Name: trigonal bipyramidal and octahedral hybridization
Uploaded: 2020-09-03T13:38:29.000Z
Duration: 3 min 35 s
Channel: JoVE

K12 Standards

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

9-12

Chemistry

Structure And Properties Of Matter

Chemical bonding

Hybridization of Atomic Orbitals II

The trigonal bipyramidal, octahedral, and other molecular shapes can be explained by assuming the participation of 3d orbitals in the process of hybridization.

The phosphorus pentachloride molecule has a trigonal bipyramidal shape, and it contains 5 valence electrons. Phosphorus uses the 3s orbital, the three 3p orbitals, and one of the 3d orbitals to form five sp3d hybrid orbitals that are involved in the phosphorus&ndash;chlorine bonds.

Sulfur hexafluoride has an octahedral structure and it contains 6 valence electrons. The 3s orbital, the three 3p orbitals, and two of the 3d orbitals on sulfur form six equivalent sp3d2 hybrid orbitals. These six sp3d2 orbitals form an octahedral structure around sulfur and participate in the formation of sulfur&ndash;fluorine bonds.

The concept of hybridization also provides an explanation for the formation of multiple bonds. The side-on overlap of two p orbitals gives rise to a &pi; bond.&nbsp;

However, a &pi;-bond can only be formed in double and triple bonds when a &sigma; bond already exists between two atoms. Because the &pi; bond exists on opposite sides of the internuclear axis, &pi; bonds are unable to rotate around this axis.

In the ethene molecule, both carbons exhibit

hybridization of atomic orbitals ii

<h4>sp3d and sp3d&nbsp;2 Hybridization</h4>

To describe the five bonding orbitals in a trigonal bipyramidal arrangement, we must use five of the valence shell atomic orbitals (the s orbital, the three p orbitals, and one of the d orbitals), which gives five sp3d hybrid orbitals. With an octahedral arrangement of six hybrid orbitals, we must use six valence shell atomic orbitals (the s orbital, the three p orbitals, and two of the d orbitals in its valence shell), which gives six sp3d&nbsp;2 hybrid orbitals. These hybridizations are only possible for atoms that have d orbitals in their valence subshells (that is, not those in the first or second period).

In a molecule of phosphorus pentachloride, PCl5, there are five P&ndash;Cl bonds (thus five pairs of valence electrons around the phosphorus atom) directed toward the corners of a trigonal bipyramid. We use the 3s orbital, the three 3p orbitals, and one of the 3d orbitals to form the set of five sp3d hybrid orbitals that are involved in the P&ndash;Cl bonds. Other atoms that exhibit sp3d hybridization include the sulfur atom in SF4 and the chlorine atoms in ClF3 and in ClF4+.&nbsp;

The sulfur atom in sulfur hexafluoride, SF6, exhibits sp3d&nbsp;2 hybridization. A molecule of sulfur hexafluoride has six bonding pairs of electrons connecting six fluorine atoms to a single sulfur atom. There are no lone pairs of electrons on the central atom. To bond six fluorine atoms, the 3s orbital, the three 3p orbitals, and two of the 3d orbitals form six equivalent sp3d&nbsp;2 hybrid orbitals, each directed toward a different corner of an octahedron. Other atoms that exhibit sp3d&nbsp;2 hybridization include the phosphorus atom in PCl6&minus;, the iodine atom in the interhalogens IF6+, IF5, ICl4&minus;, IF4&minus;, and the xenon atom in XeF4.

This text has been adapted from <a href="https://openstax.org/books/chemistry-2e/pages/8-2-hybrid-atomic-orbitals">Openstax, Chemistry 2e, Section 8.2: Hybrid Atomic Orbitals.</a>

sp3d and sp3d&nbsp;2 Hybridization

To describe the five bonding orbitals in a trigonal bipyramidal arrangement, we must use five of the valence shell ...

