Question

Positive deviation from ideal behaviour takes place because of (1) Molecular interaction between atoms and \(P \operatorname{Vin} R T>1\) (2) Molecular interaction between atoms and \(P \operatorname{VinRT}<1\) (3) Finite size of atoms and \(P V / n R T>1\) (4) Finite size of atoms and \(P V / n R T<1\)

Short answer

Option (3) is correct: Finite size of atoms and \( \frac{PV}{nRT} > 1 \).

Step-by-step solution

Understanding Deviation from Ideal Behavior

Ideal gases follow the Ideal Gas Law: \[ PV = nRT \]. Real gases deviate from this behavior due to factors like molecular interactions and finite size of molecules. Positive deviation means that the volume of the gas is greater than expected for an ideal gas under the same conditions.

Identifying the Correct Factor

Positive deviation is primarily caused by the finite size of gas molecules. This finite size causes the gas to occupy more space than predicted by the Ideal Gas Law.

Analyzing the Mathematical Expression

Given \[ \frac{PV}{nRT} > 1 \], this means that the observed volume is greater than the volume predicted by the Ideal Gas Law. The finite size of the atoms contributes to this positive deviation.

Evaluating the Choices

Among the given options:(1) Refers to molecular interactions but lacks relevance to finite size.(2) Incorrect because it refers to negative deviation.(3) Correct as it factors in finite size and the correct condition for positive deviation.(4) Incorrect because it describes negative deviation.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry and physics that describes the relationship between pressure (P), volume (V), the number of moles (n), temperature (T), and the gas constant (R). It is given by the equation:

Finite Size of Molecules

: This law assumes that gas molecules do not interact and have no volume themselves. However, real gases do not perfectly follow this law because gas molecules do occupy space and can interact with each other.
When real gases are considered, these factors cause deviations from the ideal conditions stated by the Ideal Gas Law.

Real Gases

: Real gases differ from ideal gases due to the finite size of molecules and molecular interactions. Several factors contribute to this behavior:

• Finite Size: Gas molecules occupy space. This means that the volume available for the gas molecules to move around is less than the total volume of the container. This causes positive deviation in behavior.
• Molecular Interactions: Attractive and repulsive forces between gas molecules also contribute to deviations from ideal behavior. These interactions become significant at high pressures and low temperatures.
• Van der Waals Equation: To account for real gas behavior, the Van der Waals equation modifies the Ideal Gas Law to include constants (a and b) that correct for molecular interactions and finite volume, respectively:

This equation helps to describe real gases more accurately.