1.8
ファンデルワールス方程式
理想気体の法則は二つの簡略化仮定に基づいています。第一に、気体分子間に分子間引力が存在しないこと、第二に分子自身が占める体積は容器の体積に比べて無視できるほど小さいことです。しかし、これらの仮定はすべての条件下、特に高圧・低温で成り立つわけではありません。気体は理想気体の挙動から逸脱しやすいためです…
分子間引力が無視できるほど小さく、気体分子の体積も無視できるという仮定に基づく理想気体の法則は、高圧・低温では失敗します。
ここでは、理想気体の法則を修正したファンデルワールス方程式が、補正を導入することでこれらの偏差を補正します。
圧力項の最初の補正は、実気圧と理想気圧の差を補正します。気体分子同士が引き合うため、実質気体圧力は理想的な値より低くなります。
これらの引力は、コンテナ壁との衝突の頻度と力の両方を低減します。その結果、減圧は分子のモル濃度の二乗に比例します。
2つ目の補正は体積項にあり、気体分子の実際の体積を分子間反発相互作用で除外した体積を差し引いたものとして計算します。
定数「a」と「b」はファンデルワールス係数として知られ、それぞれ気体分子間の引力相互作用と反発相互作用の強さを表します。両係数は各気体に特徴的な経験定数であり、温度の影響を受けません。
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Q1: Why does the ideal gas law fail at high pressures and low temperatures?
The ideal gas law assumes negligible intermolecular attractions and negligible molecular volume, assumptions that break down under extreme conditions. At high pressures and low temperatures, gas molecules are forced closer together, making intermolecular forces and molecular size significant. This causes deviation from ideal behavior, requiring corrections to predict real gas behavior accurately.
Q2: What does the pressure correction term in the van der Waals equation account for?
The pressure correction adjusts for attractive forces between gas molecules that reduce measured pressure below the ideal value. These intermolecular attractions decrease both collision frequency and force with container walls. The pressure reduction is directly proportional to the square of molar concentration, reflecting how attraction strength increases with molecular density.
Q3: How does the volume correction term modify the van der Waals equation?
The volume correction calculates actual available volume for molecular motion by subtracting the volume excluded by molecules themselves. For n moles where each molecule occupies volume b, the excluded volume is nb. The actual free volume becomes total volume minus nb, accounting for the physical space occupied by gas molecules.
Q4: What do the van der Waals coefficients 'a' and 'b' represent?
Coefficient 'a' represents intermolecular attraction strength; larger values indicate stronger cohesion and greater pressure correction. Coefficient 'b' represents excluded volume from repulsive interactions; larger values mean less free space available. Both are empirical constants unique to each gas and remain temperature-independent within the van der Waals model.
Q5: How do intermolecular attractions affect real gas pressure?
Intermolecular attractions pull molecules together, reducing the force and frequency of collisions with container walls. This causes real gas pressure to be lower than predicted by ideal gas behavior. The magnitude of this pressure reduction depends on molecular concentration squared, making it more significant at higher densities.
Q6: Why are van der Waals coefficients treated as temperature-independent?
Within the van der Waals model, coefficients 'a' and 'b' are treated as empirical constants characteristic of each gas that remain unaffected by temperature changes. This simplification allows the equation to provide reliable corrections across a range of conditions, though real substances may show some temperature dependence in practice.
Q7: When is the virial equation of state preferred over the van der Waals equation?
The virial equation of state is preferred for higher precision, particularly over wide ranges of temperatures and pressures. While the van der Waals equation offers valuable insights into real gas behavior, it is not universal for all substances. Virial coefficients, commonly tabulated at various temperatures, capture deviations from ideal behavior more accurately.