Question

The compressibility factor of an ideal gas is: (a) 1 (b) 2 (c) 4 (d) 0

Short answer

The compressibility factor of an ideal gas is 1, so the answer is (a) 1.

Step-by-step solution

Understanding Compressibility Factor

The compressibility factor, usually denoted by Z, is a measure of how much the behavior of a real gas deviates from an ideal gas. For an ideal gas, Z equals 1, meaning the gas follows the ideal gas law perfectly.

Ideal Gas Definition

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. According to the ideal gas law, PV = nRT, where P is pressure, V is volume, n is moles of gas, R is the ideal gas constant, and T is temperature.

Finding Z for an Ideal Gas

For an ideal gas, by definition, the compressibility factor (Z) is always 1. This indicates no deviation from ideal behavior, meaning the gas follows the ideal gas law exactly.

Selecting the Correct Answer

With our understanding that for an ideal gas the compressibility factor is 1, we can confidently choose option (a) as our answer.

Key concepts

Compressibility Factor

The compressibility factor, denoted as \(Z\), is a crucial concept in understanding the behavior of gases. It helps us determine how closely a real gas aligns with the behavior predicted by the ideal gas law. For an ideal gas, \(Z\) is exactly 1. This indicates that the gas behaves perfectly according to the expectations established by the ideal gas law. This law suggests that gases should occupy a volume directly proportional to their temperature and amount, while inversely proportional to pressure. However, real gases don't always behave ideally. The compressibility factor allows us to quantify their deviation by showing how much \(Z\) differs from 1. If \(Z\) is greater than 1, the gas is less compressible than an ideal gas; if \(Z\) is less than 1, it's more compressible. Understanding \(Z\) helps in applications requiring precise measurements of gas behavior under different conditions.

Real Gas Deviation

Real gases, unlike ideal gases, often deviate from the expected behaviors as described by the ideal gas law. Several factors contribute to these deviations:

• The presence of attractive forces between molecules.
• The actual volume occupied by the gas molecules.
• Conditions of high pressure or low temperature, where molecular interactions become significant.

Real gas deviation is typically analyzed using the compressibility factor, \(Z\). It's a measure of how much a real gas's behavior differs from that of an ideal gas. When plotting a graph of pressure vs. \(Z\), a \(Z\) value deviating from 1 indicates a significant deviation due to molecular forces or volumes. Understanding these deviations is critical in many industrial and scientific processes, as modifying conditions can sometimes help align real gas behavior more closely with ideal predictions.

Ideal Gas Law

The ideal gas law is a foundation of introductory chemistry and physics. It is expressed by the formula \(PV = nRT\). Let's break down these elements:

• \(P\) stands for the pressure of the gas.
• \(V\) represents the volume the gas occupies.
• \(n\) is the number of moles, or how much of the gas substance is present.
• \(R\) is the ideal gas constant, a fixed value that relates the units of pressure, volume, and temperature.
• \(T\) symbolizes the temperature, measured in Kelvin.

This law implies that gas molecules are point particles that interact through elastic collisions, meaning that they don't lose energy when they collide with each other or the walls of a container. Therefore, the ideal gas law offers a useful approximation for the behavior of gases under various conditions. However, it primarily applies to ideal situations and may not account for real-world complexities like intermolecular forces.

Elastic Collisions

Elastic collisions are fundamental to the concept of an ideal gas. In the context of gases, an elastic collision means no kinetic energy is lost when gas molecules collide with one another or with the walls of their container. This idealized behavior is crucial for the assumptions of the ideal gas law to hold true. In elastic collisions:

• Energy and momentum are both conserved.
• The velocity of gas molecules may change, but the total energy remains the same.
• This lack of energy loss helps maintain consistent gas pressure and temperature as outlined by the ideal gas law.

In a real-world scenario, not all collisions are perfectly elastic because intermolecular forces may affect the movement and energy retention of molecules. Understanding these concepts aids in grasping why the ideal gas law is often an approximation and highlights areas where real gas behavior may differ.