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 una reacción química, la ley de velocidad expresa la relación entre la velocidad de reacción y la concentración de reactivo. Los exponentes de las concentraciones de reactivo influyen en la velocidad de reacción individualmente y se denominan órdenes de reacción. El orden de reacción se determina experimentalmente empleando el método de velocidades iniciales, donde una reacción química se repite varias veces con concentraciones de reactivo variables para medir las velocidades de reacción iniciales.Un aumento en la concentración de reactivo, que produce un aumento linealmente proporcional en la velocidad de reacción, caracteriza una reacción de primer orden. Si duplicar la concentración de reactivo cuadriplica la velocidad inicial, entonces se observa una reacción de segundo orden. Sin embargo, si el cambio de las concentraciones de reactivo no afecta los valores de la velocidad inicial, se observa una reacción de orden cero.Cuando los datos obtenidos de las velocidades iniciales presentan una relación indiscernible entre el cambio en la concentración inicial de reactivo y la velocidad correspondiente, se calcula una relación de leyes de velocidad. Aquí, cualesquiera dos valores de concentración del reactivo y sus correspondientes velocidades de reacción se utilizan para determinar el orden de reacción. Pero, qué pasa con las reacciones con múltiples reactivos?Primero, usando el método de velocidades iniciales, se determina individualmente el orden de reacción de cada reactivo. A continuación, los órdenes de reacción individuales se expresan como exponentes de sus respectivas concentraciones de reactivo para formular la ley de velocidad. Por último, la suma de los exponentes individuales de la ley de velocidad determina el orden de reacción general.Si bien el orden de la reacción representa la dependencia de la velocidad de reacción de la concentración de reactivo, la constante de velocidad indica una medida directa de la velocidad de reacción relativa. La constante de velocidad k, es el coeficiente de proporcionalidad que relaciona la velocidad de reacción con el producto de las concentraciones de reactivo. La unidad de una constante de velocidad depende del orden de reacción general y se puede determinar reordenando la ley de velocidad para resolver la constante de velocidad.Para una reacción de orden cero, k tiene la unidad de molaridad por segundo. La unidad para una reacción de primer orden es una sobre segundos, y para una reacción de segundo orden es una sobre molaridad-segundos. Una constante de velocidad grande indica una reacción rápida.Por el contrario, una constante de velocidad menor indica una reacción lenta. Un valor de cero significa la ausencia de reacción química.

