Question

Consider the pyrosulfate ion, \(\mathrm{S}_{2} \mathrm{O}_{7}^{2-}\). It has no sulfursulfur nor oxygen-oxygen bonds. (a) Write a Lewis structure for the pyrosulfate ion using only single bonds. (b) What is the formal charge on the sulfur atoms for the Lewis structure you drew in part (a)? (c) Write another Lewis structure using six \(\mathrm{S}=\mathrm{O}\) bonds and two \(\mathrm{O}-\mathrm{S}\) bonds. (d) What is the formal charge on each atom for the structure you drew in part (c)?

Short answer

In summary, the pyrosulfate ion (\(\mathrm{S}_{2} \mathrm{O}_{7}^{2-}\)) has two possible Lewis structures: one with single bonds and another with double bonds. In the first structure, both sulfur atoms have a formal charge of +2, while all other atoms have a formal charge of 0. In the second structure, sulfur atoms with single bonds have a formal charge of 0, while sulfur atoms with double bonds have a formal charge of +2, and all oxygen atoms have a formal charge of 0.

Step-by-step solution

(a) Drawing Lewis Structure with Single Bonds:

To draw the Lewis structure for the pyrosulfate ion (\(\mathrm{S}_{2} \mathrm{O}_{7}^{2-}\)) using only single bonds, we'll start by counting the total number of valence electrons available: - Sulfur (S): 6 valence electrons × 2 atoms = 12 electrons - Oxygen (O): 6 valence electrons × 7 atoms = 42 electrons - Add 2 more electrons due to the ion's 2− charge: 2 × 1 = 2 electrons Total valence electrons = 12 + 42 + 2 = 56 electrons Now, we can arrange the atoms and single bonds: 1. Place one S atom in the center and surround it by 4 O atoms (forming \(\mathrm{S}=\mathrm{O}\) bonds). 2. Place the second S atom next to the center O atom and surround it by 3 O atoms (forming \(\mathrm{S}=\mathrm{O}\) bonds). 3. Connect the two S atoms with one O atom, which is placed between the two S atoms. 4. Distribute the remaining valence electrons as lone pairs. With this arrangement, each O atom is surrounded by 8 electrons, and each S atom is surrounded by 10 electrons, as shown in this structure: ``` O O | | O - S - O - S - O | | O O ```

(b) Calculate the Formal Charge on Sulfur:

Now, we need to determine the formal charge on the sulfur atoms for the Lewis structure drawn in part (a). The formula for calculating the formal charge is: ``` Formal Charge = (Valence Electrons) - (Non-bonding Electrons) - 0.5 × (Bonding Electrons) ``` For both Sulfur atoms: - Valence Electrons: 6 electrons - Non-bonding Electrons: 2 electrons (from lone pairs) - Bonding Electrons: 8 electrons (4 single bonds × 2 electrons per bond) Using the formula for calculating formal charge: ``` Formal Charge = 6 - 2 - 0.5 × 8 = +2 ``` The formal charge on both sulfur atoms in the Lewis structure is +2.

(c) Drawing Lewis Structure with Double Bonds:

To draw another Lewis structure for the pyrosulfate ion (\(\mathrm{S}_{2} \mathrm{O}_{7}^{2-}\)) using six \(\mathrm{S}=\mathrm{O}\) double bonds and two \(\mathrm{O}-\mathrm{S}\) single bonds, follow these steps: 1. Place one S atom in the center and surround it by 4 O atoms (3 forming \(\mathrm{S}=\mathrm{O}\) bonds and 1 forming \(\mathrm{S}-\mathrm{O}\) bond). 2. Place the second S atom next to the \(\mathrm{S}-\mathrm{O}\) bond and surround it by the remaining 3 O atoms (forming \(\mathrm{S}=\mathrm{O}\) bonds). 3. Distribute the remaining valence electrons as lone pairs. This arrangement results in the following Lewis structure: ``` O O || || O - S - O - S = O | || O O ```

(d) Calculate the Formal Charge on Each Atom:

Following the same process as in part (b), we'll now calculate the formal charge on each atom for the Lewis structure drawn in part (c). Sulfur atoms with single bonds: - Valence Electrons: 6 electrons - Non-bonding Electrons: 0 electrons - Bonding Electrons: 8 electrons (1 single bond and 2 double bonds) ``` Formal Charge = 6 - 0 - 0.5 × 8 = 0 ``` Sulfur atoms with double bonds: - Valence Electrons: 6 electrons - Non-bonding Electrons: 2 electrons (from lone pairs) - Bonding Electrons: 8 electrons (3 single bonds) ``` Formal Charge = 6 - 2 - 0.5 × 8 = +2 ``` Oxygen atoms with single bonds: - Valence Electrons: 6 electrons - Non-bonding Electrons: 4 electrons (from lone pairs) - Bonding Electrons: 4 electrons (2 single bonds) ``` Formal Charge = 6 - 4 - 0.5 × 4 = 0 ``` Oxygen atoms with double bonds: - Valence Electrons: 6 electrons - Non-bonding Electrons: 4 electrons (from lone pairs) - Bonding Electrons: 4 electrons (1 double bond) ``` Formal Charge = 6 - 4 - 0.5 × 4 = 0 ``` For the Lewis structure drawn in part (c), the formal charge is 0 for both sulfur atoms with single bonds, +2 for sulfur atoms with double bonds, and 0 for all oxygen atoms.