Name: significant figures and rounding rules
Uploaded: 2020-09-03T13:38:25.000Z
Duration: 3 min 34 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

Quantifying matter

uncertainty-in-measurement-significant-figures

Uncertainty in Measurement: Significant Figures

과학적인 측정에서 마지막 자릿수를 제외한 모든 숫자는 확실합니다. 측정의 확실성은 측정값의 자릿수와 사용하는 계측기의 정밀도의 두 가지 요인에 따라 달라집니다. 측정량에서 마지막 자리의 불확실한 숫자를 포함한 모든 숫자를 유효 숫자라고 하며 특정 규칙을 사용하여 결정할 수 있습니다.

0이 아닌 모든 숫자와 그 사이에 있는 모든 0은 유효합니다. 예를 들어 28은 유효 숫자가 두 개이며 26.25는 네 개, 208은 세 개입니다. 앞에 오는 0은 유효하지 않으며 소수점 위치만 지정합니다.

예를 들어 0.00208은 유효 숫자가 세 개입니다. 이러한 수량은 지수 표기법으로 표시할 수 있습니다. 따라서 0.00208은 2.08 10⁻³으로 쓸 수 있습니다.

후행 0은 소수점 형식의 숫자에서만 유효합니다. 2200에는 2개의 후행 0과 2개의 유효 숫자가 있는 반면, 2200.0과 2200.1에는 모두 5개의 유효 숫자가 있습니다. 소수점이 없는 수의 경우 후행 0의 유효성이 모호해집니다.

따라서 2200은 유효 숫자가 2개인 2.2 10³으로 쓰거나 유효 숫자가 세 개인 2.20 10³으로 쓸 수 있습니다. 유효 숫자는 수학적인 연산에서도 확실성을 유지하기 위해 고려해야 합니다. 덧셈과 뺄셈에서 소수점 자릿수가 가장 적은 측정값과 동일한 소수점 자릿수를 가지도록 결과를 반올림해야 합니다.

마지막 자릿수가 5보다 작으면 반내림을 수행하고 5보다 크면 반올림을 수행합니다. 마지막 자릿수가 5일 때 때로는 다른 반올림 방법을 사용합니다. 예를 들어 2.052와 1.2의 합은 3.3으로 반올림됩니다.

그러나 곱하기 또는 나누기에서는 결과를 반올림하여 가장 작은 유효 숫자를 가진 측정값과 동일한 수의 유효 숫자가 되게 해야 합니다. 따라서 2.052와 1.2의 곱은 2.5로 반올림됩니다. 과학자들은 종종 측정값의 정밀도를 높이기 위해 실험을 반복합니다.

표준 편차는 이런 정밀도의 통계적 표현이며 기대값으로부터 분산된 정도를 나타냅니다. 정밀도가 높으면 표준 편차가 작고 정밀도가 낮으면 표준 편차가 큽니다. 예를 들어, 두 그룹이 책의 두께를 센티미터 단위로 측정했다고 가정합시다.

두 그룹은 10.6 센티미터로 같은 평균값을 얻었습니다. 하지만 첫 번째 그룹의 측정이 더 정밀하여 더 작은 표준 편차를 보였습니다. 두 번째 그룹은 측정 값이 더 넓게 산포되어 표준 편차가 더 크게 나왔습니다.

측정 불확도: 유효 수치

불확실한 마지막 숫자를 포함하여 측정값의 모든 숫자를 유효 숫자 또는 유효 숫자라고 합니다. 0은 측정된 값일 수 있습니다. 예를 들어, 가장 가까운 파운드 단위로 무게를 표시하는 저울에 "140"이 표시되면 1(백), 4(십), 0(일)이 모두 유효(측정) 값입니다.

측정 결과는 유효 숫자가 측정 프로세스의 확실성을 정확하게 나타낼 때 올바르게 보고됩니다. 다음은 측정 시 유효 숫자의 수를 결정하는 일련의 규칙입니다.

