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

Para uma reação de produto químico, a lei das taxas exprime a relação entre a taxa de reação e concentração de reagentes. Os expoentes de concentrações de reagentes influenciam a taxa de reação individualmente e são chamadas ordens de reação. A ordem de reação é determinada experimentalmente empregando o método de taxas iniciais, em que para um produto químico, a reação é repetida múltiplas vezes com reagente variável concentrações a medir as taxas de reação inicial.Um aumento na concentração do reagente, produzindo um aumento linearmente proporcional na taxa de reação, caracteriza uma reação de primeira ordem. Se duplicar a concentração do reagente quadruplica a taxa inicial, depois uma reação de segunda ordem é observada. No entanto, se a mudança de concentrações de reagentes não afeta os valores iniciais da taxa, depois uma reação de ordem zero é observada.Quando os dados obtidos das taxas iniciais apresentam uma relação indiscernível entre a mudança no reagente inicial da concentração e a taxa correspondente, um rácio de leis de taxa é calculado. Aqui, quaisquer dois valores de concentração do reagente e das suas taxas de reação correspondentes são utilizados para determinar a ordem de reação. Mas e as reações com reagentes múltiplos, em primeiro lugar, utilizando o método das taxas iniciais, a ordem de reação de cada reagente é determinada individualmente.A seguir, as ordens individuais da reação são expressas como expoentes ao seu respetivo reagente de concentrações para formular a lei das taxas. Finalmente, a soma de expoentes individuais a partir da lei das taxas determina a ordem de reação global. Enquanto a ordem de reação retrata a dependência da taxa de reação sobre a concentração do reagente, uma medida direta da velocidade derivada da reação é indicada pela constante da taxa.A taxa constante k, é o coeficiente de proporcionalidade relacionando a taxa de reação para o produto de concentrações de reagentes. A unidade de uma constante da taxa depende da ordem reação global e pode ser determinada rearranjando a lei das taxas para resolver para a taxa constante. Para uma reação de ordem zero, k tem a molaridade da unidade por segundo.A unidade para uma primeira ordem de reação é de um segundo a mais, e para uma reação de segunda ordem é a molaridade por segundos. Uma grande constante de taxa indica uma reação rápida. Em contrapartida, uma menor constante de taxa indica uma reação lenta.Um valor de zero significa a ausência de qualquer reação química.

