1.8
A Equação de Van der Waals
A lei dos gases ideais baseia-se em duas suposições simplificadoras: primeiro, que não há atrações intermoleculares entre moléculas de gás, e segundo,…
A lei dos gases ideais, baseada nas suposições de atrações intermoleculares negligenciáveis e volume desprezível de moléculas de gás, falha em altas pressões e baixas temperaturas.
Aqui, a equação de van der Waals, uma versão modificada da lei dos gases ideais, compensa esses desvios introduzindo correções.
A primeira correção no termo de pressão ajusta para a diferença entre pressão real de gás e pressão de gás ideal. À medida que as moléculas de gás se atraem, a pressão real do gás é menor que o valor ideal.
Essas forças atrativas reduzem tanto a frequência quanto a força das colisões com as paredes do recipiente. Como resultado, a pressão redutora é diretamente proporcional ao quadrado da concentração molar das moléculas.
A segunda correção está no termo de volume, calculando o volume real disponível para moléculas de gás como volume total menos o volume excluído por interações intermoleculares repulsivas.
As constantes 'a' e 'b', conhecidas como coeficientes de van der Waals, representam, respectivamente, a intensidade das interações atrativas e repulsivas entre moléculas de gás. Note que ambos os coeficientes são constantes empíricas características de cada gás e permanecem inalterados pela temperatura.
View the full transcript and gain access to JoVE Core videos
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.