Name: gas laws behind the ideal equation
Uploaded: 2023-04-30T12:30:10.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Chemistry

Matter and Its Interactions

CHEM1.PS1.6

Ideal Gas Equation

Zmiennymi stanu badanego gazu są ciśnienie, objętość, temperatura i liczba moli.
Prawo Avogadro mówi, że objętość gazu jest proporcjonalna do liczby moli przy stałej temperaturze i ciśnieniu.
Podobnie prawo Boyle'a wyraża, że ciśnienie jest odwrotnie proporcjonalne do objętości gazu dla danej liczby moli i przy stałej temperaturze.
Ponadto prawo Charlesa podaje zależność między objętością i temperaturą gazu pod stałym ciśnieniem a daną liczbą moli.
Podobnie prawo Gay-Lussaca mówi, że ciśnienie gazu jest proporcjonalne do jego temperatury dla danej liczby moli i przy stałej objętości.
Te cztery prawa w połączeniu dają równanie gazu doskonałego. Stała proporcjonalności jest uniwersalną stałą gazową, o wartości 8,314 dżuli na mol kelwina w jednostkach SI. Jest ona niezależna od rodzaju gazu objętego badaniem.
Równanie gazu doskonałego opisuje każdy gaz w wyższych temperaturach i niskich ciśnieniach.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson; sekcja 18.1; strona 591–593.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. Źródło: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sekcja 2.1; strony 68–73.</li>
</ol>

równanie gazu doskonałego

Równanie gazu doskonałego to równanie stanu, które łączy zmienne stanu: ciśnienie, objętość, temperaturę i liczbę moli hipotetycznego gazu. Równanie to jest kombinacją czterech praw empirycznych, a mianowicie prawa Boyle'a, prawa Charlesa, prawa Avogadro i prawa Gay-Lussaca. Połączenie proporcjonalności powyższych czterech praw empirycznych daje w rezultacie pojedynczą stałą proporcjonalności znaną jako uniwersalna stała gazu.

<img alt="Równanie1" src="/files/ftp_upload/13667/13667_Equation_1.svg" style="text-align: center; height: 12px;" />

Ta stała gazowa jest taka sama dla wszystkich gazów rzeczywistych w określonych warunkach. Wartość uniwersalnej stałej gazu wynosi

<img alt="Równanie2" src="/files/ftp_upload/13667/13667_Equation_2.svg" style="text-align: center; height: 10px;" />

ale gdy w obliczeniach chemicznych stosuje się równanie gazu doskonałego, wartość uniwersalnej stałej gazu wynosi

<img alt="Równanie3" src="/files/ftp_upload/13667/13667_Equation_3.svg" style="text-align: center; height: 12px;" />

Równanie gazu doskonałego opisuje naturę dowolnego gazu rzeczywistego, gdy jego gęstość jest wystarczająco niska lub temperatura jest na tyle wysoka, że ​​daleko mu do skroplenia.

W rzeczywistych sytuacjach prawo gazu doskonałego stosuje się do próbki gazu o stałej liczbie cząsteczek; na przykład gaz może znajdować się w szczelnie zamkniętym pojemniku. Jeśli liczba moli jest stała, wówczas stosunek ciśnienia pomnożonego przez objętość do temperatury gazu jest stały. W takich przypadkach można zrównać stosunek ciśnienia pomnożonego przez objętość do temperatur w dwóch różnych stanach gazu. W tym przypadku temperatura musi być wyrażona w stopniach Kelvina, a ciśnienie musi być ciśnieniem bezwzględnym, które jest sumą ciśnienia manometrycznego i ciśnienia atmosferycznego.

Równania gazu doskonałego można również wyrazić w postaci stałej Boltzmanna jako

<img alt="Równanie4" src="/files/ftp_upload/13667/13667_Equation_4.svg" style="text-align: center; height: 12px;" />

Tutaj kB to stała Boltzmanna, a NA to Avogadro' ; numer. Równanie gazu doskonałego można wyprowadzić, korzystając z kinetycznej teorii gazów. Równanie gazu doskonałego jest ściśle powiązane z energią. Jednostką po obu stronach równania są dżule.

Równanie gazu doskonałego

Równanie gazu doskonałego to równanie stanu, które wiąże zmienne stanu ciśnienie, objętość, temperaturę i liczbę moli hipotetycznego ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

The Kinetic Theory of Gases

Kinetyczna teoria gazów

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 best when a gas has low density or a high temperature, so it is far from liquefaction. In many real-world cases, the gas sample has a constant number of molecules. A sealed container is one example. If the number of moles stays constant, then the ratio of pressure multiplied by volume to temperature stays constant as well.

That means the ratio can be set equal for two different states of the same gas. The temperature must be written in kelvin. The pressure must be absolute pressure, which is gauge pressure plus atmospheric pressure.

The ideal gas equation can also be written with Boltzmann’s constant, kB, and Avogadro’s number, NA. It can be derived from the kinetic theory of gases. The equation is also closely related to energy, and the units on both sides are joules.

Gas Laws Behind the Ideal Equation

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

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...

kinetic theory of an ideal gas

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...

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 Boyle’s, Charles’s, Avogadro’s, and Gay-Lussac’s laws combine into the ideal gas equation, and why kelvin and absolute pressure matter.

Gas Laws Behind the Ideal Equation | 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

Alabama Course of Study Science

9-12

Earth and Space Science

Earth's Systems

9-12.ESS.2.7.c

Florida Department of Education

SC.912.P.12

SC.912.P.12.10

Georgia Standards of Excellence

SC5.

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Gas Laws: Pressure, Volume, Temperature, and Moles

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CHEM1.PS1.1

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CHEM1.PS1.2

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CHEM1.PS1.3

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CHEM1.PS1.4

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CHEM1.PS1.5

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CHEM1.PS1.7

Gas Laws Behind the Ideal Equation

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