Name: chemical reaction basics and equilibrium
Uploaded: 2023-06-23T15:38:43.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Chemistry

Matter And Its Interactions

HS-PS1-2

Introduction to Chemical Reactions

Une réaction chimique est un processus par lequel les atomes d’une ou plusieurs substances, appelés réactifs, modifient leur arrangement en brisant leurs liaisons chimiques et en formant de nouvelles liaisons pour créer les produits.
Les réactions qui entraînent une libération nette d’énergie sont exergoniques, tandis que les réactions endergoniques sont des absorbeurs nets d’énergie.
Les réactions biochimiques qui se produisent dans le corps humain sont classées comme étant soit de synthèse, soit anaboliques, telles que la synthèse des protéines, la décomposition ou cataboliques, telles que la décomposition des polysaccharides en sucres simples, ou les réactions d'échange, telles que le transfert du phosphate de l'ATP au glucose pour former du glucose-phosphate.
De nombreuses réactions biochimiques utilisent des enzymes comme catalyseurs pour accélérer la réaction.
Toutes les réactions biochimiques progressent vers l’équilibre – un état où aucun changement net dans les concentrations de réactifs et de produits ne se produit parce que les réactions directe et inverse se produisent au même rythme.
Les réactions biochimiques fournissent de l’énergie pour maintenir l’homéostasie et remplir des fonctions essentielles telles que la croissance et la réparation.

introduction aux réactions chimiques

Toutes les réactions chimiques commencent par un réactif, terme général pour une ou plusieurs substances entrant dans la réaction. Les ions sodium et chlorure, par exemple, sont les réactifs dans la production de sel de table. Une ou plusieurs substances produites par une réaction chimique sont appelées produits. Les réactions chimiques suivent la loi de la conservation de la masse, ce qui signifie que la matière ne peut ni être créée, ni être détruite au cours d'une réaction chimique. Les composants des réactifs - le nombre d'atomes et les éléments - sont tous présents dans le(s) produit(s). De même, il n'y a rien dans les produits qui n'est pas présent dans les réactifs. Les réactions chimiques nécessitent une quantité suffisante d'énergie qui provoque la collision de la matière avec une précision et une force suffisantes pour rompre les anciens liens chimiques et en former de nouveaux. En général, l'énergie cinétique est la forme d'énergie qui alimente tout type de matière en mouvement. L'énergie potentielle est l'énergie de position ou l'énergie que la matière possède en raison de la disposition ou de la structure de ses composants. Tous les atomes ont de l'énergie cinétique, car ils sont toujours en mouvement. L'énergie nécessaire pour rompre les liens chimiques des réactifs et commencer une réaction est appelée énergie d'activation. La concentration et la température des réactifs peuvent influencer la vitesse d'une réaction chimique. La convention d'écriture des équations chimiques consiste à placer les formules des réactifs du côté gauche d'une flèche de réaction et les formules des produits du côté droit. Selon cette convention et les définitions de "réactif" et "produit", une équation chimique représente la réaction se déroulant de gauche à droite. Cependant, les réactions réversibles peuvent se produire dans les deux directions, avant (de gauche à droite) et arrière (de droite à gauche). Lorsque les vitesses des réactions avant et arrière sont égales, les concentrations des espèces réactives et des produits restent constants au fil du temps et le système est à l'équilibre. Les concentrations relatives des réactifs et des produits dans les systèmes d'équilibre varient considérablement ; certains systèmes contiennent principalement des produits à l'équilibre, d'autres contiennent principalement des réactifs, et d'autres contiennent des quantités appréciables des deux. Par exemple, dans le sang humain, les ions hydrogène en excès (H+), se lient aux ions bicarbonate (HCO3-), formant un état d'équilibre avec l'acide carbonique (H2CO3). Si nous ajoutons de l'acide carbonique à ce système, une partie de celui-ci se convertira en bicarbonate et en ions hydrogène. Cependant, les réactions biologiques atteignent rarement l'équilibre, car les concentrations des réactifs ou des produits ou des deux changent constamment, souvent avec le produit d'une réaction devenant un réactif pour une autre réaction. Pour revenir à l'exemple des ions hydrogène en excès dans le sang, la formation d'acide carbonique sera la principale direction de la réaction. Cependant, l'acide carbonique peut également quitter le corps sous forme de gaz carbonique (par inhalation) au lieu de se convertir en ion bicarbonate ; cela entraîne la réaction vers la droite selon la loi de l'action des masses. Ces réactions sont importantes pour maintenir l'homéostasie dans notre sang. Ce texte est adapté de <a href="https://openstax.org/books/anatomy-and-physiology-2e/pages/2-3-chemical-reactions">Openstax, Anatomy and Physiology 2e, Section 2.3: Chemical Reactions</a>, <a href="https://openstax.org/books/chemistry-2e/pages/13-1-chemical-equilibria">Openstax, Chemistry 2e, Section 13.1: Chemical equilibria </a>et <a href="https://openstax.org/books/biology-2e/pages/2-1-atoms-isotopes-ions-and-molecules-the-building-blocks">Openstax, Biology 2e, Section 2.1: Atoms, Isotopes, Ions and Molecules: The Building Blocks</a>

