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 would have the same values.

Step 1: Understanding Structural Isomers

Structural isomers are compounds with the same molecular formula but different structural arrangements of atoms. For this problem, ethanol (C_{2}H_{5}OH ext) and dimethyl ether (CH_{3}OCH_{3} ext) are the structural isomers of concern.

Step 2: Analyzing Heat of Vaporization (a)

The heat of vaporization is the energy required to convert a liquid into a gas at constant temperature and pressure. Since ethanol and dimethyl ether have different functional groups (alcohol vs. ether), their intermolecular forces differ, leading to different heats of vaporization.

Step 3: Evaluating Vapour Pressure (b)

Vapour pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. Due to different intermolecular forces, ethanol and dimethyl ether have different vapor pressures at the same temperature.

Step 4: Comparing Boiling Points (c)

Boiling point is determined by the strength of intermolecular forces. Ethanol, with hydrogen bonding, has a higher boiling point than dimethyl ether, which experiences weaker dipole-dipole interactions and dispersion forces.

Step 5: Assessing Gaseous Densities (d)

The gaseous density of a substance at the same temperature and pressure depends on its molar mass. Since ethanol and dimethyl ether have the same molecular formula, their molar masses are identical, leading to the same gaseous densities under identical conditions of temperature and pressure.

Key Concepts

Ethanol

Ethanol, also known as ethyl alcohol, is a colorless, volatile liquid with the formula \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \). It is commonly found in alcoholic beverages and used industrially as a solvent and a fuel. One of the key characteristics of ethanol is its ability to participate in hydrogen bonding due to the presence of the hydroxyl (\( -\mathrm{OH} \)) group. This intense bonding contributes significantly to its physical properties.

Hydrogen bonds are a type of strong intermolecular force, making ethanol have a relatively high boiling point compared to other molecules of similar size without hydrogen bonding ability, such as ethers. This property makes ethanol favorable in processes requiring significant heat to vaporize it, impacting its heat of vaporization and vapor pressure significantly.

Dimethyl Ether

Dimethyl ether (DME) is an organic compound with the formula \( \mathrm{CH}_{3} \mathrm{OCH}_{3} \). It is used as a refrigerant, aerosol propellant, and a transportation fuel. Unlike ethanol, dimethyl ether lacks hydrogen bonding because it does not have a hydroxyl group. Instead, it features dipole-dipole interactions as its primary intermolecular force.

These forces are weaker than hydrogen bonds, resulting in a much lower boiling point. This variation in intermolecular forces also means that dimethyl ether can transition to a gaseous state at relatively lower temperatures compared to ethanol. Consequently, the heat of vaporization is lower as less energy is required to separate the molecules when compared to ethanol.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between molecules. They play a crucial role in determining the physical properties of compounds, such as boiling points, melting points, and solubility. There are several types of intermolecular forces, including:

• Hydrogen bonds: Occur in molecules with \( -\mathrm{OH} \), \( -\mathrm{NH}_{2} \), or similar electronegative atoms bonded to hydrogen. These are very strong forces.
• Dipole-dipole interactions: Occur between polar molecules with positive and negative poles, but weaker than hydrogen bonds.
• Dispersion (London) forces: Found in all molecules, these forces are a result of temporary shifts in electron density, leading to transient dipoles.

Ethanol, being capable of forming hydrogen bonds, experiences stronger intermolecular forces compared to dimethyl ether, which relies on dipole-dipole interactions and dispersion forces. This difference is paramount when assessing boiling points and vapor pressures in structural isomers.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert one mole of a liquid into a gas at a constant temperature and pressure. It is measured in units of energy per amount, like joules per mole (\( \mathrm{J/mol} \)) or kilojoules per mole (\( \mathrm{kJ/mol} \)).

For structural isomers such as ethanol and dimethyl ether, the heat of vaporization varies due to differences in intermolecular forces. Ethanol, with its hydrogen bonds, demands more energy to break these bonds and convert into vapor, leading to a higher heat of vaporization. Dimethyl ether, with its weaker dipole-dipole and dispersion forces, requires less energy to vaporize, yielding a lower heat of vaporization value.

Vapour Pressure

Vapour pressure is the pressure exerted by a vapor in equilibrium with its liquid at a certain temperature. It is an indicator of a liquid's volatility and inversely related to the strength of intermolecular forces present.

For ethanol and dimethyl ether, their differing intermolecular forces result in different vapor pressures. Ethanol, characterized by stronger hydrogen bonds, has a lower vapor pressure as more energy is needed to overcome these forces. This makes ethanol less volatile compared to dimethyl ether. In contrast, dimethyl ether's weaker intermolecular attractions lead to a higher vapor pressure at the same temperature, indicating a greater tendency to evaporate into the vapor phase.