Name: avogadro's number and gas particle motion
Uploaded: 2023-04-30T12:30:33.000Z
Duration: 1 min 12 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Chemistry

Matter and Its Interactions

CHEM1.PS1.5

Kinetic Theory of an Ideal Gas

A mole is defined as the amount of substance that contains the same number of elementary entities as the number of atoms in 12 grams of carbon.
Atoms, molecules, and other particles are some elementary entities that can be represented in moles. The number of molecules or atoms in a mole is known as Avogadro&#39;s number.
The molar mass of any compound is defined as the mass of 1 mole of that compound, and is represented in grams per mole.
The kinetic molecular theory of gases is a model based on several assumptions, which explains the physical characteristics of gases at the molecular level.
The gas molecules in the container obey Newton&#39;s law and are in continuous motion, which is random and isotropic.
The gas molecules behave as point particles, as the overall volume occupied by gas molecules is small in comparison to the total volume of the container.&#160;
The collision of gas particles with each other and with the walls of the container are elastic and thus result in no net energy loss.

kinetic theory of an ideal gas

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776&#8211;1856) formed the&#160; hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.
The number of molecules in one mole is called Avogadro&#39;s number (NA), and the value of Avogadro&#39;s number is now known to be NA = 6.02 &#215; 1023 mol&#8722;1. Avogadro&#39;s number relates the mass of an amount of substance in grams to the number of protons and neutrons in an atom or molecule (12 for a carbon-12 atom), which roughly determines its mass. The unit&#160; accepted for use with the SI is the unified atomic mass unit (u), also called the dalton.
The kinetic theory of gasses is a theory that relates the macroscopic properties of gasses to the motion of the molecules. The theory is based on several assumptions about molecules in an ideal gas.
<ol>
	<li>There is a very large number N of molecules, all identical and each having mass m.</li>
	<li>The molecules obey Newton&#39;s laws and move&#160; in a random, continuous, isotropic motion, that is, it is the same in all directions.</li>
	<li>The molecules are much smaller than the average distance between them, so their total volume is much less than that of their container (which has volume V). Thus, the volume of a mole of gas molecules is negligible compared to the volume of a mole of gas in the container.</li>
	<li>The molecules make perfectly elastic collisions with the walls of the container and with each other. The other&#160; forces acting on the molecules&#160; include&#160; gravity and the attractions represented by the Van der Waals constant, are negligible .</li>
</ol>

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist ...

Education

JoVE Core

Physics

Unit 1

The Kinetic Theory of Gases

KEY TERMS AND CONCEPTS

avogadro's number and gas particle motion

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is.

Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number links the mass of a substance in grams to the number of protons and neutrons in its atoms or molecules. For carbon-12, that count is 12, which helps explain why its mass is used as a standard. The SI-accepted unit for atomic mass is the unified atomic mass unit, or dalton.

The kinetic theory of gases connects the macroscopic properties of gases to the motion of their molecules. It describes an ideal gas using a set of assumptions. There are a very large number N of identical molecules, and each one has mass m. The molecules follow Newton's laws and move in random, continuous, isotropic motion, which means the motion is the same in all directions.

In this model, the molecules are much smaller than the average distance between them. Their total volume is much less than the volume V of the container, so the volume of the gas particles is negligible compared with the container volume. The molecules also make perfectly elastic collisions with the walls of the container and with each other. Other forces, including gravity and attractions represented by the Van der Waals constant, are treated as negligible.

Avogadro's Number and Gas Particle Motion

equation of state

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

Gas Laws Behind the Ideal Equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

van der waals equation

How Real Gases Deviate from Ideal Behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects. One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a. The second...

pv-diagrams

Liquid-Gas Changes on pV Curves

pV curves show how gas pressure changes with volume. A pV diagram is a graph of pressure versus volume for the gas being studied. It helps describe how the substance behaves. When the gas acts like an ideal gas, the ideal gas equation gives the link between pressure and volume. A common pV curve is an isotherm, which is a line drawn at fixed temperature and fixed number of molecules. For an ideal gas, pressure times volume stays constant. That means volume goes down as pressure goes up. The...

