Name: estimating equilibrium with small changes
Uploaded: 2020-10-19T09:47:37.000Z
Duration: 2 min 20 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

The Small x Assumption

Die kleine x-Annahme ist eine Näherung, die unter bestimmten Bedingungen verwendet werden kann, um die Lösung des Gleichgewichtsausdrucks zu vereinfachen und die Verwendung der quadratischen Formel zu vermeiden. 
Wenn die Gleichgewichtskonstante für eine Reaktion klein ist und die Anfangskonzentrationen der Reaktanten ausreichend hoch sind, ist es möglich, dass nur eine kleine Menge der Reaktanten in Produkte umgewandelt wird.
Wenn diese Bedingungen erfüllt sind, können die Gleichgewichtskonzentrationen angenähert werden, wobei davon ausgegangen wird, dass die Änderung der Anfangskonzentrationen vernachlässigbar ist. Es muss jedoch bestätigt werden, dass die Änderung der Konzentration x weniger als 5 % der ursprünglichen Konzentrationen beträgt, um zu zeigen, dass die Annahme gültig war.
Bei der Zersetzung von 0,66 molaren Carbonyldichloridgas entstehen Kohlenmonoxid und Chlorgas, und die Gleichgewichtskonstante für diese Reaktion beträgt 2,2 × 10-10.
Zur Berechnung der Gleichgewichtskonzentrationen werden die Werte in der ICE-Tabelle zusammen mit den Änderungs- und Gleichgewichtskonzentrationen tabellarisch dargestellt.
Setzt man die Gleichgewichtskonzentrationen im Ausdruck ein, so ist K gleich x zum Quadrat dividiert durch 0,66 minus x. Da K sehr klein ist, ist davon auszugehen, dass die Änderung der Anfangskonzentration x von Carbonyldichlorid vernachlässigbar ist.
Daher kann 0,66 minus x auf 0,66 angenähert werden. Wenn gelöst, entspricht x 1,2 × 10−5 molaren.
Hier beträgt x nur 0,0018 Prozent der anfänglichen molaren Konzentration von 0,66 molaren Carbonyldichlorid, was weit unter dem zulässigen Maximum von 5 % liegt. Somit gilt hier die kleine x-Annahme.
Unter Verwendung des Wertes für x in der ICE-Tabelle beträgt die Gleichgewichtskonzentration von Carbonyldichlorid immer noch 0,66 molar mit signifikanten Werten, während die Konzentrationen von Kohlenmonoxid und Chlor beide 1,2 × 10-5 molar betragen.

<ol>
	<li>Lim, Kieran F. "Verwendung von Grafikrechnern und Tabellenkalkulationen in der Chemie: Lösung von Gleichgewichtsproblemen." Zeitschrift für chemische Bildung 85, Nr. 10 (2008): 1347. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed085p1347">https://pubs.acs.org/doi/pdf/10.1021/ed085p1347</a></li>
</ol>

