Problem 19 - Chemistry

Question

Calculate the formal charge on each atom in the following electron-dot structures: (a) Cyanate ion: \([\ddot{\mathrm{N}}=\mathrm{C}=\ddot{\mathrm{O}}]^{-}\) (b) Ozone: \(: \ddot{\mathrm{O}}-\ddot{\mathrm{O}}=\ddot{\mathrm{O}}\)

Step-by-Step Solution

Answer

Cyanate has charges 0, 0, -1; ozone has charges 0, +1, -1.

Step 1: Understanding Formal Charge Formula

The formal charge can be calculated using the formula: \( \text{Formal Charge} = \text{Valence Electrons} - \text{Non-bonding Electrons} - \dfrac{\text{Bonding Electrons}}{2} \). This will be used to calculate the charge on each atom for the given structures.

Step 2: Calculating Formal Charge on Cyanate Ion

For the cyanate ion \([\ddot{\mathrm{N}}=\mathrm{C}=\ddot{\mathrm{O}}]^{-}\):- **Nitrogen (N):** Valence electrons = 5, Non-bonding electrons = 2, Bonding electrons = 6. Formal charge = \(5 - 2 - \frac{6}{2} = 0\).- **Carbon (C):** Valence electrons = 4, Non-bonding electrons = 0, Bonding electrons = 8. Formal charge = \(4 - 0 - \frac{8}{2} = 0\).- **Oxygen (O):** Valence electrons = 6, Non-bonding electrons = 6, Bonding electrons = 2. Formal charge = \(6 - 6 - \frac{2}{2} = -1\).Thus, the cyanate ion has formal charges of 0 for N, 0 for C, and -1 for O.

Step 3: Calculating Formal Charge on Ozone

For ozone \(: \ddot{\mathrm{O}}-\ddot{\mathrm{O}}=\ddot{\mathrm{O}}\):- **Left Oxygen (O):** Valence electrons = 6, Non-bonding electrons = 4, Bonding electrons = 4. Formal charge = \(6 - 4 - \frac{4}{2} = 0\).- **Middle Oxygen (O):** Valence electrons = 6, Non-bonding electrons = 2, Bonding electrons = 6. Formal charge = \(6 - 2 - \frac{6}{2} = +1\).- **Right Oxygen (O):** Valence electrons = 6, Non-bonding electrons = 6, Bonding electrons = 2. Formal charge = \(6 - 6 - \frac{2}{2} = -1\).Thus, the ozone molecule has formal charges of 0 for the left O, +1 for the middle O, and -1 for the right O.

Key Concepts

Electron-Dot Structures

Electron-dot structures, commonly known as Lewis structures, help us visualize the valence electron arrangement in a molecule. They provide a straightforward representation of all the atoms in the molecule, along with the electrons involved in forming chemical bonds. In these diagrams:

• Dots represent valence electrons.
• Lines signify bonding electron pairs between atoms.

By outlining how electrons are arranged around each atom, electron-dot structures allow us to predict the number and type of bonds an atom can form.
This is important as it helps determine the molecule's geometry and its reactivity.
For ions, such as the cyanate ion \( [\ddot{\mathrm{N}}=\mathrm{C}=\ddot{\mathrm{O}}]^{-} \), additional dots or lines may indicate negative charges that result from excess electrons.

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a key role in chemical bonding. They are the electrons that are used to form bonds with other atoms, and they determine an element's chemical properties. The number of valence electrons can be predicted based on an element's group in the periodic table.

• Group 1 elements have 1 valence electron.
• Group 2 elements have 2 valence electrons, and so on.

Identifying valence electrons is essential in drawing electron-dot structures.
For example, in the cyanate ion, nitrogen has 5 valence electrons, carbon has 4, and oxygen has 6. Understanding the distribution of these electrons guides the formation of both single and multiple bonds and assists in calculating formal charges for each atom.
This ensures the stability of the constructed molecules follows known chemical principles.

Bonding and Non-bonding Electrons

In each molecule, electrons can be classified as either bonding or non-bonding electrons. Bonding electrons are those involved directly in forming covalent bonds. A single bond consists of a pair of bonding electrons shared between two atoms. On the other hand, non-bonding electrons, also known as lone pairs, are not shared with other atoms and remain localized on a single atom.
In electron-dot structures, bonding electrons are represented as lines between atoms, while non-bonding electrons are shown as pairs of dots.

• Bonding electrons contribute to the connection between atoms, enhancing molecule stability.
• Non-bonding electrons can influence the shape of the molecule and its reactivity due to repulsive forces.

For example, in ozone \(: \ddot{\mathrm{O}}-\ddot{\mathrm{O}}=\ddot{\mathrm{O}} \), the middle oxygen has 6 bonding electrons and 2 non-bonding electrons. Recognizing these different types of electrons is crucial in understanding the electronic structure and function of molecules.