Name: how real gases deviate from ideal behavior
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 10 s
Channel: JoVE

Уравнение идеального газа имеет два существенных недостатка: во-первых, оно не учитывает объем молекул газа, а во-вторых, оно не учитывает притягивающие межмолекулярные силы между молекулами газа. 
Если газ содержит n молей и каждый из них занимает объем b, то общий объем, занимаемый молекулами газа, равен nb. Таким образом, объем, доступный для движения молекул газа, будет равен общему объему минус nb.
Притягивающие межмолекулярные силы снижают давление пропорционально квадрату молярной плотности. При отсутствии притягивающих межмолекулярных сил для достижения того же nRT требуется более высокое давление.
Это уравнение состояния Ван-дер-Ваальса, которое пытается устранить недостатки уравнения идеального газа. Здесь a и b являются эмпирическими константами, которые зависят от типа изучаемого газа.
Уравнение Ван-дер-Ваальса адекватно предсказывает поведение реального газа, такое как переход жидкости в пар и эффект Джоуля-Томсона.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон; раздел 18.1; стр. 595 и 617.</li>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Получено из <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; раздел 2.1; стр. 75.</li>
</ol>

Уравнение Ван дер Ваальса

Van der Waals Equation

Идеальный газовый закон является приближением, которое хорошо работает при высоких температурах и низком давлении. Уравнение состояния Ван дер Ваальса (названное в честь голландского физика Иоганнеса Ван дер Ваальса, 1837–1923) улучшает его, учитывая два фактора.

Во-первых, учитываются притяжательные силы между молекулами, которые становятся сильнее при более высоких плотностях и снижают давление, путем добавления к давлению слагаемого, равного квадрату молярной плотности, умноженному на положительный коэффициент a. Во-вторых, объем молекул представлен положительной константой b, которую можно рассматривать как объем моля молекул. Это вычитается из общего объема, чтобы получить оставшийся объем, в котором могут двигаться молекулы. Константы a и b определяются экспериментально для каждого газа. Полученное уравнение имеет вид:

<img alt="Equation1" src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" />

Для газа двуокиси углерода с помощью уравнения Ван дер Ваальса константа а равна 0,364 Дж·м3/моль2, а константа b равна 4.27 x 10−5 м3/моль. Если 1 моль этого газа находится в объеме 300 см3 при 300 К, то давление газа можно рассчитать с использованием уравнения Ван дер Ваальса. Переставляя уравнение Ван дер Ваальса для давления,

<img alt="Equation2" src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" />

и подставляя известные величины в него,

<img alt="Equation3" src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" />

получаем давление газа двуокиси углерода:

<img alt="Equation4" src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" />

В пределе малой плотности (малом значении n) слагаемые a и b являются пренебрежимо малыми, и уравнение Ван дер Ваальса сокращается до идеального газового закона. С другой стороны, если второе слагаемое в уравнении Ван дер Ваальса мало, что означает, что молекулы находятся очень близко друг к другу, то давление должно быть выше, чтобы получить то же значение nRT, как можно ожидать в случае сильно сжатого газа. Однако увеличение давления меньше, чем это предполагает формулировка, потому что при высоких плотностях поправочный термин давления из уравнения Ван дер Ваальса значителен. Поскольку поправочный термин давления положителен, он требует более низкого давления для того же значения nRT. Уравнение состояния Ван дер Ваальса хорошо работает для большинства газов при различных условиях, например, для прогнозирования фазовых переходов газ-жидкость.

Закон идеального газа — это приближение, которое хорошо работает при высоких температурах и низких давлениях. Уравнение государства Ван-дер-Ваальса (названное в честь голландского ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

The Kinetic Theory of Gases

Кинетическая теория газов

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 correction accounts for the space occupied by the molecules themselves. A positive constant b represents the volume of the molecules, or the volume of a mole of molecules, and this amount is subtracted from the total volume to leave the space the gas can actually move in. The values of a and b are found experimentally for each gas.

For carbon dioxide, the van der Waals constants are a = 0.364 J·m3/mol2 and b = 4.27 x 10−5 m3/mol. If 1 mole of carbon dioxide is confined to 300 cm3 at 300 K, the pressure can be calculated by rearranging the van der Waals equation for pressure and substituting the known values.

At low density, the a and b terms are small, so the van der Waals equation reduces to the ideal gas law. At very high density, the molecules are close together, so a higher pressure is needed to reach the same nRT. Even then, the pressure increase is smaller than a simple compression argument suggests because the pressure correction term becomes significant. This makes the van der Waals equation useful for many gases, including cases that involve liquid-gas phase transitions.

How Real Gases Deviate from Ideal Behavior

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key terms and concepts

See how the van der Waals equation corrects the ideal gas law for molecular attraction and finite molecular volume, with a carbon dioxide example.

How Real Gases Deviate from Ideal Behavior | JoVE K12

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How Real Gases Deviate from Ideal Behavior

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