die kleine x-annahme

Wenn eine Reaktion eine kleine Gleichgewichtskonstante aufweist, begünstigt die Gleichgewichtslage die Reaktanten. Bei solchen Reaktionen kann eine vernachlässigbare Konzentrationsänderung auftreten, wenn die anfänglichen Konzentrationen der Reaktanten hoch und der K_c-Wert klein ist. Unter solchen Umständen entspricht die Gleichgewichtskonzentration ungefähr ihrer Anfangskonzentration. Diese Schätzung kann zur Vereinfachung der Gleichgewichtsberechnungen verwendet werden, indem angenommen wird, dass einige Gleichgewichtskonzentrationen gleich den Anfangskonzentrationen sind. Um diese Annahme zu treffen, muss jedoch die Änderung der Konzentration einer schwachen Säure oder Base, d. h. x, weniger als 5 % ihrer Anfangskonzentration betragen. Wenn x mehr als 5 % beträgt, muss zur Lösung der Gleichgewichtsgleichung die quadratische Formel verwendet werden. Berechnung von Gleichgewichtskonzentrationen unter Verwendung einer algebraisch vereinfachenden Annahme Wie hoch sind die Gleichgewichtskonzentrationen einer 0,15 M HCN-Lösung? <img alt="Eq1" src="/files/ftp_upload/11477/11477_Equation_1.png" style="text-align: center; height: 50px;"> Wenn man x verwendet, um die Konzentration jedes Produkts im Gleichgewicht darzustellen, erhält man diese ICE-Tabelle. <table style="margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="color: black; border: 1px solid black; text-align: center;"></td> <td style="color: black; border: 1px solid black; text-align: center;"> HCN (aq)           </td> <td style="color: black; border: 1px solid black; text-align: center;">H+ (aq)</td> <td style="color: black; border: 1px solid black; text-align: center;">CN− (aq)</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Anfangskonzentration (M)</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</td> <td style="color: black; border: 1px solid black; text-align: center;">0</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Änderung (M)</td> <td style="color: black; border: 1px solid black; text-align: center;">−x</td> <td style="color: black; border: 1px solid black; text-align: center;">+x</td> <td style="color: black; border: 1px solid black; text-align: center;">+x</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Gleichgewichtskonzentration (M)</td> <td style="color: black; border: 1px solid black; text-align: center;">0,15 − x</td> <td style="color: black; border: 1px solid black; text-align: center;">x</td> <td style="color: black; border: 1px solid black; text-align: center;">x</td> </tr> </tbody> </table> Ersetzen Sie die Gleichgewichtskonzentrationsterme in den Kc Ausdruck <img alt="Eq2" src="/files/ftp_upload/11477/11477_Equation_2.png" style="text-align: center; height: 95px;"> Ordnen Sie es in die quadratische Form um und lösen Sie nach x auf <img alt="Eq3" src="/files/ftp_upload/11477/11477_Equation_3.png" style="text-align: center; height: 95px;"> Somit ist [H+] = [CN–] = x = 8,6 × 10–6 M und [HCN] = 0,15 – x = 0,15 M. Beachten Sie in diesem Fall, dass die Konzentrationsänderung deutlich geringer ist als die Anfangskonzentration (eine Folge des kleinen K), und die Anfangskonzentration sich daher nur geringfügig ändert: <img alt="Eq4" src="/files/ftp_upload/11477/11477_Equation_4.png" style="text-align: center; height: 50px;"> Diese Näherung ermöglicht einen zweckmäßigeren mathematischen Ansatz für die Berechnung, der die Suche nach den Wurzeln einer quadratischen Gleichung vermeidet: <img alt="Eq5" src="/files/ftp_upload/11477/11477_Equation_5.png" style="text-align: center; height: 135px;"> Der berechnete Wert von x ist tatsächlich viel kleiner als die Anfangskonzentration <img alt="Eq6" src="/files/ftp_upload/11477/11477_Equation_6.png" style="text-align: center; height: 50px;"> und so war die Annäherung gerechtfertigt. Sollte dieser vereinfachte Ansatz einen Wert für x ergeben, der die Näherung nicht rechtfertigt, müsste die Berechnung ohne Durchführung der Näherung wiederholt werden. Dieser Text wurde angepasst von <a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">Openstax, Chemistry 2e, Section 13.4 Equilibrium Calculations</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a>

Die kleine x-Annahme

Wenn eine Reaktion eine kleine Gleichgewichtskonstante hat, begünstigt die Gleichgewichtsposition die Reaktanten. Bei solchen Reaktionen kann eine vernachlässigbare Konzentrationsänderung ...

Education

Lehre

JoVE Core

Chemie

Eins

Chemical Equilibrium

Chemisches Gleichgewicht

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

estimating equilibrium with small changes

A small equilibrium constant can make equilibrium calculations easier. In these reactions, the equilibrium position favors the reactants. When the initial reactant concentration is high and the Kc value is small, the change in concentration may be negligible. In that case, the equilibrium concentration is close to the initial concentration.

This idea helps simplify weak acid and weak base problems. Chemists can assume that some equilibrium concentrations are equal to the initial concentrations. The change in concentration is written as x. To use the shortcut, x must be less than 5% of the initial concentration. If x is greater than 5%, the quadratic formula is needed instead.

A solution of HCN shows how the approximation works. For a 0.15 M HCN solution, an ICE table gives HCN, H+, and CN− with initial concentrations of 0.15, 0, and 0 M. The change is −x for HCN and +x for each product, so the equilibrium concentrations are 0.15 − x, x, and x. Substituting these terms into the Kc expression and solving gives [H+] = [CN−] = 8.6 × 10−6 M and [HCN] = 0.15 M.