Education

JoVE Core

Chemical Bonding: Molecular Geometry and Bonding Theories

chemical-bonding-molecular-geometry-and-bonding-theories

KEY TERMS AND CONCEPTS

trigonal bipyramidal and octahedral hybridization

Trigonal bipyramidal and octahedral hybridization explain how atoms form five or six bonding orbitals. These models use valence shell atomic orbitals to match the shape of the molecule. They apply to atoms that have d orbitals in their valence subshells, so they do not apply to atoms in the first or second period.

For five bonding orbitals, an atom uses one s orbital, three p orbitals, and one d orbital. This creates five sp3d hybrid orbitals. In phosphorus pentachloride, PCl5, the five P-Cl bonds point toward the corners of a trigonal bipyramid. The phosphorus atom uses its 3s orbital, three 3p orbitals, and one 3d orbital to form these hybrid orbitals.

Other examples of sp3d hybridization include sulfur in SF4 and chlorine in ClF3 and ClF4+. These cases also fit a five-orbital arrangement around the central atom. The hybrid orbitals help show how the bonds are arranged in space.

For six bonding orbitals, an atom uses one s orbital, three p orbitals, and two d orbitals. This produces six sp3d2 hybrid orbitals. In sulfur hexafluoride, SF6, the sulfur atom bonds to six fluorine atoms and has no lone pairs of electrons. The six equivalent hybrid orbitals point toward the corners of an octahedron.

Other atoms that show sp3d2 hybridization include phosphorus in PCl6−, iodine in the interhalogens IF6+, IF5, ICl4−, and IF4−, and xenon in XeF4. These examples show how hybridization changes with the number of bonding pairs around the central atom. The model helps connect electron pairs with the shapes seen in these molecules.

Trigonal Bipyramidal and Octahedral Hybridization

trigonal-bipyramidal-and-octahedral-hybridization

vsepr theory and the basic shapes

Predicting Molecular Shape with VSEPR

VSEPR theory helps predict molecular shape and approximate bond angles around a central atom. VSEPR stands for valence shell electron-pair repulsion. The model uses the Lewis structure to count bonding pairs and lone pairs in the valence shell of the central atom. The idea behind the theory is simple. Electron pairs in the valence shell arrange themselves to reduce repulsion by staying as far apart as possible. Bonding pairs are found mainly between bonded atoms, while lone pairs stay on the...

vsepr theory and the effect of lone pairs

vsepr-theory-and-the-effect-of-lone-pairs

How Lone Pairs Change Molecular Shape

Lone pairs of electrons can change molecular shape and bond angles. Electron-pair geometry includes every region of electron density around a central atom, while molecular structure shows only where the atoms are located. These two ideas match when the central atom has no lone pairs, but they differ when lone pairs are present. Methane, CH4, is a simple example. It has four bonding pairs around carbon, so both the electron-pair geometry and the molecular structure are tetrahedral. Ammonia,...

predicting molecular geometry

VSEPR Rules for Molecular Shapes

VSEPR theory helps predict electron-pair geometry and molecular shape from a Lewis structure. First, write the Lewis structure of the molecule or polyatomic ion. Then count the electron groups around the central atom. A single, double, or triple bond each counts as one region of electron density. Next, match the number of electron groups to the electron-pair geometry. The main geometries are linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral. Then use the number of lone...

molecular shape and polarity

Bond Dipoles and Molecular Polarity

Bond dipoles and molecular polarity explain why some molecules have a charged end and others do not. In a polar covalent bond, atoms with different electronegativities share electrons unevenly. The more electronegative atom pulls electron density toward itself and becomes partially negative, while the other atom becomes partially positive. This separation of charge creates a bond dipole moment. The size of a bond dipole moment is written with the Greek letter mu, or μ. It depends on the size...

valence bond theory

Covalent Bond Strength and Orbital Overlap

Covalent bond strength depends on how atomic orbitals overlap. In valence bond theory, a covalent bond forms when two half-filled orbitals, each with one electron, overlap and the two electrons pair up. The shared electron pair is then attracted to both positively charged nuclei, which holds the atoms together. The amount of overlap affects both bond strength and energy. When atoms are far apart, there is no overlap, so the energy is set to zero by convention. As the atoms move closer, their...

