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

IPC.7.F

Determining Order of Reaction

Для химической реакции закон скорости выражает взаимосвязь между скоростью реакции и концентрацией исходного вещества. Показатели концентраций исходных веществ влияют на скорость реакции по отдельности и называются порядками реакции. Порядок реакции определяется экспериментально с использованием метода начальных скоростей, при котором химическая реакция повторяется несколько раз с различными концентрациями исходных веществ для измерения начальных скоростей реакции.Увеличение концентрации исходного вещества, приводящее к линейному пропорциональному увеличению скорости реакции, характеризует реакцию первого порядка. Если удвоение концентрации исходного вещества увеличивает начальную скорость в четыре раза, то перед нами реакция второго порядка. Однако если изменение концентрации исходного вещества не влияет на начальные значения скорости, то перед нами реакция нулевого порядка.Когда полученные данные начальных скоростей показывают неявную зависимость между изменением начальной концентрации исходного вещества и соответствующей скоростью, рассчитывается соотношение законов скорости. Здесь любые два значения концентрации исходных веществ и их соответствующие скорости реакции используются для определения порядка реакции. Но как насчет реакций с несколькими исходными веществами?Сначала отдельно определяется порядок реакции каждого исходного вещества с помощью метода начальных скоростей. Затем отдельные порядки реакций выражаются в показателях их соответствующих концентраций исходных веществ, чтобы сформулировать закон скорости. Наконец, сумма индивидуальных показателей из закона скорости определяет общий порядок реакции.В то время как порядок реакции отображает зависимость скорости реакции от концентрации исходного вещества, прямая мера относительной скорости реакции указывается константой скорости. Константа скорости k представляет собой коэффициент пропорциональности, связывающий скорость реакции с произведением концентраций исходных веществ. Единица измерения константы скорости зависит от общего порядка реакции и может быть определена путем изменения закона скорости, чтобы найти константу скорости.Для реакции нулевого порядка k соответствует единице молярности в секунду. Единица измерения для реакции первого порядка единица, деленная на секунду, а для реакции второго порядка единица, деленная на моль-секунду. Большая константа скорости указывает на быструю реакцию.И наоборот, меньшая константа скорости указывает на медленную реакцию. Нулевое значение означает отсутствие какой-либо химической реакции.

