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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Determining Order of Reaction

Voor een chemische reactie drukt de snelheidswet de relatie uit tussen de reactiesnelheid en de reactantconcentratie. De exponenten van de reactantconcentraties beïnvloeden de reactiesnelheid individueel en worden reactieorden genoemd. De reactieorde wordt experimenteel bepaald door de methode van beginsnelheden toe te passen, waarbij een chemische reactie meerdere keren wordt herhaald met verschillende reactantconcentraties om de aanvankelijke reactiesnelheden te meten.Een toename van de reactantconcentratie, waardoor een lineair evenredige toename van de reactiesnelheid ontstaat, kenmerkt een eerste orde reactie. Als een verdubbeling van de reactantconcentratie de beginsnelheid verviervoudigt, wordt een reactie van de tweede orde waargenomen. Als de verandering van reactantconcentraties echter geen invloed heeft op de aanvankelijke snelheidswaarden, wordt een nulde-orde reactie waargenomen.Wanneer de verkregen gegevens van beginsnelheden een onwaarneembare relatie vertonen tussen de verandering in de initiële reactantconcentratie en de overeenkomstige snelheid, wordt een verhouding van snelheidswetten berekend. Hier worden twee willekeurige concentratiewaarden van de reactant en hun overeenkomstige reactiesnelheden gebruikt om de reactie-orde te bepalen. Maar hoe zit het met reacties met meerdere reactanten?Ten eerste wordt met behulp van de methode van beginsnelheden de reactieorde van elke reactant afzonderlijk bepaald. Vervolgens worden de individuele reactie-orden uitgedrukt als exponenten van hun respectievelijke reactantconcentraties om de snelheidswet te formuleren. Ten slotte bepaalt de optelling van individuele exponenten uit de snelheidswet de algehele reactieorde.Terwijl de reactieorde de afhankelijkheid van de reactiesnelheid van de reactantconcentratie weergeeft, wordt een directe maat voor de relatieve reactiesnelheid aangegeven door de snelheidsconstante. De snelheidsconstante k is de evenredigheidscoëfficiënt die de reactiesnelheid relateert aan het product van reactantconcentraties. De eenheid van een snelheidsconstante hangt af van de algehele reactie-orde en kan worden bepaald door de snelheidswet te herschikken om de snelheidsconstante op te lossen.Voor een nulde-orde-reactie heeft k de eenheid molariteit per seconde. De eenheid voor een eerste-orde-reactie is één gedeeld door seconden, en voor een tweede-orde-reactie is één gedeeld door molariteit-seconden. Een grote snelheidsconstante duidt op een snelle reactie.Omgekeerd duidt een kleinere snelheidsconstante op een langzame reactie. Een waarde van nul betekent dat er geen chemische reactie is.

volgorde van reactie bepalen

Snelheidswetten beschrijven de relatie tussen de snelheid van een chemische reactie en de concentratie van de reactanten. In een snelheidswet worden de snelheidsconstante k en de reactievolgorde experimenteel bepaald door te observeren hoe de reactiesnelheid verandert naarmate de concentraties van de reactanten veranderen. Een gebruikelijke experimentele benadering voor het bepalen van snelheidswetten is de methode van initiële reactiesnelheden. Deze methode omvat het meten van de reactiesnelheden voor meerdere experimentele onderzoeken die worden uitgevoerd met verschillende initiële concentraties van reactanten. Door de gemeten snelheden voor deze proeven te vergelijken, kunnen de reactievolgordes en vervolgens de snelheidsconstante worden bepaald, die samen worden gebruikt om een snelheidswet te formuleren. 

 De snelheid van een reactie waarbij bijvoorbeeld stikstofmonoxide betrokken is met ozon [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)] kan worden bepaald op basis van de experimentele gegevens van de methode van initiële snelheden, in de laboratorium. 

 <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> 

 Uit de snelheidsgegevens blijkt een generieke snelheidswet; snelheid = k[NO]m[O3]n wordt geformuleerd. De waarden van de reactieorden m en n, en snelheidsconstante k worden bepaald op basis van de experimentele gegevens met behulp van een driedelig proces: 

 In stap 1 wordt de waarde van m bepaald op basis van de gegevens waarin [NO] varieert en [O3] constant is. In de proeven 3, 4 en 5 varieert [NO] terwijl [O3] constant blijft. Wanneer [NO] verdubbelt van proef 3 naar 4, verdubbelt de reactiesnelheid, en wanneer [NO] verdrievoudigt van proef 3 naar 5, verdrievoudigt de reactiesnelheid ook. de ssnelheid is dus ook rechtevenredig met [NO], en m in de snelheidswet is gelijk aan 1. 

