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Metallic bonding is a type of chemical bonding that arises from the electrostatic attraction between positively charged metal ions and the delocalized electrons that surround them. In this bond, electrons are free to move throughout the entire structure, which gives metals their characteristic properties such as electrical conductivity, malleability, and ductility. This bonding is particularly strong due to the extensive network of bonds formed.
For example, in the case of \(\text{Cu}(s)\) in \(\text{Ag}(s)\), both copper and silver atoms bond together through metallic bonding. These types of bonds result in the formation of a lattice structure where the electrons flow freely, holding the metal ions in place and making the metal strong and stable.

Dipole-dipole interactions occur between polar molecules, where there is an uneven distribution of electrons. This causes one end of the molecule to carry a partial positive charge while the other end carries a partial negative charge. These opposite charges attract each other, creating a dipole-dipole interaction.
In part (b) of the exercise, we see \(\text{CH}_3\text{Cl}(g)\) and \(\text{CH}_3\text{OCH}_3(g)\). Both of these molecules are polar. Methyl chloride has a polar \(\text{C-Cl}\) bond, and dimethyl ether contains an oxygen atom which makes it polar as well. The strongest intermolecular force between these two would be dipole-dipole interactions, as their polarities induce attraction between the molecules.

London dispersion forces are the weakest type of intermolecular force and occur in all molecules, whether polar or nonpolar. These forces arise from temporary shifts in the density of electrons in electron clouds, creating instantaneous dipoles that induce dipoles in neighboring molecules, resulting in an attraction between them.
In part (c) of the exercise, we consider \(\text{CH}_3\text{CH}_3(g)\) (ethane) and \(\text{CH}_3\text{CH}_2\text{CH}_2\text{NH}_2(l)\) (propylamine). Ethane is nonpolar, meaning it does not have dipole-dipole interactions or hydrogen bonding capabilities. Propylamine is a polar molecule, but since ethane is nonpolar, the strongest intermolecular force here would be London dispersion forces. These forces, while weaker than others, still play an essential role in the behavior of nonpolar molecules.