Problem 96 - Chemistry The Central Science

Question

Table 10.3 shows that the van der Wals \(b\) parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the \(b\) parameter. Refer back to the discussion in Section \(7.3 .\) Is the van der Waals radius we calculate from the \(b\) parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain.

Step-by-Step Solution

Answer

The van der Waals radius, calculated from the $b$ parameter, is more closely associated with the nonbonding atomic radius. Both the van der Waals radius and the nonbonding atomic radius represent the distances between non-interacting atoms, excluding any significant interaction or attraction between them.

Step 1: Understanding van der Waals b parameter and its units

The van der Waals b parameter represents the volume occupied by one mole of molecules. It is a measure of the effective volume of the molecules themselves, excluding the interaction between them. The parameter has units of L/mol (liters per mole).

Step 2: Relating van der Waals b parameter to atomic sizes

To calculate the sizes of atoms or molecules, we can use the van der Waals b parameter. We can assume that the van der Waals radius is half the distance between two molecules when they are at their closest approach, without significant interaction between them. By knowing the volume occupied by one mole of such molecules, we can determine their effective sizes.

Step 3: Bonding and nonbonding atomic radii

In Section 7.3, two types of atomic radii were discussed: bonding and nonbonding atomic radii. The bonding atomic radius is the distance between the nuclei of two atoms when they are joined together, while the nonbonding atomic radius is the distance between the nuclei of two non-interacting atoms.

Step 4: Comparing van der Waals radius with bonding and nonbonding atomic radii

The van der Waals radius is calculated by considering the volume occupied by one mole of non-interacting molecules. This radius is based on the closest approach between these molecules, excluding any significant interaction or attraction between them. Therefore, the van der Waals radius is more closely associated with the nonbonding atomic radius, as it also represents the distances between non-interacting atoms, rather than those involved in bonding.

Key Concepts

van der Waals radius

The van der Waals radius is a concept used to describe the size of an atom or molecule based on the space it occupies. It originates from the van der Waals equation, which accounts for the volume and attractive forces of gases. Unlike other measures, the van der Waals radius considers atoms or molecules as hard spheres that touch but do not interact strongly.
The radius is typically half of the distance between two non-bonded atoms in a molecule or crystal. This helps in understanding how molecules pack in solids and liquids. The van der Waals radius is essential in predicting molecular behavior, especially in larger, complex systems.

• Helps in visualizing molecular shapes
• Useful in studying molecular interactions and reactions
• Key in discussing molecular sizes and structures

bonding atomic radius

The bonding atomic radius refers to the distance between the nuclei of two atoms when they are bonded together. This measurement gives insights into how atoms connect and form molecules. The bonding radius varies depending on the type of bond (covalent, ionic, metallic) and can differ across elements.
Bonding radii are typically shorter than nonbonding radii because bonded atoms share electrons and are brought closer by their mutual attractions. Understanding this concept helps in predicting bond lengths and strengths in different chemical compounds, making it a valuable tool in chemistry and material science.

• Vital for understanding molecule formation
• Helps in estimating bond energies
• Influences molecular geometry and stability

nonbonding atomic radius

The nonbonding atomic radius, also known as the van der Waals radius, describes the size of an atom when it is not bonded to another atom. This measurement is usually larger than the bonding atomic radius because it reflects the full space an atom requires in its free state.
This radius is crucial when considering atoms in condensed phases (liquids and solids) where they do not interact directly but still influence each other's positions and behavior. The nonbonding radius provides insights into intermolecular forces like London dispersion forces or dipole-dipole interactions.

• Essential for predicting physical properties of matter
• Useful in understanding molecular volumes and spacing
• Helps in evaluating packing efficiency in crystals

atomic sizes

Atomic sizes encompass both bonding and nonbonding atomic radii, providing a comprehensive view of how atoms behave within molecules and as independent entities. These sizes are not fixed and depend on the atom's environment, including its state (solid, liquid, gas) and the types of atoms it interacts with.
Smaller atomic sizes often result in stronger bonds and compact structures, while larger atomic sizes are more relevant in the context of physical properties like boiling and melting points.

• Influenced by electron cloud distribution
• Determines many physical and chemical properties of elements
• Key for understanding periodic trends across the periodic table

molecular volume

Molecular volume is the space occupied by a molecule and plays a vital role in understanding molecular behavior in different environments. It is directly derived from atomic sizes and arrangements in a molecule.
Molecular volume can influence how molecules interact, dissolve, and fit together in chemical processes. It is particularly important in gases, where volume and pressure relationships define the state and behavior of gases through equations like the Ideal Gas Law and van der Waals equation.

• Crucial for studying gas laws and solutions
• Helps in the design of drugs and materials
• Informs predictions about reaction mechanisms and solubility