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

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

Determining Order of Reaction

化学反応の場合、速度の法則は反応速度と反応物濃度の関係を表します。反応物濃度の指数は、反応速度に個別に影響し、反応順序と呼ばれます。
反応順序は、反応物濃度を変えて化学反応を複数回繰り返す初期反応速度の方法を用いて実験的に決定します。
反応物濃度の増加は、反応速度の線形比例の増加をもたらし、一次反応を特徴付けます。反応物濃度を2倍にすると初期速度が4倍になると、2次反応が観察されます。
ただし、反応物濃度の変化が初期速度値に影響を与えない場合は、ゼロ次反応が観察されます。
得られた初期速度のデータが、初期反応物濃度の変化と対応する速度との間に識別できない関係を示している場合、速度法則の比率が計算されます。
ここでは、反応物の任意の2つの濃度値とそれに対応する反応速度を使用して、反応順序を決定します。
しかし、複数の反応物との反応についてはどうでしょうか?まず、初期速度の方法を使用して、各反応物の反応順序を個別に決定します。
次に、個々の反応順序をそれぞれの反応物濃度の指数として表し、速度法則を定式化します。最後に、レート法則からの個々の指数の合計が全体的な反応順序を決定します。
反応順序は反応速度の反応物濃度依存性を示していますが、相対反応速度の直接的な尺度は速度定数によって示されます。
速度定数kは、反応速度を反応物濃度の積に関連付ける比例係数です。
速度定数の単位は、全体的な反応順序に依存し、速度定数を解くために速度則を並べ替えることによって決定できます。ゼロ次反応の場合、k は単位モル濃度/秒です。単位は1次反応の1/s、2次反応の単位は1/M・sです。
レート定数が大きいほど、反応が速いことを示します。逆に、レート定数が小さいほど、反応が遅いことを示します。値が 0 の場合は、化学反応がないことを示します。

反応順序の決定

反応速度式は、化学反応の速度とその反応物の濃度との関係を表します。反応速度式では、反応物の濃度を変化させたときに反応速度がどのように変化するかを観察することで、速度定数kと反応次数を実験的に決定します。反応速度式を決定するための一般的な実験手法は、初期速度を用いる方法です。この方法では、異なる初期反応物濃度を用いて実施された複数の実験の反応速度を測定します。これらの実験で測定された反応速度を比較することで、反応次数とそれに続く速度定数を決定することができ、これらを組み合わせて反応速度式を求めることができます。
 例えば、一酸化窒素とオゾンを含む反応[NO(g) + O3 (g) ⟶ NO2 (g) + O2 (g)]の速度は、実験室での初期速度の測定法  の実験データから求めることができます。
 <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>
 この速度データから、一般的な速度則（rate = k[NO]m[O3]n）が定式化されます。反応次数mとnの値、および速度定数kの値は、3つの部分からなるプロセスを用いて実験データから決定されます。
 ステップ1: [NO]が変化し、[O3]が一定であるデータからmの値を決定します。試行3, 4, 5では、[NO]は変化し、[O3]は一定です。試行3から4で[NO]が2倍になると速度は2倍になり、試行3から5で[NO]が3倍になると速度も3倍になります。このように、速度は[NO]にも正比例し、速度則のmは1になります。
 ステップ2: [O3]を変化させ、[NO]を一定にしたデータからnの値を決定します。試行1,2,3では、[NO]は一定で、[O3]が変化します。反応速度は[O3]の変化に正比例して変化します。試行1から試行2で[O3]が2倍になると、速度は2倍になり、試行1から試行3で[O3]が3倍になると、速度の増加も3倍になります。したがって、速度は[O3]に正比例し、nは1になります。反応速度式は次のようになります。 rate = k [NO]1 [O3]1 = k [NO][O3]
 ステップ3: 1セットの濃度（例えば、試行1のデータ）とそれに対応する反応速度からkの値を決定します。
 <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />
 初期速度法のデータが、初期濃度と初期速度の関係を直接示唆しない反応では、反応速度式の比を含む計算を用いて、反応次数と速度定数を算出することができます。
 例えば、次のような反応の速度式は右記のように表すことが出来ます。 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g): 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;">  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>
 実験データからmとnの値を代数的なアプローチで求め、それに続いてkの値を決定することができます。
 ステップ1: [NO]が変化し、[Cl2]が一定であるデータからmの値を決定します。2つの異なる試行（例えば試行3と試行1）のデータを代入することで、速度則の比を表します。
 <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />
 ステップ2: [Cl2]が変化し、[NO]が一定であるデータからnの値を決定します。
 <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
 計算されたmとnの値を用いて、反応速度式は、rate = k [NO]2 [Cl2]と表されます。
 ステップ3: 速度定数kの数値を適切な単位で決定します。反応の速度の単位はmol/L·sです。kの単位は、速度則の他のすべてのパラメータの単位を代入することで求められます。この例では、濃度の単位はmol3/L3です。kの単位はL2/mol2·sとし、速度がmol/L·sの単位になるようにします。kの値は、速度則の式を解いた後、任意の実験試行（例えば試行1）の値を代入するだけで決定されます。
 <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />
 反応次数と速度定数の単位
 一部の反応では、反応速度式の反応次数が、たまたまその反応の化学式の係数と同じになることがあります。これは単なる偶然であり、実際にはそうでないことが非常に多いです。また、反応速度則には、一部の反応物について分数の次数が得られることがあり、1つの反応物の濃度が増加すると反応速度が低下する場合には、負の反応次数が観察されることもあります。反応速度は実験によってのみ決定され、反応の化学量論では確実に予測できません。
 速度定数の単位は、反応の全体的な順序に合わせて適宜変更します。0次反応の速度定数の単位はmol/L·s（またはM/s）、1次反応の速度定数の単位は1/sとします。2次反応の速度定数の単位はL/mol·s（または1/M·s）、3次反応の速度定数の単位はL2/mol2·sです。濃度と時間の具体的な単位は（mol/L）と（s）で示されていますが、濃度と時間の特性を表す単位は他にも有効なものがあります。
 上記の文章は以下から引用しました。<a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033">Openstax, Chemistry 2e, Section 12.3: Rate Laws.</a>

レートの法則は、化学反応の速度とその反応物の濃度との関係を記述します。レートの法則では、レート定数 k と ...

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Chemical Kinetics

化学反応速度論

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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.

Finding Rate Law from Initial Rates | JoVE K12

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JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

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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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