<ol>
	<li>0이 아닌 모든 숫자는 유효합니다. 왼쪽에서 0이 아닌 첫 번째 숫자부터 시작하여 이 숫자와 오른쪽의 나머지 모든 숫자를 셉니다. 이는 측정의 유효숫자 수입니다. 예를 들어 843은 유효 숫자가 3개이고, 843.12는 유효 숫자가 5개입니다.</li>
	<li>0이 아닌 두 숫자 사이의 0인 종속 0은 유효합니다. 예를 들어, 808.101에는 2개의 전용 0과 6개의 유효 숫자가 있습니다.</li>
	<li>선행 0은 0이 아닌 첫 번째 숫자 왼쪽에 있는 0입니다. 선행 숫자는 중요하지 않습니다. 단지 소수점 위치를 나타낼 뿐입니다. 예를 들어 0.008081의 앞에 오는 0은 중요하지 않습니다. 이 숫자는 지수 표기법을 사용하여 8.081 × 10^−3으로 표현할 수 있으며, 숫자 8.081에는 모든 유효 숫자가 포함되고 10^−3은 소수점 위치에 있습니다.</li>
	<li>숫자 끝의 0인 후행 0의 중요성은 위치에 따라 다릅니다. 소수점 앞(그러나 0이 아닌 숫자 뒤)과 뒤의 0은 중요합니다. 그러나 소수점이 없는 숫자의 경우 뒤에 오는 0은 중요할 수도 있고 그렇지 않을 수도 있습니다. 이 모호함은 지수 표기법을 사용하여 해결할 수 있습니다. 예를 들어 측정값 1300은 1.3 × 10^3(유효 숫자 2개), 1.30 × 10^3(10자리를 측정한 경우 유효 숫자 3개) 또는 1.300 × 10^3(1자리도 측정한 경우 유효 숫자 4개)로 쓸 수 있습니다. 정확히 잰).</li>
</ol>

계산의 유효 숫자

정확한 유효 숫자 수를 사용하여 계산 결과를 보고함으로써 측정의 불확실성을 피할 수 있습니다. 이는 숫자 반올림 규칙에 따라 결정될 수 있습니다.

<ol>
	<li>숫자를 더하거나 뺄 때 소수점 이하 자릿수가 가장 작은 숫자와 동일한 소수점 이하 자릿수로 결과를 반올림합니다.</li>
	<li>숫자를 곱하거나 나눌 때는 유효 숫자가 가장 작은 숫자와 동일한 자릿수로 결과를 반올림합니다.</li>
	<li>삭제할 숫자(유지할 숫자 바로 오른쪽에 있는 숫자)가 5보다 작은 경우 "내림"하고 유지된 숫자를 변경하지 않고 그대로 둡니다.</li>
	<li>삭제할 숫자(보유할 숫자 바로 오른쪽에 있는 숫자)가 5 이상이면 "반올림"하여 유지된 숫자를 1씩 늘립니다. 삭제한 숫자가 5인 경우 대체 반올림 방법을 사용할 수도 있습니다. . 유지된 숫자는 반올림 또는 내림 중 짝수 값을 산출합니다.</li>
</ol>

중요한 점은 반올림으로 인해 각 단계에서 오류가 누적되는 것을 피하기 위해 다단계 계산이 끝날 때 유효 숫자의 반올림을 수행하는 것이 바람직하다는 것입니다. 따라서 유효숫자와 반올림은 보고된 측정값의 확실성을 정확하게 표현하는 데 도움이 됩니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision.</a>

불확실한 마지막 숫자를 포함하여 측정의 모든 숫자를 유효 숫자 또는 유효 숫자라고 합니다. 0은 ...

Education

교육

JoVE Core

화학

하나

Introduction: Matter and Measurement

서론: 물질과 측정

KEY TERMS AND CONCEPTS

주요 용어 및 개념

significant figures and rounding rules

Significant figures and rounding rules help students report measurements with the right level of certainty. A measurement includes every digit that was actually measured, including the last uncertain digit. That is why a value can look simple but still carry useful information about the tool used to measure it.