Introduction aux Réactions Chimiques

Toutes les réactions chimiques commencent par un réactif, terme général désignant une ou plusieurs substances entrant dans la réaction. Les ions sodium et chlorure, par exemple, ...

Education

Enseignement

JoVE Core

Anatomy and Physiology

Anatomie et physiologie

Unit 1

Unité 1

Fundamentals of Chemistry

Les fondamentaux de la chimie

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

chemical reaction basics and equilibrium

Chemical reactions start with reactants and end with products. Reactants are the substances that enter a reaction, and products are the new substances that form. For example, sodium and chloride ions are the reactants in the formation of table salt.

Chemical reactions follow the law of conservation of mass. Matter is not created or destroyed during the reaction. That means the atoms and elements in the reactants are still present in the products, and nothing new appears in the products that was not already in the reactants.

Energy is needed to start many reactions. Collisions between particles must happen with enough force and precision to break old chemical bonds and form new ones. Kinetic energy is the energy of motion, while potential energy is the energy that comes from position or structure. Atoms always have kinetic energy because they are always moving. The energy needed to break the bonds of the reactants and begin the reaction is called activation energy.

Reaction rate can change with concentration and temperature. Chemical equations show reactants on the left side of an arrow and products on the right side. This convention shows the reaction moving from left to right. Some reactions are reversible, so they can also move from right to left.

In a reversible reaction, equilibrium happens when the forward and reverse reaction rates are equal. At that point, the concentrations of reactants and products stay constant over time. Some equilibrium systems contain mostly products, some contain mostly reactants, and some contain significant amounts of both. In human blood, excess hydrogen ions bind to bicarbonate ions to form carbonic acid. If carbonic acid is added, some of it changes back into bicarbonate and hydrogen ions.

Biological reactions often do not reach equilibrium because the concentrations of reactants and products keep changing. In many cases, one reaction’s product becomes a reactant for another reaction. In the blood example, carbonic acid can also leave the body as carbon dioxide gas during exhalation instead of changing back. This pulls the reaction to the right by the law of mass action and helps maintain homeostasis in the blood.

Chemical Reaction Basics and Equilibrium

what is matter?

Matter, Mass, and Weight Basics

Matter is the substance that makes up the universe, from a grain of sand to a star. Scientists define matter as anything that occupies space and has mass. Mass is the amount of matter in an object, while weight depends on gravity. Mass stays the same whether an object is on Earth or in the zero-gravity environment of outer space. Weight changes when gravity changes. An object weighs more where gravity is stronger and less where gravity is weaker. A piece of cheese that weighs a pound on Earth...

the periodic table and organismal elements

the-periodic-table-and-organismal-elements

Organismal Elements in the Periodic Table

The periodic table helps identify the elements that make up living organisms. Biology groups these as organismal elements because they are the chemical building blocks of life. These elements are found in different amounts in the body. Some are present in large quantities, while others are needed only in small amounts. The video connects the periodic table to the elements that organisms actually use. Understanding organismal elements helps students link chemistry to biology. It shows how...

atomic structure

From Atomos to the Modern Atom

Atoms are the tiny building blocks of matter, and ideas about them go back to the Greek philosopher Democritus. He suggested that everything on Earth is made of atomos, a Greek word meaning "indivisible." That idea later led to the modern word atom. In the 19th century, John Dalton developed an atomic theory that is still largely correct today. He proposed five key ideas. All matter is made of tiny particles called atoms. Atoms of the same element are alike, and atoms of different elements are...

