Question

The term that correets for the attractive forces present in a real gas in the van der Waals equation is (A) \(n b\) (B) \(\frac{a n^{2}}{r^{2}}\) (C) \(-\frac{a n^{2}}{u^{2}}\) (D) \(-n b\)

Short answer

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is (B) \(\frac{a n^{2}}{V^{2}}\).

Step-by-step solution

Understand the van der Waals Equation

The van der Waals equation is an equation of state for a fluid composed of particles that have a non-zero size and a pairwise attractive force between them. It modifies the ideal gas law to account for these two physical effects.

Identify the Corrections in the van der Waals Equation

The van der Waals equation is written as \[\left( p + \frac{{a n^2}}{{V^2}} \right)(V - nb) = nRT,\] where the term \(p + \frac{{a n^2}}{{V^2}}\) corrects for the attractive forces between particles and the \(V - nb\) term corrects for the volume occupied by the gas particles themselves.

Find the Term Correcting for Attractive Forces

The term \(\frac{{a n^2}}{{V^2}}\) is added to the pressure \(p\) to account for the intermolecular attractive forces between particles of a real gas. Therefore, it is the correction term for the attractive forces in the van der Waals equation.

Key concepts

Real Gas Behavior

When we talk about gases in a scientific context, we often simplify their behavior with models, and one of the most popular is the Ideal Gas Law. However, the Ideal Gas Law doesn't fully describe the behavior of gases under all conditions. Real gases deviate from ideal behavior due to two main factors: the volume occupied by the gas molecules themselves, and the intermolecular forces between those molecules.

Real gases behave more like ideal gases when they are at low pressure and high temperature, conditions where particles are far apart and interact less. In contrast, at high pressures and low temperatures, particles are closer together and their behaviors are influenced more by intermolecular forces and their physical size. The van der Waals equation, which you encountered in the textbook exercise, comes into play to provide a more accurate description of gas behavior under these non-ideal conditions by introducing correction terms.

Intermolecular Attractive Forces

Intermolecular attractive forces are the forces that act between molecules or atoms. They are responsible for holding substances together and are key to understanding why real gases deviate from ideal behavior. When gas particles are close to each other, these forces become significant, affecting the pressure exerted by the gas on the walls of its container.

There are several types of intermolecular forces, including van der Waals forces, dipole-dipole interactions, and hydrogen bonds. In the context of the van der Waals equation, the term that corrects for these attractions is given the symbol 'a', which reflects the strength of these forces. The larger the value of 'a', the stronger the attractive forces between particles.

Correction Terms in Gas Laws

The van der Waals equation introduces correction terms to the Ideal Gas Law to account for the behavior of real gases. One correction modifies the pressure term to consider the attractive forces between particles, while the other adjusts the volume to account for the finite size of the gas particles.

The term \(p + \frac{a n^2}{V^2}\) includes a correction for intermolecular attractive forces. The adjustment made by 'a' helps predict the lower pressure observed due to attractions reducing collisions between molecules and the container walls. The term \(V - nb\) subtracts a volume 'nb', where 'b' signifies the volume excluded by gas molecules, representing the physical space they occupy.

Modified Ideal Gas Law

The van der Waals equation is commonly referred to as a modified Ideal Gas Law because it adapts the simpler, ideal model to account for real-life conditions. By incorporating correction factors, this equation can predict gas behavior with greater accuracy under a range of temperatures and pressures.

In the equation, 'n' represents the number of moles of gas, 'R' is the universal gas constant, 'T' is the temperature, 'V' is the volume, and 'p' is the pressure. The van der Waals modifications to the pressure and volume help us understand how real gases will behave compared to the prediction of the Ideal Gas Law. By doing so, scientists and engineers can design equipment and predict gas behavior in ways that are much more aligned with how gases actually behave in the real world.