In this example, the calculated x is much smaller than the initial concentration. That means the initial HCN concentration changes very little. The shortcut is justified, and the calculation avoids solving a quadratic equation. If the result had not met the 5% rule, the calculation would need to be repeated without the approximation.

Estimating Equilibrium with Small Changes

estimating-equilibrium-with-small-changes

the equilibrium constant

Chemical Equilibrium and Kc Rules

Chemical equilibrium and the equilibrium constant Kc describe how reactants and products are balanced in a reaction. In the oxidation of sulfur dioxide, a mixture that starts with reactants only has no product at first. As the reaction moves forward toward equilibrium, reactant concentrations decrease and product concentration increases. When equilibrium is reached, the concentrations of both stay constant. A reaction can also begin with only products present. In that case, the reaction moves...

le chatelier's principle: changing concentration

le-chatelier-s-principle-changing-concentration

Shifting Equilibrium by Changing Concentration

Chemical equilibrium is a dynamic balance. At equilibrium, the forward and reverse reactions happen at equal rates. If the system is stressed in a way that changes one rate more than the other, it is no longer at equilibrium and will shift until balance is restored. This behavior is described by Le Châtelier’s principle. Changes in concentration are a major stress on an equilibrium system. Reaction rates depend mainly on concentration and temperature. For that reason, changing the amount of a...

homogeneous equilibria for gaseous reactions

homogeneous-equilibria-for-gaseous-reactions

Relating Kc and Kp in Gas Equilibria

Gas-phase equilibrium can be written using either concentration or pressure. The equilibrium constant may be shown as Kc, which uses molar concentration, or as Kp, which uses partial pressure of the reactants and products. The link between Kc and Kp comes from the ideal gas equation and the definition of molarity. Molarity is the number of moles divided by volume. In the ideal gas equation, P stands for partial pressure, V for volume, n for number of moles, R for the gas constant, and T for...

calculating the equilibrium constant

Finding Kc from Equilibrium Data

The equilibrium constant, Kc, can be found from the equilibrium concentrations of reactants and products. When those concentrations are known, the calculation is straightforward. The values are placed into the Kc expression for the reaction. One example uses nitrogen dioxide and dinitrogen tetroxide. When 0.10 mol NO2 is added to a 1.0-L flask at 25 °C, the concentrations change until equilibrium is reached. At equilibrium, [NO2] is 0.016 M and [N2O4] is 0.042 M, and these values are used to...

reaction quotient

Using Q to Track Equilibrium Changes

Reaction quotient Q helps track how far a reversible reaction has moved toward equilibrium. For a balanced reaction such as m A + n B ⇌ x C + y D, Q comes directly from the stoichiometric coefficients in the equation. When concentrations are used, the expression is written as Qc. For gases, a similar form uses partial pressures. These expressions use relative concentration and pressure values, not absolute values. That means reaction quotients are dimensionless and have no units. As a reaction...

dynamic equilibrium

Chemical Equilibrium in Reversible Reactions

Chemical equilibrium in reversible reactions happens when a reaction moves in both directions at the same time. A reversible reaction uses a double arrow to show that products can turn back into reactants. At equilibrium, the concentrations of reactants and products stay constant over time because the forward and reverse reaction rates are equal. The video uses the reversible decomposition of colorless dinitrogen tetroxide to brown nitrogen dioxide as an example. At time zero, there is finite...

calculating equilibrium concentrations

Equilibrium Concentrations from an ICE Table

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic...

le chatelier's principle: changing volume (pressure)

le-chatelier-s-principle-changing-volume-pressure

Gas Equilibrium Under Volume Changes

Gas-phase equilibrium can shift when the volume of the system changes. In these reactions, a change in pressure changes concentration because the partial pressure of an ideal gas is proportional to its molar concentration. That means pressure changes affect equilibrium in the same way as concentration changes. When the volume of a gas mixture changes, the concentrations of reactants and products change together. Since every gas in the equilibrium occupies the same space, the same volume change...

le chatelier's principle: changing temperature

le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle in Heating and Cooling

Le Chatelier's principle helps explain how chemical equilibrium responds to heating and cooling. A system at equilibrium will shift to restore balance after a temperature change, but the equilibrium constant, K, will not stay the same. Instead, the mixture reaches a new equilibrium with a different composition. This temperature effect is different from a concentration change, which shifts equilibrium without changing K. To understand why temperature matters, the reaction can be written with...

the small x assumption

A small equilibrium constant can make equilibrium calculations easier. In these reactions, the equilibrium position favors the reactants. When the initial reactant concentration is high and the Kc value is small, the change in concentration may be negligible. In that case, the equilibrium concentration is close to the initial concentration. This idea helps simplify weak acid and weak base problems. Chemists can assume that some equilibrium concentrations are equal to the initial concentrations.

key terms and concepts

Learn how a small equilibrium constant lets students use the 5% rule and an ICE table to estimate equilibrium concentrations without solving a quadratic.

