Draw Lewis structures for the following: (a) \(\mathrm{NCl}_{3}\) (b) \(\mathrm{H}_{2} \mathrm{CO}_{3}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (d) \(\mathrm{NaNO}_{3}\)

Valence electrons are the electrons that reside in the outermost shell of an atom, and these are instrumental in the process of chemical bonding. For example, in the case of nitrogen (\textsc{N}), which has five valence electrons, or chlorine (\textsc{Cl}) with seven, understanding their number is the first step in predicting how these atoms will bond with others.

During chemical reactions, valence electrons are either shared with or transferred to other atoms, leading to the formation of chemical bonds. When drawing Lewis structures, the count of valence electrons determines how atoms connect and arrange themselves in a molecule. For instance, in the exercise given for \textsc{NCl}\(_{3}\), counting valence electrons (26 in total) helps illustrate how the nitrogen and chlorine atoms will share electrons to form stable bonds.

The octet rule is a chemical rule of thumb that states atoms tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule applies to most elements, although there are some exceptions. For example, hydrogen (\textsc{H}) and helium (\textsc{He}) follow the 'duet rule', aiming for two electrons in their outer shell.

In the step-by-step solutions for \textsc{H}\(_2\)\textsc{CO}\(_3\) and \textsc{C}\(_2\)\textsc{H}\(_6\), arranging the remaining electrons to satisfy the octet rule for the oxygen and carbon atoms is a crucial step, ensuring stability and a lower energy state for the molecules. This is why, after creating bonds, the additional electrons are placed as lone pairs around the more electronegative atoms to complete their octets.

Chemical bonding refers to the force that holds atoms together in chemical compounds. This occurs when atoms either share or transfer valence electrons, resulting in the formation of ionic, covalent, or metallic bonds. For instance, in \textsc{NaNO}\(_3\), sodium (\textsc{Na}) transfers its one valence electron to the polyatomic nitrate ion (\textsc{NO}\(_3^-\)), forming an ionic bond. The nitrate ion itself is held together by covalent bonds, where nitrogen shares its electrons with the oxygen atoms.

Understanding Lewis structures, like those drawn for \textsc{NaNO}\(_3\), helps in visualizing how atoms are bonded in molecules. It's a significant step in comprehending not only the structure of a molecule but also how the individual atoms within it interact through chemical bonding.