Problem 178 - A Complete Resource Book in Chemistry for JEE Main

Question

For which of the following parameters of the structural isomers \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) and \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) would be expected to have the same values? (Assume ideal behaviour)[2004] (a) heat of vaporization (b) vapour pressure at the same temperature (c) boiling points (d) gaseous densities at the same temperature and pressure

Step-by-Step Solution

Answer

Gaseous densities at the same temperature and pressure are expected to be equal.

Step 1: Analyzing Structural Isomers

Structural isomers have the same molecular formula but different structures. The molecules in question here are ethanol \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) and dimethyl ether \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\). Ethanol is an alcohol with a hydroxyl group (-OH), whereas dimethyl ether is an ether with an -O- linkage.

Step 2: Understanding Physical Properties

The physical properties of substances are greatly influenced by the type of intermolecular forces present. Ethanol, with its -OH group, can engage in hydrogen bonding, while dimethyl ether, with an -O-, mainly participates in dipole-dipole interactions. Both can exhibit London dispersion forces.

Step 3: Comparing Heat of Vaporization

The heat of vaporization is the energy required to convert a liquid into a gas at boiling point. Due to hydrogen bonding, ethanol has a higher heat of vaporization compared to dimethyl ether. This property is strongly influenced by intermolecular forces, which differ for these substances.

Step 4: Comparing Vapour Pressure

Vapour pressure is related to the tendency of molecules to escape the liquid phase. Substances with stronger intermolecular forces, like those in ethanol, have lower vapour pressure at the same temperature compared to substances like dimethyl ether. Thus, vapour pressures differ.

Step 5: Comparing Boiling Points

The boiling point depends on the intermolecular forces within a substance. Due to hydrogen bonding, ethanol has a significantly higher boiling point compared to dimethyl ether, whose intermolecular forces are weaker.

Step 6: Comparing Gaseous Densities

In gaseous form, molecules of ethanol and dimethyl ether behave ideally and have the same molecular weights since they are structural isomers \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\). Thus, under identical conditions of temperature and pressure, their gaseous densities are expected to be equal.

Key Concepts

Physical Properties of Isomers

Structural isomers are molecules that share the same molecular formula but differ in how their atoms are arranged in space. For example, ethanol \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and dimethyl ether \( \mathrm{CH}_{3} \mathrm{OCH}_{3} \) illustrate this concept well.
The physical properties of isomers can vary significantly because the structural arrangement influences the type and strength of intermolecular forces present.

• Ethanol: Contains an -OH group, allowing it to engage in hydrogen bonding, a strong intermolecular attraction.
• Dimethyl ether: Has an -O- linkage, which allows for dipole-dipole interactions, but these are generally weaker compared to hydrogen bonding.

These differences result in varied physical properties such as boiling points, vapor pressures, and heats of vaporization.

Intermolecular Forces

The type of intermolecular forces present in a substance heavily influences its physical characteristics. Understanding these is vital to predicting the behavior of substances like ethanol and dimethyl ether.
Hydrogen bonding is the strongest type of dipole interaction found when hydrogen is bonded to highly electronegative elements like oxygen. Ethanol showcases this due to its -OH group that allows for significant hydrogen bonding.
Conversely, dipole-dipole interactions occur in molecules like dimethyl ether. These forces arise from the attraction between oppositely charged ends of polar molecules but are generally weaker than hydrogen bonds.
London dispersion forces are also present in both ethanol and dimethyl ether. These are weak intermolecular forces due to temporary dipoles induced by the movement of electrons, present in all molecules to a varying degree.

Gaseous Densities Comparison

When considering gases, the physical arrangement of molecules becomes less important than their molecular weight under ideal behavior. This is why the gaseous densities of ethanol and dimethyl ether can be the same under identical conditions of temperature and pressure.

• Both isomers have the same molecular formula \( \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} \), resulting in the same molar mass.
• In an ideal gas scenario, where volume is constant across substances with equal molecular weights, their gaseous densities are expected to be the same.

This property highlights a unique scenario where the structure does not affect density, unlike the influence it has on other physical properties.