hybridization of atomic orbitals i

Atomic Orbital Hybridization and Bond Shapes

Atomic orbital hybridization explains how electron orbitals change shape when atoms form covalent bonds. The wave function, ψ, describes the behavior of electrons in an isolated atom. When atoms bond, their wave functions combine through the linear combination of atomic orbitals, and the new orbitals are called hybrid orbitals. Hybrid orbitals do not exist in isolated atoms. They form only in covalently bonded atoms. Their shapes and directions differ from those of the original atomic orbitals.

Trigonal bipyramidal and octahedral hybridization explain how atoms form five or six bonding orbitals. These models use valence shell atomic orbitals to match the shape of the molecule. They apply to atoms that have d orbitals in their valence subshells, so they do not apply to atoms in the first or second period. For five bonding orbitals, an atom uses one s orbital, three p orbitals, and one d orbital. This creates five sp3d hybrid orbitals. In phosphorus pentachloride, PCl5, the five P-Cl...

molecular orbital theory i

Bonding and Antibonding Molecular Orbitals

Molecular orbital theory explains how electrons are arranged in molecules. It uses quantum mechanics and wave functions, written as Ψ, to describe electron behavior in a molecule. Like electrons in isolated atoms, electrons in molecules occupy discrete, quantized energy levels. A molecular orbital is the region where a valence electron is likely to be found. It is full when it contains two electrons with opposite spin. Molecular orbitals can be built by combining atomic orbitals through the...

molecular orbital theory ii

MO Diagrams, Bond Order, and Mixing

Molecular orbital diagrams show how atomic orbitals combine to make bonding and antibonding orbitals in diatomic molecules. In these diagrams, the atomic orbitals of one atom are placed on the left and the atomic orbitals of the other atom are placed on the right. The molecular orbitals appear in the center. Each horizontal line stands for one orbital, and each orbital can hold two electrons. Dashed lines show which atomic orbitals combine to form each molecular orbital. When atomic orbitals...

key terms and concepts

Learn how sp3d and sp3d2 hybridization form trigonal bipyramidal and octahedral shapes in molecules like PCl5 and SF6, with clear high school examples.

Trigonal Bipyramidal and Octahedral Hybridization | JoVE K12

chemistry

JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

Virginia  Standards of Learning

HIgh School

CH.3

CH.3.e

Physics

PH.9

PH.9.e

Alabama Course of Study Science

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

9-12.C.2.2.d

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Structure and Properties of Matter

HS-PS1-3.

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 ...

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

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 ...

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 ...

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 ...

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 ...

Thomson's e/m Experiment

In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform ...

Atomic structure
• Evolution of atomic models/theory
• Electrons
• Electron configurations

