Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The compressibility factor for an ideal gas is (a) \(1.5\) (b) \(1.0\) (c) \(2.0\) (d) \(\infty\)

Step-by-Step Solution

Answer

The compressibility factor for an ideal gas is 1.0 (option b).

Step 1: Understanding Compressibility Factor

The compressibility factor, often represented as \( Z \), is a measure used to determine how much a real gas deviates from its ideal gas behavior. For ideal gases, \( Z \) is typically set to a standard of 1 to indicate no deviation.

Step 2: Identifying Ideal Gas Conditions

An ideal gas is a theoretical concept where the particles are point masses and do not interact except through elastic collisions, leading to a compressibility factor of \( Z = 1 \). This means there are no intermolecular forces affecting the gas.

Step 3: Selecting the Correct Answer

From the provided options, we need to identify which compressibility factor indicates that the gas behaves ideally. Since the compressibility factor for an ideal gas is \( Z = 1 \), option (b) fits this condition.

Key Concepts

Understanding Ideal Gas

Ideal gases are used as a reference to simplify complex gas behaviors. In an ideal gas scenario, molecules are assumed to be point particles. This means they occupy no volume and have no mutual attractions.
This simplification allows the derivation of formulas like the ideal gas law: \(PV = nRT\). Here, \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature. These assumptions help in predicting a wide range of gas behaviors under different conditions.
For an ideal gas, the compressibility factor \(Z\) equals 1. This indicates that the gas follows the ideal gas law perfectly without deviations from predicted behavior. This typically occurs at high temperatures and low pressures, where molecular interactions are minimal.

Real Gas Deviation

Real gases deviate from ideal gas behavior due to factors like molecular volume and intermolecular forces. Compressibility factor \(Z\) helps quantify this deviation. When \(Z = 1\), the gas behaves ideally. However, real gases display deviations where \(Z eq 1\).
If \(Z > 1\), the gas exhibits positive deviation. This occurs when repulsive forces dominate, often at high pressures where molecules are forced close together. Conversely, when \(Z < 1\), attractive forces prevail leading to a negative deviation, common at low temperatures when molecules move slower and interact more.
Understanding these deviations helps in correcting the ideal gas equation to better predict real gas behaviors, especially under extreme conditions.

The Role of Intermolecular Forces

Intermolecular forces are crucial in understanding gas behavior, especially in non-ideal conditions. These forces include attractions like van der Waals forces and repulsions that affect how gases behave under different temperatures and pressures.
When considering real gases, these interactions determine the extent of deviation from ideal behavior. Attractive forces cause gas molecules to come closer, which reduces pressure at a constant volume, resulting in \(Z < 1\). Conversely, repulsive forces can increase the pressure, making \(Z > 1\).
In practical applications, equations such as the van der Waals equation incorporate these forces to better model and predict the behavior of real gases by adjusting the ideal gas law to account for molecular size and attraction.