Problem 33 - Chemistry The Molecular Science

Question

Which would you expect to have the higher fusion enthalpy, \(\mathrm{N}_{2}\) or \(\mathrm{I}_{2}\) ? Explain your choice.

Step-by-Step Solution

Answer

\(\mathrm{I}_2\) is expected to have a higher fusion enthalpy than \(\mathrm{N}_2\).

Step 1: Understand Fusion Enthalpy

Fusion enthalpy refers to the energy required to change a substance from solid to liquid at its melting point. It is influenced by the strength of intermolecular forces within the solid phase.

Step 2: Compare Molecular Structures

Both \(\mathrm{N}_2\) and \(\mathrm{I}_2\) are diatomic molecules, but \(\mathrm{N}_2\) is smaller in size with a triple bond, while \(\mathrm{I}_2\) consists of larger atoms connected by a single bond.

Step 3: Analyze Intermolecular Forces

\(\mathrm{N}_2\) has relatively weak London dispersion forces due to its smaller size and molecular mass. \(\mathrm{I}_2\), on the other hand, has stronger London dispersion forces due to its larger size and greater electron cloud polarizability.

Step 4: Consider Phase Behavior

\(\mathrm{N}_2\) is a gas at room temperature, suggesting very weak intermolecular forces and typically a lower fusion enthalpy. \(\mathrm{I}_2\) is a solid at room temperature, indicating stronger intermolecular forces requiring more energy for fusion.

Step 5: Conclude Based on Intermolecular Forces

Given that \(\mathrm{I}_2\) has stronger intermolecular forces due to its larger molecular size and higher polarizability, it is expected to have a higher fusion enthalpy compared to \(\mathrm{N}_2\).

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together in the solid and liquid phases. They are weaker than the bonds within a molecule but play a significant role in determining a substance's state of matter and properties like melting and boiling points. These forces differ from intramolecular forces, which are the forces that hold the atoms within a molecule together, such as covalent bonds.
There are several types of intermolecular forces, including:

• London dispersion forces: The weakest of all, occurring between all molecules.
• Dipole-dipole interactions: Occurring in polar molecules with permanent dipoles.
• Hydrogen bonding: A special type of strong dipole-dipole interaction happening when hydrogen is bonded to very electronegative atoms like oxygen, nitrogen, or fluorine.

In the context of fusion enthalpy, stronger intermolecular forces within a solid signify that more energy is required to overcome these forces to melt the solid. This directly affects the fusion enthalpy. Molecules like iodine (\( \text{I}_2 \)) with larger atomic radii usually have stronger intermolecular forces compared to smaller molecules like nitrogen (\( \text{N}_2 \)).
It's important to understand that these forces influence the physical properties of substances and help explain why some substances are solids while others are liquids or gases at room temperature.

Diatomic Molecules

Diatomic molecules are molecules composed of only two atoms, which can either be the same or different. Common examples of diatomic molecules include nitrogen (\( \text{N}_2 \)) and iodine (\( \text{I}_2 \)). The characteristic that both molecules share is that they are simple and maintain a linear shape, which makes them particularly interesting when studying basic molecular interactions and properties.
Because diatomic molecules are usually the simplest form of a given element in gases, their interactions in terms of intermolecular forces become crucial to comprehend their physical properties.
In the exercise, comparing \( \text{N}_2 \) and \( \text{I}_2 \) involves looking at their atomic configurations and bonds. \( \text{N}_2 \) has a triple bond, which is very strong and leads to a linear molecule with its atoms closely bound. This results in weak intermolecular forces overall. For \( \text{I}_2 \), the atoms are larger and only share a single bond, but the molecule's overall larger size leads to more significant intermolecular forces.

London Dispersion Forces

London dispersion forces are a type of weak intermolecular force. They arise due to temporary fluctuations in the electron density around a molecule, which creates an instantaneous dipole that can induce a dipole in neighboring molecules. Though weak individually, the cumulative effect of these forces can be quite significant, especially in larger atoms and nonpolar molecules.
These are the only types of intermolecular forces present in nonpolar molecules like \( \text{N}_2 \) and \( \text{I}_2 \). The strength of London dispersion forces mainly depends on:

• Size of the electron cloud: Larger electron clouds are more polarizable and can produce stronger Londone dispersion forces.
• Shape of the molecule: Longer and larger molecules result in stronger dispersion forces.

When comparing \( \text{I}_2 \) and \( \text{N}_2 \), \( \text{I}_2 \) is greater in size and possesses a larger, more easily distorted electron cloud, thereby, resulting in stronger dispersion forces compared to the smaller \( \text{N}_2 \). This is why \( \text{I}_2 \), a solid at room temperature, has a higher fusion enthalpy than gaseous \( \text{N}_2 \), indicating its significant London dispersion forces.