Problem 93 - Chemistry The Central Science

Question

(a) List two experimental conditions under which gases deviate from ideal behavior. (b) List two reasons why the gases deviate from ideal behavior. (c) Explain how the function \(P V / R T\) can be used to show how gases behave nonideally.

Step-by-Step Solution

Answer

Two experimental conditions that cause gases to deviate from ideal behavior are low temperature and high pressure. Two reasons for this deviation are the presence of intermolecular forces and the finite size of gas particles. The function \(PV/RT\) can be used to show the non-ideal behavior of gases, as a value greater than 1 indicates positive deviation (repulsive forces dominate), while a value less than 1 indicates negative deviation (attractive forces dominate), and the ideal gas behavior is represented by \(PV/RT = 1\).

Step 1: a) Experimental Conditions for Deviation

Two experimental conditions that can lead to gases deviating from ideal behavior are: 1. Low Temperature: Gases tend to deviate from ideal behavior at low temperatures because the intermolecular forces between the gas particles become significant, resulting in nonideal behavior. 2. High Pressure: Gases also deviate from ideal behavior when subjected to high pressure. Under high pressure, the volume of the gas molecules becomes significant relative to the total volume of the gas, causing deviations from ideal gas behavior.

Step 2: b) Reasons for Deviation from Ideal Behavior

Two reasons why gases deviate from ideal behavior are: 1. Intermolecular forces: Ideal gas assumptions ignore the presence of any intermolecular forces between gas particles. However, in reality, gas particles have some weak intermolecular forces (such as Van der Waals forces) which make the gases deviate from ideal behavior. 2. Molecular size: Ideal gas assumptions consider gas particles as point masses with negligible volume. In reality, gas particles have a finite size, and at high pressure or low temperature conditions, the volume occupied by the gas particles becomes significant, causing deviations from the ideal gas behavior.

Step 3: c) Explanation of \(PV/RT\) Function

The function \(PV/RT\) is useful in understanding the non-ideal behavior of gases. For an ideal gas, the product of its pressure (P), volume (V), and the inverse of the gas constant (R) and absolute temperature (T) should equal 1, i.e., \(PV/RT = 1\). However, under certain conditions, gases do not follow the ideal gas equation, and the value of \(PV/RT\) differs from 1. A value of \(PV/RT\) greater than 1 indicates a positive deviation from ideal behavior. This implies that the repulsive forces between the gas particles are dominating and causing the gas to occupy a larger volume than predicted by the ideal gas equation. A value of \(PV/RT\) less than 1 indicates a negative deviation from ideal behavior. This implies that the attractive forces between gas particles are significant, causing the gas to be compressed to a smaller volume than predicted by the ideal gas equation. By comparing the value of the \(PV/RT\) function with 1, it is possible to deduce and analyze the non-ideal behavior of gases.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental concept in chemistry used to describe the behavior of gases under certain conditions. It's expressed by the equation \(PV = nRT\), where:

• \(P\) is the pressure of the gas.
• \(V\) is the volume it occupies.
• \(n\) is the number of moles of the gas.
• \(R\) is the universal gas constant.
• \(T\) is the temperature measured in Kelvin.

This equation assumes that gas particles do not interact and occupy no volume, making it accurate under conditions of high temperature and low pressure. Under such conditions, gases behave ideally because the particles are too far apart to have significant interactions. However, when these assumptions don’t hold, we observe deviations from this ideal behavior.

Intermolecular Forces

Intermolecular forces play a crucial role in the behavior of real gases. These are the forces of attraction or repulsion between neighboring particles. In the context of gases, they include:

• Van der Waals forces: Weak attractions between molecules that can impact gas behavior, particularly at low temperatures.
• Dipole-dipole interactions: Occur between polar molecules, affecting how tightly the gas particles come together.
• London dispersion forces: Present in all molecules, especially significant in non-polar molecules.

These forces become more noticeable at low temperatures and high pressures. At these conditions, particles are close enough for these intermolecular forces to influence behavior, leading to deviations from the ideal gas predictions.

Molecular Size

The size of gas molecules also affects their behavior, particularly at high pressures. In the ideal gas model, molecules are assumed to have negligible volume. However, real gas molecules occupy space. At higher pressures, the volume of the molecules becomes an important factor.

• When gas particles are cramped into a confined space, their actual volume leads to less free space for movement.
• This crowding effect causes increased interactions between particles, influencing properties such as pressure and volume.

Due to their finite size, gas particles deviate from the predictions of the Ideal Gas Law, necessitating adjustments in calculations to accommodate their volume.

Deviation from Ideal Gas

Deviation from the ideal gas behavior occurs when the assumptions of the Ideal Gas Law are not met. Specifically:

• At low temperatures, attractive intermolecular forces cause gas particles to pull closer together, leading to deviations.
• At high pressures, the significant molecular volume becomes non-negligible compared to the overall volume.

The function \(PV/RT\) is used to measure these deviations. For an ideal gas, this value is 1. Deviations occur as follows:

• Positive deviation (\(PV/RT > 1\)): Occurs when repulsive forces predominate, causing the gas to occupy more volume than predicted.
• Negative deviation (\(PV/RT < 1\)): Happens when attractive forces are dominant, shrinking the volume below the ideal prediction.

By analyzing \(PV/RT\), it's possible to understand how and why gases deviate from ideal conditions, offering insights into intermolecular interactions and molecular sizes.