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

理想气体方程有两个重要缺陷：第一，它未考虑气体分子本身的体积；第二，它未考虑气体分子之间存在的相互吸引力。
如果气体包含 n 摩尔的分子，且每个分子占据体积 b，则气体分子所占据的总体积为 nb。因此，气体分子可移动的有效体积为总体积减去 nb。
分子间的吸引力使压力降低，降低程度与摩尔密度的平方成正比。若不存在分子间吸引力，则需要更高的压力才能达到相同的 nRT 值。
这是范德华状态方程，旨在解决理想气体方程的不足之处。其中，a 和 b 是经验常数，其数值取决于所研究气体的种类。
范德华方程能够充分预测实际气体的行为，例如液体到蒸气的相变以及焦耳-汤姆逊效应。

<ol>
	<li>Young， HD 和 Freedman， RA （2012）。大学物理与现代物理。加利福尼亚州旧金山:皮尔逊;第 18.1 节;第 595 页和第 617 页。</li>
	<li>OpenStax 的。（2019）. 大学物理学第 2 卷。[Web 版本]。取自 <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>;第 2.1 节;第 75 页。</li>
</ol>

范德华方程

Van der Waals Equation

理想气体定律是一种在高温和低压下运行良好的近似定律。 范德华状态方程（以荷兰物理学家约翰内斯·范德华命名，1837-1923 年）通过考虑两个因素对其进行了改进。

首先，分子之间的吸引力在密度较高时更强并会降低压力，通过在压力上添加一项等于摩尔密度的平方乘以正系数a。 其次，分子的体积由正常数b表示，可以将其视为一摩尔分子的体积。 从总体积中减去该值即可得到分子可以移动的剩余体积。每种气体的常数a和b是通过实验确定的。 所得方程为

<img alt="Equation1" src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" />

对于范德华方程的二氧化碳气体，常数a为0.364 J·m3/mol2 b 为 4.27 x 10−5 m3/mol。 如果 1 摩尔该气体在 300 K 下被限制在 300 cm3 的体积中，则可以使用范德华方程计算该气体的压力。 重新整理压力的范德华方程，

<img alt="Equation2" src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" />

并代入其中的已知量，

<img alt="Equation3" src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" />

给出二氧化碳气体的压力

<img alt="Equation4" src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" />

在低密度极限（小n）下，a和b项可以忽略不计，范德华方程减少 到理想气体定律。 另一方面，如果范德华方程的第二项很小，这意味着分子非常接近，那么压力必须更高才能给出相同的nRT，正如在 高度压缩气体的情况。 然而，压力的增加小于该论点所暗示的，因为在高密度下，范德华方程中的压力修正项很重要。 由于压力修正项为正，因此需要较低的压力才能给出相同的nRT。 范德华状态方程适用于各种条件下的大多数气体，例如预测液-气相变。

理想气体定律是一种在高温和低压条件下效果良好的近似模型。范德华状态方程（以荷兰……命名）

Education

教育

JoVE Core

Physics

物理学

Unit 1

第一单元

The Kinetic Theory of Gases

气体分子动理论

KEY TERMS AND CONCEPTS

关键术语与概念

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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