Many planets in our solar system contain organic chemicals including methane (CH \(_{4}\) ) and traces of ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right),\) propyne \(\left(\mathrm{H}_{3} \mathrm{CCCH}\right),\) and diacetylene (HCCCCH). Write the Lewis structures for each of these molecules.

Valence electrons play a pivotal role in chemical bonding and molecule formation. These are the electrons that reside in the outermost shell of an atom and are responsible for the atom's chemical properties.

For instance, in methane (CH₄), carbon has four valence electrons while each hydrogen has one. To acquire stability, carbon shares its four electrons with four hydrogens, so each atom achieves its respective complete outer shell - the 'octet rule' for carbon and the 'duet rule' for hydrogen.

The ability to count valence electrons correctly is essential when drawing Lewis structures for molecules, as demonstrated in the solution steps for various hydrocarbons found in planets of our solar system.

Understanding the mechanism of chemical bonding is vital for interpreting molecule formation and properties. Chemical bonds are the attractive forces holding atoms together in a compound, and there are several types including ionic, covalent, and metallic bonds.

In the context of Lewis structures for organic chemicals, covalent bonding is particularly relevant. A covalent bond is formed when atoms -- like carbon and hydrogen in hydrocarbons -- share pairs of valence electrons. Drawing Lewis structures helps reveal not just the presence of covalent bonds, but also their types, such as single, double, or triple bonds that satisfy the octet rule for most atoms involved in the bonding.

The spatial arrangement of atoms in a molecule defines its molecular geometry, which is a direct consequence of the chemical bonding within the molecule.

Methane is a perfect geometric example, forming a tetrahedral shape because the electron pairs around the carbon atom repel each other to the farthest distances possible in a 3D space for minimized repulsion. In contrast, ethylene (C₂H₄) has a planar geometry because of the double bond's influence on the electron pair distribution around the carbon atoms.

As seen in the step-by-step solutions, after drawing the Lewis structures, one can predict molecular geometry by applying the VSEPR (Valence Shell Electron Pair Repulsion) theory. This theory states that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsive forces, leading to the molecule's geometric shape.