determinando el orden de reacción

Las leyes de velocidad describen la relación entre la velocidad de reacción química y la concentración de sus reactivos. En una ley de velocidad, la constante de velocidad k y los órdenes de reacción se determinan experimentalmente observando cómo cambia la velocidad de la reacción a medida que cambian las concentraciones de los reactivos. Un enfoque experimental común para la determinación de las leyes de velocidad es el método de las velocidades iniciales. Este método consiste en medir las velocidades de reacción en múltiples ensayos experimentales realizados utilizando diferentes concentraciones iniciales de reactivos. La comparación de las velocidades medidas para estos ensayos permite determinar los órdenes de reacción y, posteriormente, la constante de velocidad, que en conjunto se utilizan para formular una ley de velocidad.
 La velocidad de una reacción, por ejemplo, que involucra óxido nítrico con ozono [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)] puede determinarse a partir de los datos experimentales del método de las velocidades iniciales, en el laboratorio.
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;"> Prueba     </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 de los datos de velocidad, se una ley general de velocidad; velocidad = k [NO]m [O]3n. Los valores de los órdenes de reacción m y n, y la constante de velocidad k se determinan a partir de los datos experimentales mediante un proceso de tres pasos:
 En el paso 1, el valor de m se determina a partir de los datos en los que [NO] varía y [O3] es constante. En los ensayos 3, 4 y 5, [NO] varía mientras que [O3] permanece constante. Cuando [NO] se duplica de los ensayos 3 al 4, la velocidad se duplica, y cuando [NO] se triplica de los ensayos 3 al 5, la velocidad también se triplica. Por lo tanto, la velocidad también es directamente proporcional a [NO], y m en la ley de velocidad es igual a 1.
 En el paso 2, el valor de n se determina a partir de datos en los que [O3] varía y [NO] es constante. En los ensayos 1,2 y 3, [NO] es constante y [O3] varía. La velocidad de reacción cambia en proporción directa al cambio en [O3]. Cuando [O3] se duplica del ensayo 1 al 2, la velocidad se duplica; cuando [O3] se triplica del ensayo 1 al 3, la velocidad aumenta también tres veces. Así, la velocidad es directamente proporcional a [O3], y n es igual a 1. Por lo tanto, la ley de velocidad es: Velocidad = k [NO]1 [O3]1 =k [NO][O3]
 En el paso 3, el valor de k se determina a partir de un conjunto de concentraciones (por ejemplo, los datos del ensayo 1) y sus correspondientes velocidades.
 <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />
 En las reacciones en las que los datos del método de las velocidades iniciales no implican directamente la relación entre las concentraciones iniciales y las velocidades iniciales, se puede emplear un cálculo que implique la relación de las leyes de velocidad para calcular el orden de reacción y la constante de velocidad.
 Por ejemplo, la ley de velocidad general para la reacción 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) se expresa como: Velocidad = k [NO]m [Cl2]n.
 Los datos del método de las velocidades iniciales son:
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;"> Prueba   </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;"> Velocidad 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>
 Los valores de m y n pueden determinarse a partir de los datos experimentales utilizando un enfoque algebraico, tras el cual el valor de k es determinado.
 En el paso 1, el valor de m se determina a partir de los datos en los que [NO] varía y [Cl2] es constante. Una proporción de leyes de velocidades se expresa sustituyendo los datos de dos ensayos diferentes (por ejemplo, el ensayo 3 y el ensayo 1).
 <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />
 En el paso 2, el valor de n se determina a partir de datos en los que [Cl2] varía y [NO] es constante.
 <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
 Utilizando los valores calculados de m y n, la ley de velocidad se expresa como velocidad = k [NO]2 [Cl2].
 En el paso 3, el valor numérico de la constante de velocidad k es determinado con las unidades apropiadas. Las unidades para la velocidad de una reacción son mol/L·s. Las unidades de k se obtienen sustituyendo las unidades de todos los demás parámetros de la ley de velocidades. En este ejemplo, las unidades de concentración son mol3/L3/sup>. Las unidades para k deben ser de L2/mol2·s de modo que la velocidad sea en términos de mol/L·s. El valor de k se determina una vez que se ha resuelto la expresión de la ley de velocidades, simplemente sustituyendo los valores de cualquiera de los ensayos experimentales (por ejemplo, el ensayo 1).
 <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />
 El orden de reacción y las unidades de la constante de velocidad
 En algunas reacciones, los órdenes de reacción en la ley de velocidad son los mismos que los coeficientes en la ecuación química para la reacción. Esto es simplemente una coincidencia y muy a menudo no es así. Las leyes de velocidad pueden mostrar órdenes fraccionarios para algunos reactivos, y en ocasiones se observan órdenes de reacción negativos cuando un aumento en la concentración de un reactivo provoca una disminución en la velocidad de la reacción. Las leyes de velocidad son determinadas solo experimentalmente y no son predecibles de manera confiable mediante la estequiometría de la reacción.
 Las unidades de una constante de velocidad variarán según corresponda para acomodar el orden general de la reacción. Las unidades de la constante de velocidad para una reacción de orden cero es mol/L·s (o M/s) y la de una reacción de primer orden es 1/s. Las unidades de la constante de velocidad para una reacción de segundo orden es L/mol·s (o 1/M·s) y las de una reacción de tercer orden son L2/mol2·s. Aunque las unidades específicas de concentración y tiempo se indican como (mol/L) y (s), cualquier otra unidad válida puede utilizarse para representar las propiedades de concentración y tiempo.
 Este texto es adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033"> Openstax, Química 2e, Sección 12.3: Leyes de velocidad.</a>

Determinando el Orden de Reacción

Las leyes de velocidad describen la relación entre la velocidad de una reacción química y la concentración de sus reactivos. En una ley de tasas, la constante de tasa k y ...

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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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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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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 ...

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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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