkeit einer Reaktion, beispielsweise von Stickstoffmonoxid mit Ozon [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)], kann aus den experimentellen Daten der Methode der Anfangsgeschwindigkeiten bestimmt werden Labor. <table style="margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="color: black; border: 1px solid black; text-align: center;">  Trial     </td> <td style="color: black; border: 1px solid black; text-align: center;"> [NO] (mol/L)</td> <td style="color: black; border: 1px solid black; text-align: center;">[O3] (mol/L)</td> <td style="color: black; border: 1px solid black; text-align: center;">  Δ[NO2]/Δt (mol/L·s)  </td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">1</td> <td style="color: black; border: 1px solid black; text-align: center;">     1.00 × 10−6      </td> <td style="color: black; border: 1px solid black; text-align: center;">   3.00 × 10−6    </td> <td style="color: black; border: 1px solid black; text-align: center;">    6.60 × 10−5     </td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">2</td> <td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">6.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">1.32 × 10−4</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">3</td> <td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">1.98 × 10−4</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">4</td> <td style="color: black; border: 1px solid black; text-align: center;">2.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">3.96 × 10−4</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">5</td> <td style="color: black; border: 1px solid black; text-align: center;">3.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td> <td style="color: black; border: 1px solid black; text-align: center;">5.94 × 10−4</td> </tr> </tbody> </table> Aus den Tarifdaten ein generisches Tarifgesetz; rate = k[NO]m[O3]n wird formuliert. Die Werte der Reaktionsordnungen m und n sowie die Geschwindigkeitskonstante k werden aus den experimentellen Daten mithilfe eines dreiteiligen Prozesses bestimmt: In Schritt 1 wird der Wert von m aus den Daten bestimmt, bei denen [NO] variiert und [O3] konstant ist. In den Versuchen 3, 4 und 5 variiert [NO], während [O3] konstant bleibt. Wenn sich [NEIN] von Versuch 3 auf 4 verdoppelt, verdoppelt sich die Rate, und wenn sich [NEIN] von Versuch 3 auf 5 verdreifacht, verdreifacht sich auch die Rate. Somit ist die Rate auch direkt proportional zu [NO] und m im Ratengesetz ist gleich 1. In Schritt 2 wird der Wert von n aus Daten bestimmt, bei denen [O3] variiert und [NO] konstant ist. In den Versuchen 1, 2 und 3 ist [NO] konstant und [O3] variiert. Die Reaktionsgeschwindigkeit ändert sich direkt proportional zur Änderung von [O3]. Wenn sich [O3] von Versuch 1 auf 2 verdoppelt, verdoppelt sich die Rate; Wenn sich [O3] von Versuch 1 bis 3 verdreifacht, verdreifacht sich auch die Rate. Somit ist die Rate direkt proportional zu [O3] und n ist gleich 1. Das Geschwindigkeitsgesetz lautet also: Rate = k [NO]1 [O3]1 = k [NO][O3] In Schritt 3 wird der Wert von k aus einem Satz von Konzentrationen (z. B. den Daten aus Versuch 1) und der entsprechenden Rate bestimmt. <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;"> Bei Reaktionen, bei denen die Daten aus der Methode der Anfangsgeschwindigkeiten nicht direkt die Beziehung zwischen Anfangskonzentrationen und Anfangsgeschwindigkeiten implizieren, kann eine Berechnung unter Einbeziehung des Verhältnisses der Geschwindigkeitsgesetze zur Berechnung der Reaktionsordnung und Geschwindigkeitskonstante verwendet werden. Beispielsweise wird das allgemeine Geschwindigkeitsgesetz für die Reaktion 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) wie folgt ausgedrückt: Geschwindigkeit = k [NO]m [Cl2]n. Die Daten aus der Methode der Anfangszinsen sind: <table style="margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="color: black; border: 1px solid black; text-align: center;">  Trial    </td> <td style="color: black; border: 1px solid black; text-align: center;">  [NO] (mol/L)  </td> <td style="color: black; border: 1px solid black; text-align: center;">  [Cl2] (mol/L)  </td> <td style="color: black; border: 1px solid black; text-align: center;">  Initial Rate (mol/L·s)     </td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">1</td> <td style="color: black; border: 1px solid black; text-align: center;">0.10</td> <td style="color: black; border: 1px solid black; text-align: center;">0.10</td> <td style="color: black; border: 1px solid black; text-align: center;">0.00300</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">2</td> <td style="color: black; border: 1px solid black; text-align: center;">0.10</td> <td style="color: black; border: 1px solid black; text-align: center;">0.15</td> <td style="color: black; border: 1px solid black; text-align: center;">0.00450</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">3</td> <td style="color: black; border: 1px solid black; text-align: center;">0.15</td> <td style="color: black; border: 1px solid black; text-align: center;">0.10</td> <td style="color: black; border: 1px solid black; text-align: center;">0.00675</td> </tr> </tbody> </table> Die Werte von m und n können aus den experimentellen Daten mithilfe eines algebraischen Ansatzes bestimmt werden, woraufhin der Wert von k bestimmt wird. In Schritt 1 wird der Wert von m aus den Daten bestimmt, bei denen [NO] variiert und [Cl2] konstant ist. Ein Verhältnis von Geschwindigkeitsgesetzen wird ausgedrückt, indem Daten aus zwei verschiedenen Versuchen (z. B. Versuch 3 und Versuch 1) ersetzt werden. <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;"> In Schritt 2 wird der Wert von n aus Daten bestimmt, bei denen [Cl2] variiert und [NO] konstant ist. <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;"> Unter Verwendung der berechneten Werte von m und n wird das Geschwindigkeitsgesetz ausgedrückt als Rate = k [NO]2 [Cl2]. In Schritt 3 wird der Zahlenwert der Geschwindigkeitskonstante k mit geeigneten Einheiten bestimmt. Die Einheiten für die Geschwindigkeit einer Reaktion sind mol/L·s. Die Einheiten für k werden durch Ersetzen der Einheiten aller anderen Parameter im Geschwindigkeitsgesetz ermittelt. In diesem Beispiel sind die Konzentrationseinheiten mol3/L3. Die Einheiten für k sollten L2/mol2·s sein, sodass die Rate in mol/L·s ausgedrückt wird. Der Wert von k wird bestimmt, sobald der Ausdruck des Geschwindigkeitsgesetzes gelöst wurde, indem einfach die Werte aus einem der experimentellen Versuche (z. B. Versuch 1) ersetzt werden. <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;"> Einheiten für Reaktionsordnung und Geschwindigkeitskonstante Bei einigen Reaktionen stimmen die Reaktionsordnungen im Geschwindigkeitsgesetz zufällig mit den Koeffizienten in der chemischen Gleichung für die Reaktion überein. Dies ist lediglich ein Zufall und sehr oft nicht der Fall. Geschwindigkeitsgesetze können für einige Reaktanten gebrochene Ordnungen aufweisen, und manchmal werden negative Reaktionsordnungen beobachtet, wenn eine Erhöhung der Konzentration eines Reaktanten zu einer Abnahme der Reaktionsgeschwindigkeit führt. Geschwindigkeitsgesetze werden nur durch Experimente bestimmt und können durch die Reaktionsstöchiometrie nicht zuverlässig vorhergesagt werden. Die Einheiten für eine Geschwindigkeitskonstante variieren entsprechend der Gesamtordnung der Reaktion. Die Einheit der Geschwindigkeitskonstante für eine Reaktion nullter Ordnung ist mol/L·s (oder M/s) und die für eine Reaktion erster Ordnung 1/s. Die Einheit der Geschwindigkeitskonstante für eine Reaktion zweiter Ordnung ist L/mol·s (oder 1/M·s) und die für eine Reaktion dritter Ordnung L2/mol2·s. Obwohl die spezifischen Einheiten für Konzentration und Zeit als (mol/L) und (s) angegeben sind, können alle anderen gültigen Einheiten zur Darstellung der Eigenschaften von Konzentration und Zeit verwendet werden. Dieser Text ist adaptiert von <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033">Openstax, Chemistry 2e, Section 12.3: Rate Laws.</a>