chemical symbols

Chemical Symbols and Element Names

Chemical symbols are short abbreviations that stand for an element or a single atom of that element. Mercury, for example, has the symbol Hg. The same symbol can point to one atom of mercury in the microscopic domain or to a sample labeled as many atoms of mercury in the macroscopic domain. Many symbols come from the element’s common name. Others are shortened from a name in another language. Most chemical symbols use one or two letters. For a few elements with atomic numbers above 112,...

atomic number and mass number

Atomic Identity, Mass, and Isotopes

Atomic identity depends on the number of protons in the nucleus, and mass depends on protons and neutrons together. The number of protons is the atomic number, or Z. It defines the element. For example, any atom with six protons is carbon, no matter how many neutrons or electrons it has. In a neutral atom, the number of protons equals the number of electrons. Because of that, the atomic number also tells you the number of electrons in the atom. The total number of protons and neutrons is...

atomic weight

Atomic Mass and Mole Calculations

Atomic mass and mole calculations help explain how much matter is in atoms and compounds. Protons and neutrons have about the same mass, about 1.67 × 10 -24 grams. Scientists define that mass as one atomic mass unit, or amu, also called one Dalton. Electrons are much lighter than protons. They weigh only 9.11 × 10 -28 grams, or about 1/1800 of an atomic mass unit. Because of that small mass, electrons do not add much to an element’s overall atomic mass. When chemists calculate atomic mass,...

isotopes and radioisotopes

Radioisotopes in Medicine and Imaging

Radioisotopes are unstable isotopes that can be used to study the body and treat disease. An isotope is an atom of the same element that has a different mass because it contains a different number of neutrons. It still has the same number of protons, so it remains chemically identical. English chemist Frederick Soddy explained this idea in the early 1900s and later received the Nobel Prize in Chemistry in 1921. Some isotopes have more neutrons than usual and are called heavy isotopes. These...

electron behavior

Electron Shells and Discovery

Electrons are negatively charged subatomic particles that stay near the positively charged nucleus of an atom. They occupy spaces linked to energy levels called shells. They are also arranged into subshells and orbitals within each shell. An electron’s shell shows its general energy level. Electrons closer to the nucleus have less energy, while electrons farther away have more energy. The outer shells have more space, so they can hold more electrons than the inner shells. Subshells describe...

introduction to chemical bonds

How Atoms Bond to Reach Stability

Atoms bond to become more stable, and their outermost electrons play the biggest role in that process. The inner electron shell can hold two electrons. The next two shells can each hold eight electrons. This is called the octet rule. It states that, except for the innermost shell, atoms are most stable when their valence shell, or outer shell, has eight electrons. When atoms do not have enough electrons to fill that outer shell, they form chemical bonds with other atoms. A chemical bond is the...

ionic bonds

Ionic Bonds and Charge Transfer

Ionic bonds form when atoms transfer electrons and become charged particles. A positive ion and a negative ion attract each other because opposite charges pull together. This type of bonding helps explain how some substances are held together. In many cases, an atom loses one or more electrons, while another atom gains them. The atom that loses electrons becomes a cation, which is a positively charged ion. The atom that gains electrons becomes an anion, which is a negatively charged ion. The...

covalent bonds

Polar and Nonpolar Covalent Bonds

Covalent bonds form when atoms share electrons to fill their valence shells. The way those shared electrons are pulled depends on electronegativity, which is an atom's tendency to attract electrons in a bond. That difference also helps explain why some molecules are polar and others are nonpolar. Atoms with similar electronegativities form nonpolar covalent bonds. In these bonds, electrons are shared equally, so there is no charge across the molecule. When two atoms have different...

hydrogen bonds

Hydrogen Bonding and DNA Stability

Hydrogen bonding helps explain why some molecules stick together more strongly than others. A hydrogen bond forms when a weakly positive hydrogen atom, already bonded to an electronegative atom, is attracted to another electronegative atom on a nearby polar molecule. Common examples include water, hydrogen fluoride, and ammonia. This attraction happens because hydrogen has a much lower electronegativity than atoms such as fluorine, oxygen, and nitrogen. The electronegativity difference, along...

