Problem 150 - A Complete Resource Book in Chemistry for JEE Main

Question

For which of the following parameters 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 vaules? (assume ideal behaviour) [2004] (a) gaseous densities at the same temperature and pressure (b) heat of vaporization (c) boiling points (d) vapour pressure at the same temperature

Step-by-Step Solution

Answer

They have the same gaseous densities at the same temperature and pressure (option a).

Step 1: Understanding the Problem

We are given two isomers: ethanol (\(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\)) and dimethyl ether (\(\mathrm{CH}_{3}\mathrm{OCH}_{3}\)). We need to identify which parameters among the options provided would be the same for both isomers assuming ideal behavior.

Step 2: Analyzing Option A

The density of a gas is given by the formula \( \rho = \frac{PM}{RT} \), where \(M\) is the molar mass, \(P\) is the pressure, \(R\) is the gas constant, and \(T\) is the temperature. Both isomers have the same molar mass of 46 g/mol, therefore they will have the same gaseous densities at the same temperature and pressure.

Step 3: Analyzing Option B

The heat of vaporization is related to intermolecular forces. Ethanol has hydrogen bonding while dimethyl ether does not, hence they will have different heats of vaporization due to different intermolecular forces.

Step 4: Analyzing Option C

Boiling points are influenced by the strength of intermolecular forces. Due to ethanol's hydrogen bonding, its boiling point is higher than that of dimethyl ether, which does not have hydrogen bonds. Therefore, their boiling points will not be the same.

Step 5: Analyzing Option D

Vapor pressure at the same temperature is also affected by intermolecular forces. Ethanol's hydrogen bonding results in lower vapor pressure compared to dimethyl ether; hence, they will not have the same vapor pressures at the same temperature.

Step 6: Conclusion

Based on the above analysis, the only parameter where these isomers are expected to have the same values is their gaseous densities at the same temperature and pressure.

Key Concepts

Gaseous Density

Gaseous density is an important concept in chemistry, especially when studying gases and their behavior. It is defined as the mass of a gas per unit volume, often expressed in grams per liter (g/L) under specified conditions of temperature and pressure. For any gas, the density can be calculated using the ideal gas equation in the form: \( \rho = \frac{PM}{RT} \), where:

• \( \rho \) is the density.
• \( M \) is the molar mass of the gas (g/mol).
• \( P \) is the pressure (usually in atm).
• \( R \) is the ideal gas constant \( (0.0821 \, \text{L atm/(K mol)}) \).
• \( T \) is the temperature in Kelvin (K).

When comparing gaseous densities of different substances, if the gases are measured under the same conditions of temperature and pressure, their densities directly depend on their molar masses. In the case of ethanol \( (\mathrm{C}_2\mathrm{H}_5\mathrm{OH}) \) and dimethyl ether \( (\mathrm{CH}_3\mathrm{OCH}_3) \), both have the same molar mass of 46 g/mol. As a result, at the same temperature and pressure, they will exhibit the same gaseous density, regardless of their different structural forms.

Intermolecular Forces

Intermolecular forces are interactions that occur between molecules, affecting their physical properties like boiling points, melting points, and solubilities. There are several types of intermolecular forces:

• Dipole-Dipole Interactions: Occur between polar molecules with permanent dipoles.
• Hydrogen Bonds: An especially strong type of dipole-dipole interaction that occurs when hydrogen is bonded to electronegative elements such as nitrogen, oxygen, or fluorine.
• London Dispersion Forces: Also known as van der Waals forces, present in all molecules, especially important in non-polar molecules.

Ethanol and dimethyl ether demonstrate how these forces impact physical properties. Ethanol can engage in hydrogen bonding due to the presence of an -OH group, leading to higher boiling points and stronger intermolecular attractions. In contrast, dimethyl ether lacks significant hydrogen bonding capabilities, relying mainly on weaker dipole-dipole interactions and London dispersion forces. This difference explains the variation in their heats of vaporization, boiling points, and vapor pressures.

Molar Mass

Molar mass is a basic concept in chemistry that refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all elements in a molecular formula. Understanding molar mass is crucial because it allows us to convert between amounts of substance, often measured in moles, and its mass in grams.In structural isomers like ethanol \( (\mathrm{C}_2\mathrm{H}_5\mathrm{OH}) \) and dimethyl ether \( (\mathrm{CH}_3\mathrm{OCH}_3) \), even though they have the same number of each type of atom—and therefore the same molar mass—their chemical properties can differ significantly. This is because their different arrangements of atoms alter their intermolecular interactions. Despite these differences in chemical behavior, having the same molar mass means that under ideal conditions of temperature and pressure, their gaseous densities will also be the same, highlighting the role of molar mass in understanding gas behavior.