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

理想気体方程式には2つの大きな欠点があります:第一に、それはガス分子の体積を考慮しないこと、第二に、それはガス分子間の引力的な分子間力を考慮しない。 
ガスがn個のモルを含み、それぞれが体積bを占める場合、ガス分子が占める総体積はnbです。したがって、気体分子が移動できる体積は、総体積からnbを引いたものになります。
引力的な分子間力は、モル密度の2乗に比例して圧力を減少させます。引力のある分子間力がない場合、同じnRTに到達するにはより高い圧力が必要です。
これは、理想気体方程式の欠点に対処しようとするファンデルワールス状態方程式です。ここで、a と b は、調査対象のガスの種類に依存する経験定数です。
ファンデルワールス方程式は、液体から蒸気への遷移やジュールトムソン効果など、実際の気体の振る舞いを適切に予測します。

<ol>
	<li>ヤング、H.D.およびフリードマン、RA(2012)。現代物理学と大学物理学。カリフォルニア州サンフランシスコ:ピアソン;セクション18.1;595ページと617ページ。</li>
	<li>OpenStaxです。(2019). 大学物理学 Vol.2.【Web版】。<a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2 から取得</a>。セクション2.1;75ページ。</li>
</ol>

ファンデルワールス方程式

Van der Waals Equation

理想気体の法則は、高温低圧でうまく機能する近似です。 ファン デル ワールス状態方程式 (オランダの物理学者ヨハネス ファン デル ワールス、1837 ～ 1923 年にちなんで命名) は、2 つの要素を考慮することで状態方程式を改善します。

まず、分子間の引力は、密度が高くなるほど強くなり、圧力を低下させるため、モル密度の 2 乗に正の係数を掛けたものに等しい項を圧力に追加することによって考慮されます。a。 次に、分子の体積は正の定数bで表され、分子 1 モルの体積と考えることができます。 これを総体積から差し引いて、分子が移動できる残りの体積を求めます。 定数 a と b は各ガスについて実験的に決定されます。 結果として得られる方程式は次のとおりです。

<img alt="Equation1" src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" />

ファンデルワールス方程式による二酸化炭素ガスの場合、定数 a は 0.364 J·m3/mol2 であり、定数です。 b は 4.27 x 10−5 m3/mol です。 このガス 1 モルが 300 K で 300 cm3 の体積に閉じ込められている場合、ガスの圧力はファン デル ワールス方程式を使用して計算できます。 圧力に関するファンデルワールス方程式を整理します。

<img alt="Equation2" src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" />

既知の量をそれに代入します。

<img alt="Equation3" src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" />

二酸化炭素ガスの圧力を与える

<img alt="Equation4" src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" />

低密度限界 (n が小さい) では、a 項と b 項は無視でき、ファン デル ワールス方程式は次のようになります。 理想気体の法則へ。 一方、ファン デル ワールス方程式の第 2 項が小さい場合、つまり分子が互いに非常に接近していることを意味し、同じnRTを得るには、次の式で予想されるように、圧力をより高くする必要があります。 高度に圧縮されたガスの状況。 ただし、高密度ではファンデルワールス方程式からの圧力補正項が重要であるため、圧力の増加はその議論が示唆するよりも小さくなります。 圧力補正項は正であるため、 同じnRTを得るにはより低い圧力が必要です。 ファン デル ワールスの状態方程式は、液体から気体の相転移の予測など、さまざまな条件下でほとんどの気体に対してうまく機能します。

理想気体の法則は、高温と低圧でうまく機能する近似です。ファンデルワールスの状態方程式(オランダ語にちなんで名付けられました...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The Kinetic Theory of Gases

気体分子運動論

KEY TERMS AND CONCEPTS

主要用語と概念

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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