Bestimmung der Reaktionsreihenfolge

Geschwindigkeitsgesetze beschreiben das Verhältnis zwischen der Geschwindigkeit einer chemischen Reaktion und der Konzentration ihrer Reaktanten. In einem Geschwindigkeitsgesetz ist die Geschwindigkeitskonstante k und ...

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finding rate law from initial rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change.

One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and, after that, the rate constant. These values are used to write the rate law.

For the reaction of nitric oxide with ozone, NO(g) + O3(g) → NO2(g) + O2(g), the data show how this works in the lab. When [NO] is held constant and [O3] changes, the rate changes in the same way. When [O3] doubles, the rate doubles. When [O3] triples, the rate triples. This shows that the reaction is first order in O3. A similar comparison using trials where [O3] stays constant shows that the rate is also directly proportional to [NO], so the reaction is first order in NO as well. The rate law is therefore rate = k[NO][O3].

In other reactions, the orders are found with an algebraic ratio of rate laws. For the reaction 2 NO(g) + Cl2(g) → 2 NOCl(g), the rate law is written as rate = k[NO]m[Cl2]n. Using the trial data, one step gives m = 2 and another gives n = 1. The rate law becomes rate = k[NO]2[Cl2]. The value of k is then found by using one trial and solving for the constant.

The units of the rate constant depend on the overall order of the reaction. Rate is measured in mol/L·s, and the units for k must match the rate law. For this example, the concentration terms give mol3/L3, so k must have units of L2/mol2·s. In general, a zero-order reaction has k in mol/L·s, a first-order reaction has k in 1/s, a second-order reaction has k in L/mol·s, and a third-order reaction has k in L2/mol2·s.

Reaction order does not always match the coefficients in the balanced equation. That match can happen, but it is only a coincidence. Rate laws can also include fractional orders, and some reactants can have negative orders if a higher concentration lowers the reaction rate. Because of this, rate laws are determined by experiment, not by stoichiometry. Although the examples here use mol/L and s, other valid concentration and time units can also be used.

Finding Rate Law from Initial Rates

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determining order of reaction

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change. One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and,...

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key terms and concepts

Use initial-rate data to find reaction order and the rate constant. Explore examples with NO, ozone, and NOCl, plus how rate constant units change.

Finding Rate Law from Initial Rates | JoVE K12

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Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

Use patterns within the Periodic Table to predict the relative physical and chemical properties of elements.

IPC.7.B

Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Balmer Series

The Bohr Model
Niels Bohr proposed a model for the hydrogen atom in 1913 that described discrete energy states are associated with a fixed electron orbit ...

Beer's Law

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range ...

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Finding Rate Law from Initial Rates

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