ions, molecules, and compounds

Atomic Charges, Bonds, and Compounds

Atoms can gain or lose electrons during chemical reactions and become ions. An ion is an atom with an electrical charge. This charge is positive or negative, and it often helps the atom reach a full valence shell. Some atoms are more likely to donate electrons, while others are more likely to accept them. Potassium is one example. It has atomic number 19 and one electron in its valence shell, so it is likely to donate that electron and become a slightly positive ion called a cation. Fluorine...

states of matter

Solids, Liquids, Gases, and Plasma

Solids, liquids, gases, and plasma are the main forms of matter described here. Solids are rigid and keep a definite shape. Liquids flow and take the shape of their container, although gravity gives the surface a flat or slightly curved top. Solids and liquids also have volumes that stay nearly the same even when pressure changes. Gases behave differently from solids and liquids. A gas takes both the shape and the volume of its container. In matter with this behavior, the particles are far...

colloids and suspensions

Suspensions, Sedimentation, and Colloids

Suspensions and colloids are two common kinds of mixtures seen in everyday life. Mud and water, flour and water, and tempera paint are suspensions. These mixtures are heterogeneous, which means their particles are not spread out evenly. The particles are relatively large and can be seen with the naked eye or a magnifying glass. Suspension particles make mixtures cloudy, and they settle out after mixing. The settling of particles in a suspension is called sedimentation. A blood test can measure...

introduction to chemical reactions

Chemical reactions start with reactants and end with products. Reactants are the substances that enter a reaction, and products are the new substances that form. For example, sodium and chloride ions are the reactants in the formation of table salt. Chemical reactions follow the law of conservation of mass. Matter is not created or destroyed during the reaction. That means the atoms and elements in the reactants are still present in the products, and nothing new appears in the products that...

types of chemical reactions: anabolic and catabolic

types-of-chemical-reactions-anabolic-and-catabolic

Anabolism, Catabolism, and ATP Use

Anabolism and catabolism are the two main kinds of metabolic reactions in the body. Metabolism is the total set of anabolic and catabolic reactions that keep life running. These reactions follow the first law of thermodynamics, which says energy cannot be created or destroyed. It can only change form. Anabolism builds larger, more complex molecules from smaller ones. These anabolic, or biosynthesis, reactions need energy in the form of ATP. They join monosaccharides into polysaccharides, fatty...

types of chemical reactions: exchange and reversible

types-of-chemical-reactions-exchange-and-reversible

Electron Transfer and Chemical Equilibrium

Exchange reactions and reversible reactions are two important ideas in chemistry. In an exchange reaction, synthesis and decomposition happen at the same time. Chemical bonds are both formed and broken. These reactions can absorb chemical energy, store it, and release it. A special type of exchange reaction is the oxidation-reduction reaction, or redox reaction. In a redox reaction, electrons move from one compound to another. The electrons often come from hydrogen atoms, which contain one...

energy transfer in chemical reactions

Chemical Energy and Reaction Types

Chemical reactions depend on energy transfer, chemical bonds, and the way matter collides. A reaction needs enough energy for particles to meet with the right force and precision. That energy can break old bonds and help form new ones. Kinetic energy is the energy of motion. A person lifting a brick uses kinetic energy to move the brick into place on a wall. Once the wall is built, it stores potential energy, which is the energy of position or structure. If the wall falls, that stored energy...

factors influencing the rate of chemical reactions

factors-influencing-the-rate-of-chemical-reactions

Chemical Reaction Rates and Catalysts

Chemical reaction rates depend on how often particles collide and whether those collisions have enough energy to start a reaction. That starting energy is called activation energy. Factors that affect reaction rate either lower that energy or make successful collisions more likely. Concentration and pressure can speed reactions up because they put more particles in the same space. When more particles are present, they are more likely to bump into one another. Chemists can also increase...

acids, bases and neutralization reactions

How pH Affects Cells and Digestion

Acids, bases, and pH help control how cells and body systems work. In biology, pH can strongly affect enzymes, proteins, and nucleic acids. Enzymes work best within a certain pH range, and pH changes can alter their structure or denature them, which changes how they function. Acids release hydrogen ions, or H+, in solution. A hydrogen ion is a proton, so it is very reactive in chemical reactions. Strong acids release all of their H+ in water and ionize completely. Hydrochloric acid (HCl) is a...

key terms and concepts

Learn how reactants become products, how mass is conserved, what activation energy means, and how reversible reactions reach equilibrium in blood.

