Problem 154 - A Complete Resource Book in Chemistry for JEE Main

Question

" \(a\) ' and "b' are van der Wall's constants for gases. Chlorine is more easily liquefied than ethane because [2011] (a) a for \(\mathrm{Cl}_{2}<\) a for \(\mathrm{C}_{2} \mathrm{H}_{6}\) but \(\mathrm{b}\) for \(\mathrm{Cl}_{2}>\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) a and \(\mathrm{b}\) for \(\mathrm{Cl}_{2}<\mathrm{a}\) and \(\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) a and \(\mathrm{b}\) for \(\mathrm{Cl}_{2}>\mathrm{a}\) and \(\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (d) a for \(\mathrm{Cl}_{2}>\) a for \(\mathrm{C}_{2} \mathrm{H}_{6}\) but \(\mathrm{b}\) for \(\mathrm{Cl}_{2}<\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\)

Step-by-Step Solution

Answer

Option (d) is correct: a for Cl2 > a for C2H6 but b for Cl2 < b for C2H6.

Step 1: Introduction to Van der Waals Constants

Van der Waals constants, 'a' and 'b', are used to account for the real behavior of gases. The constant 'a' measures the magnitude of intermolecular forces, while 'b' accounts for the finite size of gas molecules.

Step 2: Identify Chlorine and Ethane Constants

More easily liquefiable gases have stronger intermolecular forces, which corresponds to a higher 'a' constant. It also correlates to smaller 'b' constants since such gases can be compressed more easily.

Step 3: Comparison of Constants for Liquefaction

Since chlorine is more easily liquefied than ethane, the 'a' constant for chlorine (a for Cl2) must be greater than that for ethane (a for C2H6). This indicates stronger intermolecular forces in chlorine. Additionally, since chlorine can be compressed more easily as a result of these strong forces, it should have a smaller 'b' constant.

Step 4: Selecting the Correct Option Based on Analysis

From the provided options, option (d) states: 'a for Cl2 > a for C2H6 but b for Cl2 < b for C2H6', which aligns with the established condition of stronger forces and easier compressibility for chlorine.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces that occur between molecules. They play a crucial role in determining the properties of gases, liquids, and solids. These forces include types like dipole-dipole interactions, hydrogen bonds, and van der Waals forces. When we talk about gases, the van der Waals constant 'a' is particularly important. This constant is a measure of the magnitude of intermolecular forces present in a gas. A higher 'a' value indicates stronger forces between the molecules. Stronger intermolecular forces contribute to the ease of liquefaction of a gas. For instance, chlorine ( cl _2) has a higher 'a' constant than ethane ( C _2 H _6), meaning chlorine molecules attract each other more strongly, allowing them to liquefy more easily. Keep in mind:

• Stronger intermolecular forces result in higher 'a' constants.
• Stronger forces help explain why certain gases are more easily liquefied.
• Understanding these forces is key to grasping how real gases behave differently from ideal gases.

Liquefaction of Gases

Liquefaction is the process of turning a gas into a liquid. This occurs when the attractive forces between molecules become significant enough to pull them close together. The Van der Waals constant 'a' plays a crucial role in liquefaction because it represents the strength of these attractive forces. Gases with a higher 'a' value can be liquefied more easily because they have stronger intermolecular attractions. Meanwhile, the 'b' constant is also important here as it accounts for the physical size of the gas molecules and the space they occupy. For effective liquefaction:

• A higher 'a' constant indicates stronger intermolecular forces.
• A smaller 'b' constant contributes to easier compressibility and hence easier liquefaction.
• Chlorine, by having a higher 'a' and a lower 'b' than ethane, is more easily liquefied.

Gas Compressibility

Gas compressibility refers to how easily a gas can be compressed into a smaller volume. This property is heavily influenced by intermolecular forces and the size of the gas molecules, represented by the van der Waals constants 'a' and 'b'. A substance with stronger intermolecular forces and a smaller molecular size will have a higher compressibility factor. This is because the molecules are held together more tightly by the forces, but take up less space due to their size. Key points on compressibility:

• The 'a' constant signifies the strength of intermolecular attraction. Higher 'a' means stronger forces and potential for greater compactness.
• The 'b' constant reflects the volume occupied by the molecules. A smaller 'b' suggests less intrinsic volume and higher compressibility.
• Gases like chlorine, with high 'a' and low 'b', exhibit greater compressibility compared to gases like ethane with lower 'a' and higher 'b'.