 In stap 2 wordt de waarde van n bepaald op basis van gegevens waarin [O3] varieert en [NO] constant is. In de proeven 1,2 en 3 is [NO] constant en varieert [O3]. De reactiesnelheid verandert in directe verhouding tot de verandering in [O3]. Wanneer [O3] verdubbelt van proef 1 naar 2, verdubbelt de snelheid; wanneer [O3] verdrievoudigt van proef 1 naar 3, verdrievoudigt de snelheid ook. De reactiesnelheid is dus recht evenredig met [O3], en n is gelijk aan 1. De snelheidswet is dus: reactiesnelheid = k [NO]1 [O3]1 = k [NO][O3] In stap 3 wordt de waarde van k bepaald op basis van één reeks concentraties (bijvoorbeeld de gegevens van proef 1) en de bijbehorende snelheid. <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;"> Bij reacties waarbij de gegevens uit de methode van initiële snelheden niet direct de relatie tussen initiële concentraties en initiële snelheden impliceren, kan een berekening met betrekking tot de verhouding van snelheidswetten worden gebruikt om de reactievolgorde en snelheidsconstante te berekenen. De algemene snelheidswet voor de reactie 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) wordt bijvoorbeeld uitgedrukt als: snelheid = k [NO]m [Cl2]n. De gegevens uit de methode van initiële tarieven zijn: <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> De waarden van m en n kunnen worden bepaald uit de experimentele gegevens met behulp van een algebraïsche benadering, waarna de waarde van k wordt bepaald. In stap 1 wordt de waarde van m bepaald uit de gegevens waarin [NO] varieert en [Cl2] constant is. Een verhouding van snelheidswetten wordt uitgedrukt door gegevens uit twee verschillende onderzoeken te vervangen (bijvoorbeeld proef 3 en proef 1). <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;"> In stap 2 wordt de waarde van n bepaald op basis van gegevens waarin [Cl2] varieert en [NO] constant is. <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;"> Met behulp van de berekende waarden van m en n wordt de snelheidswet uitgedrukt als snelheid = k [NO]2 [Cl2]. In stap 3 wordt de numerieke waarde van de snelheidsconstante k bepaald met geschikte eenheden. De eenheden voor de snelheid van een reactie zijn mol/L·s. De eenheden voor k worden geconcludeerd door de eenheden van alle andere parameters in de snelheidswet te vervangen. In dit voorbeeld zijn de concentratie-eenheden mol3/L3. De eenheden voor k moeten L2/mol2·s zijn, zodat de snelheid uitgedrukt wordt in mol/L·s. De waarde van k wordt bepaald zodra de uitdrukking van de snelheidswet is opgelost, door eenvoudigweg de waarden uit een van de experimentele proeven te vervangen (bijvoorbeeld proef 1). <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;"> Reactievolgorde en snelheidsconstante-eenheden Bij sommige reacties zijn de reactievolgordes in de snelheidswet hetzelfde als de coëfficiënten in de chemische vergelijking voor de reactie. Dit is slechts toeval en is vaak niet het geval. Snelheidswetten kunnen voor sommige reactanten fractionele ordes vertonen, en soms worden negatieve reactievolgordes waargenomen wanneer een toename van de concentratie van één reactant een afname van de reactiesnelheid veroorzaakt. Snelheidswetten worden alleen experimenteel bepaald en worden niet betrouwbaar voorspeld door reactie-stoichiometrie. De eenheden voor een snelheidsconstante zullen naar behoefte variëren om tegemoet te komen aan de algehele volgorde van de reactie. De eenheid van de snelheidsconstante voor een reactie van de nulde orde is mol/L·s (of M/s) en die voor een reactie van de eerste orde is 1/s. De eenheid van de snelheidsconstante voor een reactie van de tweede orde is L/mol·s (of 1/M·s) en die voor een reactie van de derde orde is L2/mol2·s. Hoewel de specifieke eenheden voor concentratie en tijd worden aangegeven als (mol/L) en (s), kunnen alle andere geldige eenheden worden gebruikt om de eigenschappen van concentratie en tijd weer te geven.

Volgorde van reactie bepalen

Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and ...

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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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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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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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