Content elaboration: Physical Science included properties and locations of protons, neutrons and electrons, atomic number, mass number, cations and anions, isotopes and the strong nuclear force which holds the nucleus together. In this course, the historical development of the atomic model and the positions of electrons are explored in greater detail. Atomic models are constructed to explain experimental evidence and make predictions. The changes in the atomic model over time exemplify how scientific knowledge changes as new evidence emerges and how technological advancements like electricity extend the boundaries of scientific knowledge. Thompson's study of electrical discharges in cathode-ray tubes led to the discovery of the electron and the development of the plum pudding model of the atom. Rutherford's experiment, in which he bombarded gold foil with a-particles, led to the discovery that most of the atom consists of empty space with a relatively small, positively charged nucleus. Bohr used data from atomic spectra to propose a planetary model of the atom in which electrons orbit the nucleus, like planets around the sun. Later, Schrödinger used the idea that electrons travel in waves to develop a model in which electrons travel randomly in regions of space called orbitals (quantum mechanical model). Based on the quantum mechanical model, it is not possible to predict exactly where electrons are located but there is a region of space surrounding the nucleus in which there is a high probability of finding an electron (electron cloud or orbital). Data from atomic spectra (emission and absorption) gives evidence that electrons can only exist at certain discrete energy levels and not at energies between these levels. Atoms are usually in the ground state where the electrons occupy orbitals with the lowest available energy. However, the atom can become excited when the electrons absorb a photon with the precise amount of energy (indicated by the frequency of the photon) to move to an orbital with higher energy. Any photon without this precise amount of energy will be ignored by the electron. The atom exists in the excited state for a very short amount of time. When an electron drops back down to the lower energy level, it emits a photon that has energy equal to the energy difference between the levels. The amount of energy is indicated by the frequency of the light that is given off and can be measured. Each element has a unique emission and absorption spectrum due to its unique electron configuration and specific electron energy jumps that are possible for that element. Being aware of the quantum mechanical model as the currently accepted model for the atom is important for science literacy as it explains and predicts subatomic interactions, but details should be reserved for more advanced study. Electron energy levels consist of sublevels (s, p, d and f), each with a characteristic number and shape of orbitals. Orbital diagrams and electron configuration can be constructed to show the location of the electrons in an atom using established rules. Valence electrons are responsible for most of the chemical properties of elements. In this course, electron configuration (extended and noble gas notation) and orbital diagrams can be shown for any element in the first three periods. Although the quantum mechanical model of the atom explains the most experimental evidence, other models can still be helpful. Thinking of atoms as indivisible spheres is useful in explaining many physical properties of substances, such as the state (solid, liquid or gas) of a substance at room temperature. Bohr's planetary model is useful to explain and predict periodic trends in the properties of elements.

Atomic structure

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 ...

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 ...

Periodic Table
• Properties
• Trends

Content elaboration: In the Physical Science course, the concept that elements are placed in order of increasing atomic number in the periodic table such that elements with similar properties are placed in the same column is introduced. How the periodic table is divided into groups, families, periods, metals, nonmetals and metalloids is also included and will be revisited here. In this course, with more information about the electron configuration of elements, similarities in the configuration of the valence electrons for a particular group can be observed. The electron configuration of an atom can be determined from the position on the periodic table. The repeating pattern in the electron configuration for elements on the periodic table explains many of the trends in the properties observed. Atomic theory is used to describe and explain trends in properties across periods or down columns including atomic radii, ionic radii, first ionization energies, electronegativities and whether the element is a solid or gas at room temperature. Additional ionization energies, electron affinities and periodic properties of the transition elements, and the lanthanide and actinide series are reserved for more advanced study.

Periodic Table

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 ...

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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 ...

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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, ...

VSEPR Theory and the Basic Shapes

Overview of VSEPR Theory

Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure, including approximate ...

VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons&nbsp;on Molecule Geometry

It is important to note that electron-pair geometry around a central atom is not the same ...

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries

The following procedure uses VSEPR theory to determine the electron pair geometries and the ...

Molecular Shape and Polarity

Dipole Moment of a Molecule

Polar covalent bonds connect two atoms with differing electronegativities, leaving one atom with a partial positive charge ...

Valence Bond Theory

Overview of Valence Bond Theory

Valence bond theory describes a covalent bond as the overlap of half-filled atomic orbitals (each containing a single ...

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, &#x3C8;, contains information about each orbital and the wavelike properties of electrons in an ...

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Molecular orbital theory describes the distribution of electrons in molecules in the same way as the distribution of ...

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

The relative energy levels of atomic and molecular orbitals are typically shown in a molecular orbital diagram. For a ...

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 ...

