For \(\mathrm{H}_{2} \mathrm{CO}\) : a) Is the sum of the bonding electrons and lone pair electrons around the carbon atom consistent with the Lewis model? b) Is the sum of the bonding electrons and lone pair electrons (nonbonding electrons) around the oxygen atom consistent with the Lewis model?

Valence electrons are the outermost electrons of an atom and are important in determining how the atom can bond with others. In chemistry, these electrons play a pivotal role in the formation of molecules. For instance, hydrogen (H) has one valence electron, carbon (C) has four, and oxygen (O) has six.

Understanding the number of valence electrons in an element is crucial for drawing Lewis structures. The Lewis structure is a graphical representation of how atoms bond and lone pairs of electrons in a molecule. For the molecule \( \mathrm{H}_2\mathrm{CO} \), we count the valence electrons by adding the valence electrons for each atom: hydrogen contributes 1 electron per atom, carbon contributes 4, and oxygen contributes 6, leading to a total of 12 valence electrons that need to be distributed in the Lewis structure.

The octet rule is a chemical rule of thumb that reflects the observation that atoms of main-group elements 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 the s- and p-block elements of the periodic table and dictates that the atoms involved in chemical bonds seek to have eight electrons in their valence shell for stability.

This rule guides us in determining the most stable structure for a molecule. For the carbon atom in \( \mathrm{H}_2\mathrm{CO} \), it does not initially follow the octet rule as step 2 of the solution shows it only being surrounded by 4 bonding electrons. However, this apparent discrepancy is resolved by considering the molecule's complete Lewis structure which reveals that there are double bonds, thus providing the carbon atom with the additional electrons needed to comply with the octet rule.

Lone pair electrons refer to pairs of valence electrons that are not shared with another atom in a covalent bond. These non-bonding electrons belong exclusively to one atom and play a significant role in the shape and reactivity of molecules. In the Lewis structure of \( \mathrm{H}_2\mathrm{CO} \), the oxygen atom, for example, has two lone pairs, which are pairs of electrons that are non-bonding.

Lone pair electrons can influence the molecule's geometry and are often represented as dots next to the atom in Lewis structures. Their presence is crucial for understanding reactions and interactions between molecules since they can participate in chemical reactions by forming additional bonds or repelling other electron pairs, affecting molecular polarity and intermolecular forces.

Bonding electrons, in contrast to lone pair electrons, are the valence electrons that are shared between atoms to form covalent bonds. Each shared electron pair constitutes a single covalent bond, represented by a single line connecting the two atoms in a Lewis structure.

For \( \mathrm{H}_2\mathrm{CO} \) as described in the solution steps, carbon shares its four valence electrons with two hydrogen atoms and one oxygen atom, resulting in a total of four bonding electrons. This allows carbon to adhere to the octet rule when considering the double bond it forms with oxygen, which provides it with additional electrons necessary for stability. The concept of bonding electrons is fundamental to understanding molecule formation and the structural layout of different compounds.