Zero can also be significant when it is part of a measured value. For example, if a scale reads 140 pounds to the nearest pound, the 1, 4, and 0 are all significant. Reporting measurements this way shows how certain the result really is.

To count significant figures, all nonzero digits are significant. Start with the first nonzero digit on the left and count that digit and every digit to the right. By this rule, 843 has three significant figures, and 843.12 has five.

Zeros can change the count in different ways. Captive zeros, which are zeros between two nonzero digits, are significant, as in 808.101, which has six significant figures. Leading zeros are not significant because they only show where the decimal point is. For example, 0.008081 has four significant figures, and it can also be written as 8.081 × 10^-3.

Trailing zeros are significant only in some cases. Zeros at the end of a number are significant if they come after a decimal point, or if they are before a decimal point but still follow a nonzero digit. If a number has no decimal point, trailing zeros may or may not be significant. Exponential notation can remove that uncertainty. For example, 1300 could mean 1.3 × 10^3, 1.30 × 10^3, or 1.300 × 10^3, depending on how many digits were measured.

The same idea applies to calculations. When adding or subtracting, round the answer to the same number of decimal places as the value with the fewest decimal places. When multiplying or dividing, round the answer to the same number of significant figures as the value with the fewest significant figures. If the digit to be dropped is less than 5, round down. If it is 5 or greater, round up.

An alternative method may be used when the digit being dropped is 5. In that case, the retained digit is rounded to the even value. It is also best to round only at the end of a multistep calculation. That helps avoid extra error from rounding too early. Significant figures and rounding together help students show measurement certainty correctly.

Significant Figures and Rounding Rules

scientific laws and theories

How Science Explains Laws and Theories

Scientific laws and scientific theories describe science in two different ways. A law is a concise verbal or mathematical statement that summarizes many experimental observations. It describes or predicts aspects of the natural world that stay the same under the same conditions. A scientific theory is different because it explains why natural events happen. It is a unifying principle that gives a well-supported and testable explanation for a broad set of observations. Strong theories are the...

the scientific method

How Scientists Test a Hypothesis

Chemistry uses the scientific method to turn observations into testable answers. Scientists begin by observing a phenomenon in the physical world and then asking a question about it. This process helps explain everyday chemistry through evidence. A question leads to a hypothesis, which is a tentative explanation for what is being observed. Scientists often use earlier research and published literature to shape that idea. A strong hypothesis must be testable, meaning it can be supported by...

physical and chemical properties of matter

physical-and-chemical-properties-of-matter

Distinguishing Physical and Chemical Changes

Matter can be identified by its properties, which are the features that help us tell one substance from another. These properties fall into two main groups: physical properties and chemical properties. Understanding the difference helps explain how matter changes. A physical property is a feature of matter that is not linked to a change in chemical composition. Examples include density, color, hardness, melting point, boiling point, and electrical conductivity. Some physical properties can be...

what is energy?

Energy Forms and Conservation

Energy is a property of matter that appears in many forms. On Earth, most energy starts with the Sun. Plants capture light energy from the Sun and use photosynthesis to turn it into chemical energy. That stored energy can then move through living things and materials in several ways. People get energy from plant foods, and wood or coal, which come from fossilized plants, can be burned to produce heat and electricity. Energy is defined as the ability to do work. Work happens when a force moves...

classifying matter by state

States of Matter and Their Properties

States of matter help describe how matter behaves in chemistry. Matter is anything that has mass and takes up space. It is found everywhere, including air, water, soil, mountains, and even our bodies. The three common states on Earth are solid, liquid, and gas. A solid has a definite shape and a definite volume. Its particles, such as atoms or molecules, are packed very closely together and held in place by strong forces, so they only vibrate slightly. This tight arrangement makes solids...