Estimating Equilibrium with Small Changes | JoVE K12

chemistry

JoVE Core Chemie erweckt allgemeine Konzepte der Chemie durch kompakte und leicht verständliche animierte Videolektionen zum Leben. Außerdem zeigen wir in den Videos Wissenschaftler in Aktion bei klassischen und neuartigen Forschungsexperimenten, wie sie heutzutage in Laboren weltweit durchgeführt wurden.

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Next Generation Science Standards

High School

Physical Science

Matter and Its Interactions

HS-PS1-6

Florida Department of Education

SC.912.P.12

SC.912.P.12.13

Texas Essential Knowledge and Skills

Physics

PHYS.2

PHYS.2.C

Chemistry and Physics

IPC.2

IPC.2.C

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-6.

Scientific Laws and Theories

Scientific Laws

In science, a law is defined as a concise, verbal or mathematical, statement that summarizes a vast number of experimental observations. ...

The Scientific Method

Chemistry is an empirical science. Scientists often pose questions to understand the chemistry in everyday life and seek answers to these questions. To ...

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 ...

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Use models to explain how the scientific understanding of atomic structure has evolved.

PS.Chm.1.1

Radioactivity and Nuclear Equations

Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The nucleus of an atom is composed of protons and, except for ...

Types of Radioactivity

The most common types of radioactivity are &#945; decay, &#946; decay, &#947; decay, neutron emission, and electron capture.
Alpha (&#945;) decay is the ...

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10&#8722;15 meters, a nucleus is ...

Nuclear Binding Energy

The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect ...

Radioactive Decay and Radiometric Dating

Radioactivity is a spontaneous disintegration of an unstable nuclide and is a random process, as all the nuclei in the sample do not decay simultaneously. ...

Nuclear Fission

Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger ...

Nuclear Power

Controlled nuclear fission reactions are used to generate electricity. Any nuclear reactor that produces power via the fission of uranium or plutonium by ...

Nuclear Fusion

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process ...

Nuclear Transmutation

Nuclear transmutation is the conversion of one nuclide into another. It can occur by the radioactive decay of a nucleus, or the reaction of a nucleus with ...

Use models to compare nuclear reactions including alpha decay, beta decay and gamma decay; nuclear fusion and nuclear fission.

PS.Chm.1.2

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 ...

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and ...

electron-configuration-of-multielectron-atoms

Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the ...

Use models to explain how electrons are distributed in atoms.

PS.Chm.1.3

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, ...

Use the Periodic Table as a model to predict the relative properties of elements based on the pattern of valence electrons in the outermost energy levels of atoms.

PS.Chm.2.1

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 ...

Construct an explanation to infer the atomic size, reactivity, electronegativity, and ionization energy of an element based on its position in the Periodic Table.

PS.Chm.2.2

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Lewis Symbols and the Octet Rule

Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

The Born-Haber Cycle

Lattice Energy&#xA0;

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a ...

trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

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 ...

Resonance

The Lewis structure of a nitrite anion (NO2&minus;) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O ...

Formal Charges

In some cases, there are seemingly more than one valid Lewis structures for molecules and polyatomic ions. The concept of formal charges can be used to ...

Exceptions to the Octet Rule

Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:


	...

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, ...

Analyze and interpret data to explain the mechanisms and properties of the two main types of intramolecular (ionic and covalent) bonds.

PS.Chm.3.1

molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

surface-tension-capillary-action-and-viscosity

Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

Construct an explanation to summarize the influences intermolecular forces have on the properties of chemical compounds.

PS.Chm.3.2

Analyze the structure of atoms and isotopes.

Estimating Equilibrium with Small Changes

Description

Transcript

Tags

More videos by Standards