Chemical bonding
• lonic
• Polar/covalent

Content elaboration: Content in the Physical Science course included recognizing that atoms with unpaired electrons tend to form ionic and covalent bonds with other atoms, forming molecules, ionic lattices or network covalent structures. In this course, electron configuration, electronegativity values and energy considerations will be applied to bonding and the properties of materials with different types of bonding. Atoms of many elements are more stable when they are bonded to other atoms. In such cases, as atoms bond, energy is released to the surroundings, resulting in a system with lower energy. An atom's electron configuration, particularly the valence electrons, determines how an atom interacts with other atoms. Molecules, ionic lattices and network covalent structures have different, yet predictable, properties that depend on the identity of the elements and the types of bonds formed. Differences in electronegativity values can be used to predict where a bond fits on the continuum between ionic and covalent bonds. The polarity of a bond depends on the electronegativity difference and the distance between the atoms (bond length). Polar covalent bonds are introduced as an intermediary between ionic and pure covalent bonds. The concept of metallic bonding is also introduced to explain many of the properties of metals (e.g., conductivity). Since most compounds contain multiple bonds, a substance may contain more than one type of bond. Carbon atoms can bond together and with other atoms, especially hydrogen, oxygen, nitrogen and sulfur, to form chains, rings and branching networks that are present in a variety of important compounds, including synthetic polymers, fossil fuels and the large molecules essential to life.

Chemical Formulas

A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of ...

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Ionic Compounds: Formulas and Nomenclature

An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to ...

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Molecular Compounds: Formulas and Nomenclature

Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular ...

Organic Compounds

All living things are formed mostly of carbon compounds called organic compounds. The category of organic compounds includes both natural and synthetic ...

Classification of Elements and Compounds

Pure substances consist of only one type of matter. A pure substance can be an element or a compound. An element consists of only one type of atom, while ...

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models ...

Representing compounds
• Formula writing
• Nomenclature
• Models and shapes (Lewis structures, ball and stick, molecular geometries)

Content elaboration: Using the periodic table, formulas of ionic compounds containing specific elements can be predicted. This can include ionic compounds made up of elements from groups 1, 2, 17, hydrogen, oxygen and polyatomic ions (given the formula and charge of the polyatomic ion). Given the formula, a compound can be named using conventional systems that include Greek prefixes and Roman numerals where appropriate. Given the name of an ionic or covalent substance, formulas can be written. Many different models can be used to represent compounds including chemical formulas, Lewis structures, and ball and stick models. These models can be used to visualize atoms and molecules and to predict the properties of substances. Each type of representation provides unique information about the compound. Different representations are better suited for particular substances. Lewis structures can be drawn to represent covalent compounds using a simple set of rules and can be combined with valence shell electron pair repulsion (VSEPR) theory to predict the three-dimensional electron pair and molecular geometry of compounds. Lewis structures and molecular geometries will only be constructed for the following combination of elements: hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens.

Representing compounds

Measurement: Standard Units

Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement ...

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, ...

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Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

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Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such ...

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Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a ...

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach ...

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 ...

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, ...

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Formula Mass and Mole Concepts of Compounds

Formula Mass of Covalent Compounds

Chemical formulas represent the elemental makeup of substances. For covalent compounds, the formula represents the ...

Quantifying matter

Content elaboration: In earlier grades, properties of materials were quantified with measurements that were always associated with some error. In this course, scientific protocols for quantifying the properties of matter accurately and precisely are studied. Using the International System of Units (SI), significant digits or figures, scientific notation, error analysis and dimensional analysis are vital to scientific communication. There are three domains of magnitude in size and time: the macroscopic (human) domain, the cosmic domain and the submicroscopic (atomic and subatomic) domain. Measurements in the cosmic domain and submicroscopic domains require complex instruments and/or procedures. Matter can be quantified in a way that macroscopic properties such as mass can reflect the number of particles present. Elemental samples are a mixture of several isotopes with different masses. The atomic mass of an element is calculated given the mass and relative abundance of each isotope of the element as it exists in nature. Because the mass of an atom is very small, the mole is used to translate between the atomic and macroscopic levels. A mole is equal to the number of atoms in exactly 12 grams of the isotope carbon-12. The mass of one mole of a substance is equal to its molar mass in grams. The molar mass for a substance can be used in conjunction with Avogadro's number and the density of a substance to convert between mass, moles, volume and number of particles of a sample.

Quantifying matter

Trigonal Bipyramidal and Octahedral Hybridization

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