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is. Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number...

molecular kinetic energy

Gas Pressure and Molecular Motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

distribution of molecular speeds

Molecular Speed Curves and Vapor Pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

mean free path and mean free time

Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

escape velocities of gases

Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

key terms and concepts

Learn how Avogadro's number, the mole, and kinetic theory connect gas mass, particle motion, elastic collisions, and ideal gas behavior.

Avogadro's Number and Gas Particle Motion | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Arizona Science Standards

Physical Science

HS+C.P1

HS+C.P1U1.3

Florida Department of Education

SC.912.P.10

SC.912.P.10.5

SC.912.P.12

SC.912.P.12.10

SC.912.P.12.11

formula-mass-and-mole-concepts-of-compounds

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 ...

Expressing Solution Concentration

A solute is a component of a solution that is typically present at a much lower concentration than the solvent. Solute concentrations are often described ...

determining-the-mass-percent-composition-in-an-aqueous-solution

Determining the Mass Percent Composition in an Aqueous Solution

Source: Laboratory of Dr. Neal Abrams &#8212; SUNY College of Environmental Science and Forestry
Determining the composition of a solution is an important ...

Solutions and Concentrations

Source: Laboratory of Dr. Michael Evans &#8212; Georgia Institute of Technology
A solution is a homogeneous mixture containing some components in small ...

Reaction Stoichiometry

A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and ...

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Stoichiometry, Product Yield, and Limiting Reactants

Chemical equations represent how a chemical reaction proceeds from reactants to products through physical or chemical change using chemical formulas.
...

Understand and be prepared to use values specific to chemical processes: the mole, molar mass, molarity, and percent composition. EXPLANATION: During the early and mid-1800s, a tremendous amount of early research poured into building an understanding of the way that atoms combine. This work required analysis of the percent composition of different substances. Joseph Proust's work with tin oxides led him to publish his law of definite proportions noting that a given pure substance will have a constant ratio for the combination of elements making up the substance. Building on Proust's work, John Dalton published his law of multiple proportions and atomic theory noting that multiple patterns exist for the way that atoms combine, yet the combining atoms are invariable. Meanwhile Amedeo Avogadro hypothesizes that given equal pressures and temperatures, two equal volumes of gas will contain equal numbers of atoms. Acknowledging that the exact number of atoms was unknown in these gaseous volumes, the Latin word "mole" was used. "Mole" translates to "lump" recognizing the ambiguous quantity of gas. A number of attempts have been undertaken historically to quantify the mole. Robert Millikan's oil drop experiment revealed the change of a single electron, which could then be divided into Faraday's Constant for the charge of a mole of electrons. Dividing the charge of a mole of electrons by the charge of a single electron yields the number of electrons in a mole, $6.022\times10^{\wedge}23$. Students should be familiar with how to translate between the given quantities. Student's first use atomism/Dalton's atomic theory in third grade noting that matter is made up of particles too small to be seen. This the first time where students will undertake the process of counting these invisible particles. Electrolysis of water provides a tangible experience to demonstrate the constituent parts of water, though the definite proportions of water may not be easily seen due to the solubility of the gasses produced. The concept of relative mass can be explored by comparing small groups of like items. For example, relative masses of beans can be compared with pinto, white, and black beans. If bags are created with equal numbers of like beans, students can develop a concept of why the smallest bean will have a relative mass of 1, analogous to hydrogen.

CHEM1.PS1.1

Chemical Equations

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

Balancing Redox Equations

Electrochemistry is the science involved in the interconversion of electrical and chemical reactions. Such reactions are called reduction-oxidation, or ...