determinação da ordem de reação

As leis de velocidade descrevem a relação entre a velocidade de uma reação química e a concentração dos seus reagentes. Em uma lei de velocidade, a constante de velocidade k e as ordens de reação são determinadas experimentalmente observando como a velocidade de reação muda à medida que as concentrações dos reagentes são alteradas. Uma abordagem experimental comum para a determinação das leis de velocidade é o método das velocidades iniciais. Este método envolve a medição das velocidades de reação para ensaios experimentais múltiplos efetuados com diferentes concentrações iniciais de reagentes. A comparação das velocidades medidas para estes ensaios permite determinar as ordens de reação e, posteriormente, a constante da velocidade, que em conjunto são utilizadas para formular uma lei de velocidade.
A velocidade de uma reação, por exemplo, envolvendo óxido nítrico com ozono [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)] pode ser determinada a partir dos dados experimentais do método das velocidades iniciais , no laboratório.
<table style="margin-left: auto; margin-right: auto;">
<tbody>
<tr>
<td style="color: black; border: 1px solid black; text-align: center;">  Teste     </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>
A partir dos dados de velocidade, é formulada uma lei de velocidade genérica; velocidade = k[NO]m[O3]n. Os valores das ordens de reação m e n e da constante de velocidade k são determinados a partir dos dados experimentais, utilizando um processo de três passos:
No passo 1, o valor de m é determinado a partir dos dados onde [NO] varia e [O3] é constante. Nos testes 3, 4 e 5, [NO] varia enquanto que [O3] permanece constante. Quando [NO] duplica do teste 3 para o 4, a velocidade duplica, e quando [NO] triplica do teste 3 para o 5, a velocidade também triplica. Assim, a velocidade também é diretamente proporcional a [NO], e m na lei de velocidade é igual a 1.
No passo 2, o valor de n é determinado a partir dos dados onde [O3] varia e [NO] é constante. Nos testes 1,2 e 3, [NO] é constante e [O3] varia. A velocidade de reação muda na proporção direta à mudança de [O3]. Quando [O3] duplica do teste 1 para o 2, a velocidade duplica; quando [O3] triplica do teste 1 para o 3, o aumento da velocidade também triplica. Assim, a velocidade é diretamente proporcional a [O3], e n é igual a 1. A lei de velocidade é portanto: velocidade = k [NO]1 [O3]1 = k [NO][O3]
No passo 3, o valor de k é determinado a partir de um conjunto de concentrações (por exemplo, os dados do ensaio 1) e da sua velocidade correspondente.
<img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />
Nas reações em que os dados do método das velocidades iniciais não impliquem diretamente a relação entre as concentrações iniciais e as velocidades iniciais, pode ser utilizado um cálculo que envolve a relação das leis de velocidade para calcular a ordem de reação e a constante de velocidade.
Por exemplo, a lei de velocidade geral para a reação 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) é expressa como: velocidade = k [NO]m [Cl2]n
Os dados do método das velocidades iniciais são:
<table style="margin-left: auto; margin-right: auto;">
<tbody>
<tr>
<td style="color: black; border: 1px solid black; text-align: center;">  Teste    </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;">  Velocidade Inicial (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>
Os valores de m e n podem ser determinados a partir dos dados experimentais utilizando uma abordagem algébrica, após a qual o valor de k é determinado.
No passo 1, o valor de m é determinado a partir dos dados onde [NO] varia e [Cl2] é constante. Uma relação de leis de velocidade é expressa substituindo os dados de dois testes diferentes (por exemplo, o teste 3 e o teste 1).
<img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />
No passo 2, o valor de n é determinado a partir dos dados onde [Cl2] varia e [NO] é constante.
<img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
Usando os valores calculados de m e n a lei de velocidade é expressa como velocidade = k [NO]2 [Cl2].
No passo 3, o valor numérico da constante de velocidade k é determinado com unidades apropriadas. As unidades para a velocidade de uma reação são mol/L·s. As unidades para k são concluídas substituindo as unidades de todos os outros parâmetros na lei de velocidade. Neste exemplo, as unidades de concentração são mol3/L3. As unidades para k devem ser L2/mol2·s de modo a que a velocidade esteja em mol/L·s. O valor de k é determinado assim que a expressão da lei de velocidade tiver sido resolvida, simplesmente substituindo os valores de qualquer um dos testes experimentais (por exemplo, teste 1).
<img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />
Unidades de Ordem de Reação e Constante de Velocidade
Em algumas reações, as ordens de reação na lei da velocidade são as mesmas que os coeficientes na equação química para a reação. Isto é apenas uma coincidência e muitas vezes não é o caso. As leis de velocidade podem apresentar ordens fracionárias para alguns reagentes, e ordens de reação negativas são às vezes observadas quando um aumento na concentração de um reagente causa uma diminuição na velocidade de reação. As leis de velocidade são determinadas apenas por experiências e não são previstas de forma confiável pela estequiometria da reação.
As unidades para uma constante de velocidade irão variar conforme apropriado para acomodar a ordem geral da reação. A unidade da constante de velocidade para uma reação de ordem zero é mol/L·s (ou M/s) e para uma reação de primeira ordem é 1/s. A unidade da constante de velocidade para uma reação de segunda ordem é L/mol·s (ou 1/M·s) e para uma reação de terceira ordem é L2/mol2·s. Embora as unidades específicas de concentração e tempo sejam indicadas como (mol/L) e (s), podem ser utilizadas quaisquer outras unidades válidas para representar as propriedades de concentração e tempo.
Este texto é adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033">Openstax, Chemistry 2e, Section 12.3: Rate Laws.</a>

Determinação da Ordem de Reação

As leis de taxa descrevem a relação entre a taxa de uma reação química e a concentração de seus reagentes. Em uma lei de taxa, a constante de taxa k e ...

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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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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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