measurement: standard units

Measurement: SI Units and Conversions

Measurement gives three kinds of information: a number, a unit, and an estimate of uncertainty. The number shows size or magnitude. The unit gives a standard for comparison. The uncertainty reflects possible error in the measurement. Numbers can be written in more than one way. A value may appear in decimal form or in scientific notation, which is also called exponential notation. For example, the maximum take-off weight of a Boeing 777-200ER airliner is 298,000 kilograms, or 2.98 × 10^5 kg. <br...

classifying matter by composition

Matter: Elements, Compounds, and Mixtures

Matter can be grouped by composition into pure substances and mixtures. A pure substance has a constant composition throughout and uniform properties. For example, any sample of sucrose has the same composition and the same physical properties, such as melting point, color, and sweetness, no matter where it is isolated from. A mixture contains two or more kinds of matter in varying amounts. Its parts can be separated by physical changes, such as evaporation. The components keep their own...

measurement: derived units

SI Units, Density, and Property Types

SI units and derived units help describe physical properties in chemistry. The International System of Units, or SI system, uses agreed-upon base units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. Units made by combining these base units are called SI-derived units. Speed is one example. If distance is measured in meters and time in seconds, the derived unit for speed is meters per second, or m/s. Miles per hour is...

dimensional analysis

Using Conversion Factors to Cancel Units

Dimensional analysis is a method for using conversion factors to cancel units and solve measurement problems. It is also called the factor label method. The main rule is that units must be treated the same way as the numbers attached to them. A conversion factor is a ratio of two equal quantities written in different units. For example, 1 meter is equal to 1.0936 yards. That relationship can be used to build a factor that converts one unit into the other. When a value is multiplied or divided...

uncertainty in measurement: accuracy and precision

uncertainty-in-measurement-accuracy-and-precision

Measurement Error: Reading Results Correctly

Measurement error affects how scientists judge the quality of their results. Repeated measurements help show whether results are precise and accurate. A measurement is precise when repeated values are very similar. A measurement is accurate when it is very close to the true or accepted value. Precise values agree with each other, while accurate values agree with the true value. A pharmaceutical quality control chemist can use this idea to check machines that dispense 500 mL of cough syrup. The...

uncertainty in measurement: reading instruments

uncertainty-in-measurement-reading-instruments

Measurement Uncertainty and Significant Figures

Measurement uncertainty and significant figures show how carefully a value can be read from an instrument. Counting is different. If the number of objects does not change during counting, the result is exact. Defined quantities are exact too. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Most other measurements are not exact because the measuring process has limits. The result depends on the device used and on the person...

uncertainty in measurement: significant figures

Significant figures and rounding rules help students report measurements with the right level of certainty. A measurement includes every digit that was actually measured, including the last uncertain digit. That is why a value can look simple but still carry useful information about the tool used to measure it. Zero can also be significant when it is part of a measured value. For example, if a scale reads 140 pounds to the nearest pound, the 1, 4, and 0 are all significant. Reporting...

key terms and concepts

Learn how to count significant figures, identify leading and trailing zeros, and apply rounding rules in measurement calculations for high school chemistry.

Significant Figures and Rounding Rules | JoVE K12

chemistry

JoVE Core 화학은 간결하고 이해하기 쉬운 애니메이션을 통해 일반 화학 개념을 설명합니다. 또한, 과학자가 직접 고전실험과 연구실험을 진행하는 실사 영상을 제공합니다.

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CHEM.1

CHEM.1.E

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BIO.1

BIO.1.E

Georgia Standards of Excellence

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Stoichiometry Problem-Solving

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 ...

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, ...

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

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 ...

Hybridization of Atomic Orbitals II

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 ...

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 bonding

Chemical Formulas

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

ionic-compounds-formulas-and-nomenclature

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 ...

molecular-compounds-formulas-and-nomenclature

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, ...

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 ...

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 ...

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

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.

Significant Figures and Rounding Rules

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