Question

Draw Lewis structures for these ions and show which atom in each bears the formal charge. (a) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\) (b) \(\mathrm{CO}_{3}{ }^{2-}\) (c) \(\mathrm{OH}^{-}\)

Short answer

Answer: In CH₃NH₃⁺, the nitrogen atom bears the formal charge. In CO₃²⁻, the single-bonded oxygen atom bears the formal charge. In OH⁻, the oxygen atom bears the formal charge.

Step-by-step solution

Calculate the total number of valence electrons

For \(\mathrm{CH}_{3}\mathrm{NH}_{3}^{+}\): Carbon has 4 valence electrons, Hydrogen has 1 valence electron, and Nitrogen has 5 valence electrons. Since the ion has a positive charge, subtract one electron. Thus, the total number of valence electrons is: \(4 + 3\times1 + 5 + 3\times1 - 1 = 12\)

Create skeleton structure

Arrange the atoms as \(\mathrm{C - N}\), and then add three hydrogen atoms around the carbon and three hydrogen atoms around the nitrogen. Connect the central atoms to the outer atoms with single bonds. H | H-C-N-H | H

Complete the octets of the other atoms

The structure already accounts for all 12 valence electrons, and all atoms have a complete octet.

Calculate the formal charge

Now, we need to find the formal charge of each atom in the molecule: - Formal charge of Carbon = Valence electrons - Non-bonding electrons - 1/2(Bonding electrons) = \(4 - 0 - 1/2(8) = 0\) - Formal charge of Nitrogen = \(5 - 0 - 1/2(8) = +1\) Thus, the nitrogen atom bears the formal charge in \(\mathrm{CH}_{3}\mathrm{NH}_{3}^{+}\). #b) CO_3^{2-}#

Calculate the total number of valence electrons

For \(\mathrm{CO}_{3}{ }^{2-}\): Carbon has 4 valence electrons, and Oxygen has 6 valence electrons. Adding two electrons from its negative charge, the total number of valence electrons is: \(4 + 3\times6 + 2 = 24\)

Create skeleton structure

Arrange the atoms as a central carbon atom surrounded by three oxygen atoms. Connect the central atom to each of the outer atoms with single bonds. O | C-O \ O

Complete the octets of the other atoms

Add six electrons to each oxygen atom to complete their octets. Modify the structure by adding a double bond between carbon and one of the oxygen atoms to complete the carbon octet. O=C-O \ O^{-}

Calculate the formal charge

Now, we need to find the formal charge of each atom in the molecule: - Formal charge of Carbon = \(4 - 0 - 1/2(8) = 0\) - Formal charge of double-bonded Oxygen = \(6 - 4 - 1/2(4) = 0\) - Formal charge of single-bonded Oxygen = \(6 - 6 - 1/2(2) = -1\) Thus, the single-bonded oxygen atom bears the formal charge in \(\mathrm{CO}_{3}{ }^{2-}\). #c) OH^−#

Calculate the total number of valence electrons

For \(\mathrm{OH}^{-}\): Oxygen has 6 valence electrons, Hydrogen has 1 valence electron, and the ion has a negative charge, adding an electron. Thus, the total number of valence electrons is: \(6 + 1 + 1 = 8\)

Create skeleton structure

Connect the hydrogen atom to the oxygen atom with a single bond. O-H

Complete the octets of the other atoms

Add six electrons to the oxygen atom to complete its octet. O-H ||

Calculate the formal charge

Now, we need to find the formal charge of each atom in the molecule: - Formal charge of Oxygen = \(6 - 6 - 1/2(2) = -1\) - Formal charge of Hydrogen = \(1 - 0 - 1/2(2) = 0\) Thus, the oxygen atom bears the formal charge in \(\mathrm{OH}^{-}\).