Определение порядка реакции

Законы скорости описывают взаимосвязь между скоростью химической реакции и концентрацией реагентов. В законе о скорости константа скорости k и порядки реакции определяются экспериментально путем наблюдения за изменением скорости реакции по мере изменения концентраций реагенты. Общий экспериментальный подход к определению норм внесения является методом начальных ставок. Этот метод включает в себя измерение скорости реакции для нескольких экспериментальных исследований, проведенных с использованием различных начальных концентраций реагент. Сравнение измеренных ставок для этих испытаний позволяет определить порядок действий и, впоследствии, константу ставок, которая вместе используется для формулирования закона ставок. 
 Скорость реакции, например, с участием оксида азота с озоном [NO (g) + O3 (g) ⟶ NО2 (g) + O2 (g)], может быть определена на основе экспериментальных данных метода начальных скоростей, в лаборатории. 
 <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[NО2]/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>
 From the rate data, a generic rate law; rate = k[NO]m[O3]n is formulated. The values of the reaction orders m and n, and rate constant k are determined from the experimental data using a three-part process:
 In step 1, the value of m is determined from the data in which [NO] varies, and [O3] is constant. In trials 3, 4 and 5, [NO] varies while [O3] remains constant. When [NO] doubles from trial 3 to 4, the rate doubles, and when [NO] triples from trial 3 to 5, the rate also triples. Thus, the rate is also directly proportional to [NO], and m in the rate law is equal to 1.
 In step 2, the value of n is determined from data in which [O3] varies, and [NO] is constant. In trials 1,2 and 3, [NO] is constant and [O3] varies. The reaction rate changes in direct proportion to the change in [O3]. When [O3] doubles from trial 1 to 2, the rate doubles; when [O3] triples from trial 1 to 3, the rate increases also triples. Thus, the rate is directly proportional to [O3], and n is equal to 1. The rate law is thus: rate = k [NO]1 [O3]1 = k [NO][O3]
 In step 3, the value of k is determined from one set of concentrations (for instance, the data from trial 1) and its corresponding rate.
 <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />
 In reactions where the data from the method of initial rates does not directly imply the relation between initial concentrations and initial rates, a calculation involving the ratio of rate laws can be employed to calculate the reaction order and rate constant.
 For example, the general rate law for the reaction 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) is expressed as: rate = k [NO]m [Cl2]n.
 The data from the method of initial rates are:
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;"> Эксперимент   </td>
 <td style="color: black; border: 1px solid black; text-align: center;"> [NO] (моль/л)  </td>
 <td style="color: black; border: 1px solid black; text-align: center;"> [CL2] (моль/л)  </td>
 <td style="color: black; border: 1px solid black; text-align: center;"> Начальная скорость (моль/л·с)     </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>
 Значения m и n могут быть определены на основе экспериментальных данных с помощью алгебраического подхода, после чего определяется значение k. 
 На шаге 1 значение m определяется из данных, в которых изменяется [NO] и [Cl2] является постоянным. Соотношение законов о процентной ставке выражается заменой данных двух разных судебных процессов (например, суд 3 и суд 1). 
 <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />
 На шаге 2 значение n определяется на основании данных, в которых изменяется [Cl2], и [NO] является постоянным. 
 <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
 С помощью вычисленных значений m и n закон нормы выражается как ставка = k [НЕТ]2 [К2]. 
 На шаге 3 числовое значение константы расхода k определяется соответствующими единицами измерения. Единицами измерения скорости реакции являются моль/л. ·Единицы для k заключаются путем замены единиц всех других параметров в законе ставок. В данном примере единицы концентрации — mol3/L3. Единицы измерения k должны быть L2/mol2·s, чтобы скорость была в моль/л. ·Значение k определяется после того, как выражение закона нормы внесения было решено путем простого подстановки значений в ходе любого из экспериментальных испытаний (например, судебного разбирательства 1). 
 <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />
 Порядок реакции и Единицы постоянной скорости 
 В некоторых реакциях порядки реакции в норме нормы происходят так же, как и коэффициенты в химическом уравнении для реакции. Это просто совпадение, и очень часто это не так. Законы о норме могут представлять дробные приказы для некоторых реагенты, а иногда при увеличении концентрации одного реагент происходит снижение скорости реакции. Законы о тарировании определяются только экспериментом и не могут быть надежно предсказаны стехиометрией реакции. 
 Единицы измерения постоянной скорости будут изменяться в зависимости от общего порядка реакции. Единица постоянной скорости для реакции нулевого порядка — моль/л·с (или м/с) и то, что для реакции первого порядка — 1/с. Единица постоянной скорости реакции второго порядка — л/моль·с (или 1/м·с), а для реакции третьего порядка — L2/mol2·с. Хотя конкретные единицы концентрации и времени указаны как (моль/л) и (с), для представления свойств концентрации и времени можно использовать любые другие допустимые единицы. 
 Этот текст был адаптирован к <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033"> Openstax, Chemistry 2e, раздел 12.3: Законы о тарифе. </a>

Законы скорости описывают взаимосвязь между скоростью химической реакции и концентрацией ее реагентов. В законе скорости константа скорости k и ...

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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

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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.

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Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

lewis-structures-of-molecular-compounds-and-polyatomic-ions

Lewis Structures of Molecular Compounds and Polyatomic Ions

To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Dr&#xFC;de called the ...

Model basic atomic structure and relate an element's atomic structure to its bonding, reactivity, and placement on the Periodic Table.

IPC.7.A

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

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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