Demonstrate that atoms, and therefore mass, are conserved during a chemical reaction by balancing chemical reactions. EXPLANATION: Standard 7.PS1.4 explores the idea that chemical reactions are rearrangements of atoms, and students undertake the process of balancing chemical reactions with that standard in seventh grade. The introduction of molar masses in high school makes an explicit connection between the number of atoms, as previously investigated, and the actual masses of the atoms, permitting the collection of more concrete evidence for the conservation of mass in chemical reactions.

CHEM1.PS1.2

Reaction Yield

The theoretical yield of a reaction is the amount of product estimated to form based on the stoichiometry of the balanced chemical equation. The ...

A balanced chemical equation provides the information of chemical formulas of the reactants and products involved in the chemical change. A ...

Limiting Reactant

The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in ...

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Chemical Equilibria: Systematic Approach to Equilibrium Calculations

In systems with multiple equilibria, the equilibrium calculations use a systematic approach involving a series of steps to make sure there are as many ...

Perform stoichiometric calculations involving the following relationships: mole- mole; mass-mass; mole-mass; mole- particle; and mass- particle. Show a qualitative understanding of the phenomenon of percent yield, limiting, and excess reagents in a chemical reaction through pictorial and conceptual examples. (states of matter liquid and solid; excluding volume of gasses). EXPLANATION: This standard builds on the idea that balancing chemical reactions provides evidence for conservation of mass and that the behavior of atoms follows predictable patterns. Students now have the opportunity to utilize this understanding as they perform and evaluate chemical reactions. (The concepts of limiting reagent and percent yield are presented; however, students are not expected to determine these values algebraically. Use of molar volume in stoichiometric processes is beyond the scope of this standard.)

CHEM1.PS1.3

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, ...

Introduction to Chemical Reactions

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

Chemical Reactions in Aqueous Solutions

Chemical substances interact in many different ways. Certain chemical reactions exhibit common patterns of reactivity. Due to the vast number of chemical ...

Precipitation Reactions

In a precipitation reaction, aqueous solutions of soluble salts react to give an insoluble ionic compound &#x2013; the precipitate. The reaction occurs ...

Oxidation-Reduction Reactions

Oxidation&ndash;Reduction Reactions

Earth&rsquo;s atmosphere contains about 20% molecular oxygen, O2, a chemically reactive gas that plays an essential ...

Oxidation Numbers

In redox reactions, the transfer of electrons occurs between reacting species. Electron transfer is described by a hypothetical number called the ...

Acids, Bases and Neutralization Reactions

An acid-base reaction is one in which a hydrogen ion, H+, is transferred from one chemical species to another. Such reactions are of central importance to ...

Synthesis and Decomposition Reactions

Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The ...

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

Types of Chemical Reactions: Exchange and Reversible

An exchange reaction is a chemical reaction in which both synthesis and decomposition occur, chemical bonds are both formed and broken, and chemical ...

Use the reactants in a chemical reaction to predict the products and identify reaction classes (synthesis, decomposition, combustion, single replacement, double replacement). EXPLANATION: Chemical reactions are rearrangements of atoms that follow predicable patterns. There are patterns both at the macroscopic level in the behavior of some of the reaction classes, as well as patterns in the rearrangements of the atoms underlying the reaction. Students should be able to predict the products of the reactions, which also requires the ability to recognize the general patterns for each type of reaction.

CHEM1.PS1.4

kinetic-molecular-theory-gas-laws-explain-properties-gas

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws ...

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Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ...

Ideal Gas Law

Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between their ...

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Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

Through experiments, scientists established the mathematical relationships between pairs of variables, such as pressure and temperature, pressure and ...

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Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a ...

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Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, &nbsp;suggests that the volume of a given quantity of gas ...

