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

Le variabili di stato per il gas oggetto di studio sono la pressione, il volume, la temperatura e il numero di moli.
La legge di Avogadro afferma che il volume del gas è proporzionale al suo numero di moli a temperatura e pressione costanti.
Allo stesso modo, la legge di Boyle esprime che la pressione è inversamente proporzionale al volume del gas per un dato numero di moli e a temperatura costante.
Inoltre, la legge di Charles fornisce la relazione tra il volume e la temperatura del gas a pressione costante e un dato numero di moli.
Allo stesso modo, la legge di Gay-Lussac afferma che la pressione di un gas è proporzionale alla sua temperatura per un dato numero di moli e a volume costante.
Queste quattro leggi combinate danno l'equazione dei gas ideali. La costante di proporzionalità è la costante universale dei gas, con un valore di 8,314 joule per mole kelvin nelle unità SI. È indipendente dal tipo di gas oggetto dello studio.
L'equazione dei gas ideali descrive qualsiasi gas a temperature più elevate e basse pressioni.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson; sezione 18.1; pagine 591–593.</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto da <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sezione 2.1; pagine 68-73.</li>
</ol>

equazione dei gas ideali

L'equazione dei gas ideali è un'equazione di stato che mette in relazioni variabili di stato come la pressione, il volume, e il numero di moli di un ipotetico gas. Questa equazione è una combinazione di quattro leggi empiriche, chiamate legge di Boyle, legge di Charles, legge di Avogadro, e legge di Gay-Lussac. Quando vengono combinate le proporzionalità delle quattro leggi empiriche precedenti, il risultato è una singola proporzionalità costante conosciuta come costante universale dei gas.

<img alt="Equation1" src="/files/ftp_upload/13667/13667_Equation_1.svg" style="text-align: center; height: 12px;" />

Questa costante dei gas è uguale per tutti i gas sotto certe condizioni. Il valore della costante universale dei gas è:

<img alt="Equation2" src="/files/ftp_upload/13667/13667_Equation_2.svg" style="text-align: center; height: 10px;" />

Tuttavia, quando l'equazione dei gas ideali viene usata nei calcoli chimici, il valore della costante universale dei gas è:

<img alt="Equation3" src="/files/ftp_upload/13667/13667_Equation_3.svg" style="text-align: center; height: 12px;" />

Questa equazione dei gas ideali descrive la natura di qualunque gas reale quando la sua densità è abbastanza bassa o la sua temperatura è abbastanza alta da essere lontano dalla liquefazione.

In situazioni reali, la legge dei gas ideali è applicata ad un campione di gas con un numero di molecole costanti; per esempio, il gas può essere in un contenitore sigillato. Se il numero di moli è costante, allora il rapporto di pressione moltiplicato per il volume e la temperatura di un gas è costante. In tali casi, il rapporto di pressione moltiplicato per il volume e la temperatura di due diversi stati del gas può essere equiparato. Qui, la temperatura dev'essere espressa in kelvin, e la pressione dev'essere pressione assoluta, che è la somma della pressione manometrica e della pressione atmosferica.

L'equazione dei gas ideali può essere espressa anche in termini di costante di Boltzmann:

<img alt="Equation4" src="/files/ftp_upload/13667/13667_Equation_4.svg" style="text-align: center; height: 12px;" />

Qui, kB è la costante di Boltzmann, e NA è il numero di Avogadro. L'equazione dei gas ideali può essere derivata usando la teoria cinetica dei gas. L'equazione dei gas ideali è strettamente connessa all'energia. Le unità su entrambi i lati sono i joules.

Equazione dei gas ideali

L'equazione dei gas ideali è un'equazione di stato che mette in relazione le variabili di stato pressione, volume, temperatura e il numero di moli di un ipotetico ...

Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

The Kinetic Theory of Gases

La teoria cinetica dei gas

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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

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Arizona Science Standards

Physical Science

HS+C.P1

HS+C.P1U1.3

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9-12

Earth and Space Science

Earth's Systems

9-12.ESS.2.7.c

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SC.912.P.12

SC.912.P.12.10

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SC5.

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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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