Chemical Reaction Basics and Equilibrium | JoVE K12

anatomy and physiology

JoVE Core Anatomy and Physiology showcases the anatomical and physiological details of the human body in comprehensive, clear, and engaging video animations. This collection of lessons focuses on the structures, components, functions, and requirements of the human body. It is complemented by scientist-in-action videos that demonstrate the application of this knowledge in real-world medical and research settings.

HS-PS1-4

HS-PS1-5

HS-PS1-7

Tennessee Academic Standards

Matter and Its Interactions

CHEM1.PS1.4

Energy

CHEM1.PS3.3

Minnesota Academic Standards in Science

9-12

2.2.1 9C.1.2.1.2

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

C-PS1-2

C-PS1-4

C-PS1-5

C-PS1-6

C-PS1-7

Georgia Standards of Excellence

Physical Science

SPS3.

Chemical Reaction

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 ...

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 And Organismal Elements

Atomic Structure

The Greek philosopher Democritus proposed that everything on Earth is made up of tiny particles called atomos, Greek for &#34;indivisible,&#34; from which ...

Electron Configurations

Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest ...

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central&#160;core called the nucleus, with electrons present around the ...

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 ...

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 ...

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 ...

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude ...

Electric Charges

From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the ...

sources-and-properties-of-electric-charge

Sources and Properties of Electric Charge

All objects we see around us consist of atoms, which combine to form molecules. The lightest element in the universe is hydrogen, and a hydrogen atom ...

Types of Forces

In most situations, forces can be grouped into two categories: contact forces and field forces.&#160; Contact forces occur as a result of direct physical ...

Electric Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
An electric field is generated ...

Intermolecular Forces

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

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions ...

Chemical Bonds


Atoms participate in a chemical bond formation&#160;to acquire a completed valence-shell electron configuration similar to that of the noble gas nearest ...

Electron Behavior

Electrons are negatively charged subatomic particles attracted to and orbit around the positively-charged nucleus of an atom. They reside in spaces ...

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 ...

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level and the composition of the nucleus of atoms.  Clarification Statement: Chemistry: Examples of properties that could be predicted from patterns could include reactivity of metals, types of bonds formed, numbers of bonds formed, atomic radius, atomic mass, or reactions with oxygen. Emphasis is on main group elements and qualitative understanding of the relative trends of ionization energy and electronegativity.

HS-PS1-1

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3&#8211;12 are ...

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 ...

Chemical Reactions

A chemical reaction is a process by which the bonds in the atoms of substances are rearranged to generate new substances. Matter cannot be created or ...

Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are ...

All chemical reactions begin with a reactant, the general term for one or more substances entering the reaction. Sodium and chloride ions, for example, ...

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. ...

stoichiometry-product-yield-and-limiting-reactants

Stoichiometry, Product Yield, and Limiting Reactants

Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Preparation of 25% v/v Ethylenediamine in Deionized WaterExpand
	Here, we show the laboratory ...

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 ...

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When ...

Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.  Clarification Statement: Chemistry: Examples of chemical reactions could include the reaction of sodium and chlorine, carbon and oxygen, or carbon and hydrogen. Reaction classification aids in the prediction of products (e.g. synthesis, decomposition, single displacement, double displacement, and acid-base).

Intermolecular vs Intramolecular Forces

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

comparison-between-electrical-and-gravitational-forces

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To ...

intermolecular-forces-and-physical-properties

Intermolecular Forces and Physical Properties



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

electric-field-of-two-equal-and-opposite-charges

Electric Field of Two Equal and Opposite Charges

Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. ...

Electric Field

Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by ...

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 ...

Electric Dipoles and Dipole Moment

Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent ...

Plan and conduct an investigation to gather evidence to compare the structure of substances at the macroscale to infer the strength of electrical forces between particles.  Clarification Statement: Emphasis is on understanding the strengths of forces between particles, not on naming specific intermolecular forces (such as dipole-dipole). Examples of particles could include ions, atoms, molecules, and network solids (such as graphite). Examples of macro-properties of substances could include the melting point and boiling point, vapor pressure, and surface tension.

HS-PS1-3

Chemical Reaction Basics and Equilibrium

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