Write the Lewis structure for each of the following compounds: (a) methanethiol, \(\mathrm{CH}_{3} \mathrm{SH}\), one of the compounds found in bad breath and some cheeses; (b) carbon disulfide, \(\mathrm{CS}_{2}\), which is used to make rayon; (c) dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}, \mathrm{a}\) common solvent.

Valence electrons are the electrons occupying the outermost shell of an atom. These electrons play a pivotal role in chemical bonding because they can be lost, gained, or shared to form chemical bonds. For instance, in the Lewis structure exercise for methanethiol (\texttt{CH}\(_3\)\texttt{SH}), carbon has 4 valence electrons, hydrogen has 1 each (though they are only able to form a duet as opposed to an octet), and sulfur has 6 valence electrons. Understanding the count of valence electrons is the first step in predicting how atoms will bond chemically.

In simpler terms, think of valence electrons as the hands of atoms; they're what atoms use to hold onto each other, forming bonds to create molecules. When drawing Lewis structures, starting by counting valence electrons for each atom is crucial as it informs how atoms connect and share these 'hands' to achieve stability.

The octet rule is a principle that predicts how atoms combine to form compounds. It states that atoms are most stable when they have eight electrons in their valence shell, which is why atoms tend to gain, lose, or share electrons to reach that stable state. There are, of course, exceptions to this rule, but for many elements, particularly those in main groups of the periodic table, the octet rule is a handy guideline.

For example, in the exercise of drawing the Lewis structure for carbon disulfide (\texttt{CS}\(_2\)), each sulfur atom adheres to the octet rule by sharing four electrons with the central carbon atom through a double bond, achieving octets for both sulfur atoms and carbon atom. It's akin to a 'give and take' in relationships, where atoms 'negotiate' to share or transfer valence electrons to feel 'complete' or stable with a full set or octet of valence electrons.

Chemical bonding is the process through which atoms combine to form molecules or compounds. Bonds can come in different strengths and types, such as ionic, covalent, and metallic bonds. The Lewis structures drawn for compounds such as dichloromethane (\texttt{CH}\(_2\)\texttt{Cl}\(_2\)), illustrate the covalent bonding type, where atoms share their valence electrons to achieve stability according to the octet rule.

Covalent bonding is like a partnership where atoms share valence electrons. In our exercise example with dichloromethane, both carbon and chlorine have to share electrons in such a way that carbon achieves an octet and each chlorine has an octet, signifying balanced sharing and a stable molecule. Chemical bonds are what make the myriad of materials and substances around us, defining their properties and behaviors in different environments.