Question

According to the van der Waals correction to get the pressure of ideal gas in observed pressure a definite fraction for correction is (a) subtracted (b) added (c) divided (d) unchanged

Short answer

The correct answer is (a) subtracted

Step-by-step solution

Understand van der Waals equation

The ideal gas law is expressed as \(PV = nRT\). The Van der Waals equation applies two corrections to this law: one for the effect of finite molecular size, and the other for molecular attractions. The equation is expressed as: \[ P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2\] Here, \(a\) and \(b\) are constants that depend on the gas. The effect of the finite size of the molecules is represented by \(b\), and the effect of intermolecular attractions is represented by \(a\).

Understand correction for ideal gas pressure

To get from ideal gas pressure to real or observed pressure, we need to correct the ideal gas pressure. Using the van der Waals equation, this is done by subtracting an amount \(a\left(\frac{n}{V}\right)^2\) from the ideal pressure \( \frac{nRT}{V}\). The net pressure from the van der Waals equation would thus be lesser than the ideal gas pressure.

Choose the correct option

Now, based on the understanding achieved in steps 1 and 2, we can choose the correct option regarding the definite fraction for correction to the pressure of an ideal gas. In the van der Waals equation, a certain amount is subtracted from the ideal gas pressure to account for the intermolecular attractions.

Key concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry and physics that describes the behavior of an ideal gas, which is a theoretical gas composed of randomly moving, non-interacting particles. The law is given by the equation \(PV = nRT\), where \(P\) stands for the pressure of the gas, \(V\) is the volume it occupies, \(n\) is the amount of substance (in moles), \(R\) is the ideal gas constant, and \(T\) is the absolute temperature. The law assumes that the gas particles are point particles with no volume and do not exert any forces, other than collisions, on each other. This makes it easy to predict the behavior of a gas under different conditions of temperature and pressure. However, real gases deviate from this ideal behavior due to the volume of the particles and the forces between them, which the ideal gas law does not account for.

To grasp the concept effectively, one should perform hands-on experiments, like changing the temperature or pressure of a contained gas and observing the changes in its volume. These practical experiences reinforce the relationships between the variables in the ideal gas equation.

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including attractions or repulsions which affect the physical properties of substances such as melting point, boiling point, and viscosity. Different types of intermolecular forces include dipole-dipole interactions, London dispersion forces, and hydrogen bonds.

To envision how these forces work, visualize several magnets in proximity: just as magnets can either repel or attract each other depending on their orientation, molecules can also interact in similar ways based on the nature of the intermolecular forces present. Understanding these forces assists in explaining why some substances are gases at room temperature while others are liquids or solids, as stronger intermolecular forces will generally result in a higher melting or boiling point.

Examples of Intermolecular Forces:

• Hydrogen Bonds: Occur between hydrogen and a highly electronegative atom such as oxygen, nitrogen, or fluorine.
• Dipole-Dipole Interactions: Occur between polar molecules, where a positively charged end of one molecule is attracted to the negatively charged end of another.
• London Dispersion Forces: Occur between all molecules, even nonpolar ones, due to the random movement of electrons leading to temporary dipoles.

These interactions play a crucial role in the physical properties of substances and are important to consider when predicting the behavior of real gases.

Real Gases

Real gases are actual gases that deviate from the idealized behavior laid out by the ideal gas law, especially under conditions of high pressure or low temperature. These deviations occur because the gas particles in real gases have a finite volume and intermolecular forces between them cannot be ignored. The van der Waals equation is a more accurate model that takes these factors into account, modifying the ideal gas law to better reflect real gas behavior.

The van der Waals equation introduces two corrections to the ideal gas law: one for the volume occupied by the gas molecules, represented by \(b\), and one for the intermolecular forces, represented by \(a\). This results in the corrected formula for the pressure of a real gas: \[ P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2 \]. The subtraction of the term \(a\left(\frac{n}{V}\right)^2\) accounts for the attractive forces, which effectively reduce the pressure exerted by the gas on the walls of its container.

Understanding Real Gases Through Experimentation:

To fully appreciate the concept, one might explore the behavior of different gases at varying pressures and temperatures, noting the deviations from ideal predictions. Such an experiment could involve measuring the pressure of a gas while systematically changing its volume, then comparing the results with the predictions of both the ideal gas law and the van der Waals equation.