Question

In your own words, define or explain the following terms or symbols: (a) \(\Delta H_{\text {vap }} ;\) (b) \(T_{c} ;\) (c) instantaneous dipole; (d) coordination number; (e) unit cell.

Short answer

\(\Delta H_{\text {vap }}\) is the enthalpy change of vaporization. \(T_{c}\) stands for critical temperature. An instantaneous dipole is a temporary dipole resulting from the electron cloud's transient asymmetry. Coordination Number is the number of atoms directly connected to an atom within a compound or a crystal lattice. A unit cell is the smallest unit of a crystal structure that covers its entire pattern.

Step-by-step solution

Defining \(\Delta H_{\text {vap }}\)

\(\Delta H_{\text {vap }}\) stands for the enthalpy change of vaporization. It's the amount of energy required to transform a quantity of liquid into gas, under constant pressure, without changing the temperature.

Explaining \(T_{c}\)

\(T_{c}\) generally denotes critical temperature. It is the maximum temperature at which distinct liquid and gas phases can occur. Beyond this temperature, there is only one phase, and the substance exists as a supercritical fluid.

Understanding Instantaneous Dipole

An instantaneous dipole refers to a temporary, rapidly-changing dipole that can occur even in a non-polar molecule. It results from fleeting asymmetry in the electron cloud around an atom or a molecule, leading to a very short-lived dipole moment.

Defining Coordination Number

Coordination Number is a term used in chemistry to denote the number of other atoms directly surrounding an atom in a molecule or a crystal lattice, particularly in metallic bonding or ionic bonding situations.

Explaining Unit Cell

A Unit Cell is the smallest, repeating unit of a crystal lattice that contains the entire pattern for the crystal structure. It is a three-dimensional geometric arrangement of atoms or molecules from which the complete lattice can be generated by simple translation.

Key concepts

Enthalpy of Vaporization

The enthalpy of vaporization, commonly denoted by \(\Delta H_{\text{vap}}\), is a key concept in thermodynamics and chemistry. It is the energy required to convert a given amount of liquid into a gas at a constant pressure, without changing the temperature. This process involves breaking intermolecular forces, such as hydrogen bonds, present in the liquid state. As energy is added to a liquid, its molecules gain enough kinetic energy to overcome these forces and transition into the gas phase.
Understanding \(\Delta H_{\text{vap}}\) is crucial for various applications, such as calculating boiling points and understanding phase changes. It's measured in units of energy per mole, typically kilojoules per mole (kJ/mol). The larger \(\Delta H_{\text{vap}}\), the stronger the intermolecular forces a liquid must overcome to vaporize.
Moreover, in practical terms, it's critical in designing cooling systems and understanding natural processes like evaporation in our climate system.

Critical Temperature

Critical temperature, symbolized as \(T_c\), is a fascinating concept in the study of phase transitions. It is the highest temperature at which a substance can exist as a liquid. Beyond this temperature, the distinction between liquid and gas phases ceases to exist; the substance transforms into a supercritical fluid.
This change occurs because, at elevated temperatures, the energy is sufficient to overcome the attractive forces completely. At \(T_c\), the physical properties of the liquid and its vapor become identical. As a result, there is no defined surface tension, and substances mix at any ratio.
Recognizing the critical temperature is fundamental in industries that utilize supercritical fluids, such as in supercritical fluid extraction processes and in optimizing chemical reactions under controlled conditions.

Instantaneous Dipole

An instantaneous dipole is an intriguing phenomenon that arises in the atomic world. It occurs when electrons, which are in constant motion around the nucleus, create fleeting asymmetries in their distribution. This temporary dipole forms even in non-polar molecules, where there is no permanent dipole moment.
The presence of instantaneous dipoles can induce dipoles in neighboring atoms or molecules, leading to weak interactions known as London dispersion forces or van der Waals forces. These forces, although weak and short-lived, play a considerable role in the physical properties of substances. They are pivotal in explaining why non-polar gases can liquefy under high pressure and low temperature.
This concept is crucial for understanding how molecules interact in phases and contributes to explanations of boiling and melting points.

Coordination Number

In chemistry, the coordination number refers to the count of atoms, ions, or molecules that are bonded or immediately adjacent to a central atom in a complex or crystal. This number is vital as it influences the geometry and stability of the molecule or crystal structure.
It is prominently used in describing transition metal complexes and crystal lattices. For example, in a crystal lattice, such as sodium chloride (NaCl), each sodium ion is surrounded by six chloride ions, giving it a coordination number of six.
The coordination number provides insight into the spatial arrangement and the bond angles, crucial for understanding the chemical and physical behavior of substances.

Unit Cell

The unit cell is the fundamental building block of a crystal lattice. It is the smallest structure that, when repeated in three dimensions, fully represents the crystal’s overall three-dimensional structure. The unit cell is defined by its lattice parameters—edge lengths and angles between them.
In essence, the geometric pattern of a unit cell, whether simple cubic, body-centered cubic, or face-centered cubic, dictates everything about the crystal's macroscopic properties. It informs us about how particles are packed, leading to an understanding of density, symmetry, and even electrical conductivity in materials.
Unit cells are pivotal in materials science and crystallography. Analyzing them helps scientists and engineers design better materials and understand those occurring naturally, from metals to minerals.