Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Positive deviation from ideal behaviour takes place because of (a) Molecular interaction between atoms and \(P V / n R T>1\) (b) Molecular interaction between atoms and \(P V \ln R T<1\) (c) Finite size of atoms and \(P V / n R T>1\) (d) Finite size of atoms and \(\mathrm{PV} / \mathrm{nRT}<1\)

Step-by-Step Solution

Answer

The correct answer is (c) Finite size of atoms and \(\frac{PV}{nRT} > 1\).

Step 1: Understand Ideal Behavior Criteria

For an ideal gas, the condition \( PV = nRT \) holds, where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature. When \( \frac{PV}{nRT} = 1 \), it indicates ideal behavior. Deviations occur due to non-ideal properties of gases.

Step 2: Analyze Positive Deviation

Positive deviation from ideal behavior occurs when \( \frac{PV}{nRT} > 1 \). This means that the actual volume or pressure is higher than what would be expected for an ideal gas. Typically, this happens when repulsive forces are at play or molecules have significant volume.

Step 3: Examine Molecular Interactions

Molecular interactions refer to the attractive or repulsive forces between gas particles. In positive deviations, repulsive forces dominate because particles effectively occupy larger volume, causing them to push away from each other more.

Step 4: Consider the Finite Size of Atoms

The finite size of atoms or molecules means that these particles occupy a definite volume. Thus, in conditions where this becomes significant, gases will deviate positively from the ideal gas law as the available volume is less than expected.

Step 5: Identify Correct Explanation

Since positive deviation is caused by the finite volume of particles leading to \( \frac{PV}{nRT} > 1 \), the correct choice must reflect these factors.

Key Concepts

Ideal Gas Law

The ideal gas law is an equation that describes the behavior of gases under certain conditions. It combines several gas properties into a single relationship: \[ PV = nRT \] - **P** represents pressure. - **V** is volume. - **n** is the number of moles. - **R** is the gas constant. - **T** stands for temperature. When a gas perfectly adheres to this equation, it behaves ideally. In practical scenarios, however, gases often deviate from this ideal behavior, especially under high pressure or low temperature. The law assumes that gas molecules do not interact and occupy no volume. Thus, deviations are expected when molecular interactions or finite size of particles become significant.

Molecular Interactions

Molecular interactions refer to the attractive or repulsive forces that occur between gas particles. These forces are negligible in an ideal gas. However, real gases experience these interactions, which can impact their behavior.

• Attractive Forces: Pull particles together and can cause gases to condense.
• Repulsive Forces: Push particles apart and become significant when particles are close together, like at high pressures.

In the case of positive deviation from ideal behavior, repulsive forces dominate. This is because as pressure increases, molecules are forced closer together, making their finite size and volume more pronounced. This causes the gas to occupy more volume than predicted by the ideal gas law, resulting in \( \frac{PV}{nRT} > 1 \).

Finite Size of Particles

Gases consist of particles that have a definite, although very small, size. The ideal gas law assumes negligible particle size, which is true under many conditions but not all. In reality, each particle occupies space, which affects how gases behave: - As pressure increases, or at lower volumes, the volume occupied by the particles themselves becomes a larger part of the total volume. - This leads to positive deviations in ideal behavior, where measured pressure and volume ratios exceed ideal gas predictions. Such deviations occur because the finite size of particles reduces the free space available for movement, impacting the compliance with the ideal gas law. Thus, when considering the finite size of atoms, particularly under high-pressure conditions, the assumption of particles occupying no space breaks down, which is crucial in understanding positive deviations from ideal behavior.