Conduct investigations to explore and characterize the behavior of gasses (pressure, volume, and temperature), develop models to represent this behavior, and construct arguments to explain this behavior. Evaluate the relationship (qualitative and quantitatively) at STP between pressure and volume (Boyle's Law), temperature and volume (Charles' Law), temperature and pressure (Gay-Lussac Law) and moles and volume (Avogadro's Law), and evaluate and explain these relationships with respect to kinetic molecular theory. Be able to understand, establish, and predict the relationships between volume, temperature, and pressure using combined gas law both qualitatively and quantitatively. EXPLANATION: When exploring the behavior of gasses, it is important to consider experimental design. Experiments used to show the relationships between these sets of variables should include one independent and one dependent variable. Other variables should be held constant. Pressure should serve as the dependent variable because it cannot be manipulated directly. Avogadro's Law can be used to relate the amount of gas in two different containers in lieu of knowing actual number of gas particles in an individual container. Individual demonstrations can be performed to explore each of the different gas laws.

Ideal Gas Equation

The ideal gas equation is an equation of state that relates the state variables pressure, volume, temperature, and the number of moles of a hypothetical ...

Source: Laboratory of Dr. Andreas Z&#252;ttel - Swiss Federal Laboratories for Materials Science and Technology
The ideal gas law describes the behavior ...

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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

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Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities ...

pV-Diagrams

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Use the ideal gas law, PV = nRT, to algebraically evaluate the relationship among the number of moles, volume, pressure, and temperature for ideal gases. EXPLANATION: If students have collected data during investigations for CHEM1.PS1.5, these data can then be used to linearize. With pressure assigned as the dependent variable and plotted against (moles) (temperature)/volume, the slope of the graph will be the gas constant, yielding the ideal gas law. After developing the mathematical model, this model can be used to make predictions for other systems.

CHEM1.PS1.6

Separation of Mixtures via Precipitation

Source: Laboratory of Dr. Ana J. Garc&#237;a-S&#225;ez &#8212; University of T&#252;bingen
Most samples of interest are mixtures of many different ...

States of Matter and Phase Changes

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Distillation: Vapor&ndash;Liquid Equilibria

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Filtration

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Centrifugation

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...

Sublimation

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For example, solid carbon dioxide, or dry ...

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Recrystallization: Solid&ndash;Solution Equilibria

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Precipitation and Co-precipitation

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When different ions form sparingly soluble salts with the same ...

Electrodeposition

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While reduction occurs at the cathode ...

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Extraction: Partition and Distribution Coefficients

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Extraction: Effects of pH

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Extraction: Advanced Methods

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Chromatography: Introduction

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Dialysis

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Analyze solutions to identify solutes and solvents, quantitatively analyze concentrations (molarity, percent composition, and ppm), and perform separation methods such as evaporation, distillation, and/or chromatography and show conceptual understanding of distillation. Construct argument to justify the use of certain separation methods under different conditions. EXPLANATION: In seventh grade, students developed an understanding that chemical and physical properties of a sample of matter could be used to identify a substance. Building on this understanding, students now explore the use of these physical and chemical properties to separate mixtures. Analysis of the substances is performed to aid in further discussion and facilitate further quantitative analysis.

CHEM1.PS1.7

Acids and bases play several important roles in biology. The pH of a biological system can significantly impact the function of biological molecules, ...

Bronsted-Lowry Acids and Bases

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Lewis Acids and Bases

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Acid/Base Strengths and Dissociation Constants

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Identify acids and bases as a special class of compounds with a specific set of properties. EXPLANATION: The concept of pH is first introduced in seventh grade as a chemical property of matter. Students should be introduced to multiple explanations of acid and base behavior to permit classification of common substances (e.g. baking soda, ammonia, carbon dioxide) as acids or bases. To further develop discussions of solubility, qualitative discussions of the differences between strong and weak acids are appropriate. (Calculations of pH or ion concentrations are beyond the scope of this standard. Discussions of pOH are beyond the scope of this standard. Conjugate pairs are beyond the scope of this standard.)

CHEM1.PS1.8

Avogadro's Number and Gas Particle Motion

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