Question

Draw a Lewis structure for the \(\mathrm{C}_{2}^{2-}\) ion.

Short answer

The Lewis structure for the \\([\mathrm{C}_2]^{2-}\\) ion involves a triple bond between the carbon atoms: C≡C.

Step-by-step solution

Determine Total Valence Electrons

First, determine the total number of valence electrons in the molecule. Carbon (C) is in group 14 and has 4 valence electrons. Since there are two carbon atoms, the total is initially 8 valence electrons. However, the ion has a 2- charge, indicating that there are 2 additional electrons. Thus, the total number of valence electrons is 8 + 2 = 10.

Arrange Atoms and Distribute Electrons

Arrange the two carbon atoms next to each other: C – C. Begin placing electrons around each carbon atom, ensuring that you use all 10 electrons and strive for a complete octet around each carbon atom.

Form Multiple Bonds

If necessary, form double or triple bonds to ensure that each carbon atom has a complete octet of electrons. With 10 valence electrons, placing all 10 electrons between the carbon atoms as bonds fulfills both carbon's octet requirements: \( C \equiv C \), indicating a triple bond between the carbon atoms.

Verify the Structure

Check that all 10 electrons are used and each carbon achieves an octet: The structure should have each carbon atom involved in 3 bonds and 2 lone pairs shared between them, totaling 10 electrons.

Confirm Overall Charge

Ensure that the final structure reflects the overall 2- charge by confirming each carbon atom's formal charge is minimized. Each carbon shares 8 electrons (4 from each triple bond and no lone pairs), showing out they effectively are neutral within the context of the bond.

Key concepts

Valence Electrons

Valence electrons are the outermost electrons in an atom that are involved in chemical bonding. For carbon, which is in group 14 of the periodic table, each atom possesses 4 valence electrons.

• Valence electrons determine an element's reactivity and the types of bonds it can form.
• In the \( \mathrm{C}_2^{2-} \) ion, each carbon atom contributes 4 electrons, giving a base total of 8.
• The 2- charge indicates an additional two electrons, resulting in a total of 10 valence electrons to be considered when drawing the Lewis structure.

This understanding is crucial as it sets the stage for arranging these electrons to satisfy further bonding rules, making sure that each atom meets specific stability criteria.

Octet Rule

The octet rule is a key concept in chemistry, describing how atoms tend to form bonds until they are surrounded by eight electrons, achieving a stable electron configuration similar to that of noble gases.

• For carbon, attaining an octet means having four covalent bonds, filled with shared electrons.
• In the context of \( \mathrm{C}_2^{2-} \), this rule necessitates ensuring that each carbon atom ends up with 8 electrons shared around it.

To achieve this with 10 total electrons between two carbons, adjustments such as forming double or triple bonds may be necessary. When the electrons are organized primarily as shared bonds between the carbons, both can meet the octet requirement.

Formal Charge

Formal charge is a helpful tool for determining the most stable Lewis structure by having the smallest possible charges on each atom. It is calculated with the formula: \[ \text{Formal charge} = \text{valence electrons} - (\text{non-bonding electrons} + \frac{1}{2}\text{bonding electrons}) \]

• In the \( \mathrm{C}_2^{2-} \) ion, each carbon atom shares 8 electrons through a triple bond, without extra lone pairs.
• The calculation would show that if the electrons in the bonds are evenly shared, the atoms maintain a formal charge of zero.
• A formal charge of zero is preferred as it often correlates with more stable molecular configurations.

This adjustment helps in validating that the Lewis structure not only balances the electrons in distribution but also aligns with the ion's overall electric charge.

Triple Bond

A triple bond occurs when two atoms share three pairs of electrons. In chemical structures, these are among the strongest and shortest covalent bonds.

• For the \( \mathrm{C}_2^{2-} \) ion, the triple bond between the carbon atoms is crucial in distributing all 10 valence electrons effectively.
• This arrangement helps achieve the necessary octet for both atoms, as each carbon effectively shares 6 electrons in the bonding pairs.

A triple bond is denoted as \( C \equiv C \), signifying three shared electron pairs. This configuration allows both carbon atoms in the diatomic ion to achieve full octets, providing stability to the structure through strong covalent interactions.