Lewis Diagrams, Resonance, and Formal Charge

Consider the neutral molecules of water ($\mathrm{H_2O}$) and ammonia ($\mathrm{NH_3}$). Data: atomic numbers $Z(\mathrm{H}) = 1$, $Z(\mathrm{N}) = 7$, $Z(\mathrm{O}) = 8$.

1. a) Determine the total number of valence electrons in each molecule and draw their corresponding Lewis structures.
2. b) State, giving reasons, how many bonding pairs and how many non-bonding (lone) pairs of electrons the central atom has in each, justifying whether the octet and duet rules are satisfied.

In aqueous solution, soluble carbonates release the polyatomic anion $\mathrm{CO_3^{2-}}$. Data: atomic numbers $Z(\mathrm{C}) = 6$, $Z(\mathrm{O}) = 8$. The following diagram shows the basic nuclear skeleton of this species:

1. a) On paper, complete the Lewis structure for the ion $\mathrm{CO_3^{2-}}$ by distributing the $24$ total valence electrons, and draw the three equivalent resonance structures.
2. b) Calculate the formal charge of each atom in one of the resonance structures and briefly explain why resonance is not a real physical oscillation between single and double bonds.

You can do this on paper and send a photo with your answer.

The ammonium cation ($\mathrm{NH_4^+}$) forms when neutral ammonia reacts with a hydrogen ion ($\mathrm{H^+}$). Data: atomic numbers $Z(\mathrm{H}) = 1$, $Z(\mathrm{N}) = 7$.

1. a) Draw the Lewis structure of the cation $\mathrm{NH_4^+}$, identify the type of bond by which the additional proton is incorporated and justify whether the four $\mathrm{N\text{--}H}$ bonds in the resulting cation are indistinguishable.
2. b) Calculate the formal charge of the nitrogen atom and of each hydrogen atom in the ion $\mathrm{NH_4^+}$, comparing it with the formal charge of nitrogen in the $\mathrm{NH_3}$ molecule.

You can do this on paper and send a photo with your answer.

The cyanate anion ($\mathrm{OCN^-}$) is a linear species whose nuclear skeleton has carbon as the central atom: $\mathrm{[O\text{--}C\text{--}N]^-}$. Data: atomic numbers $Z(\mathrm{C}) = 6$, $Z(\mathrm{N}) = 7$, $Z(\mathrm{O}) = 8$; Pauling electronegativities: $\chi(\mathrm{C}) = 2.55$, $\chi(\mathrm{N}) = 3.04$, $\chi(\mathrm{O}) = 3.44$.

1. a) Draw three non-equivalent resonance Lewis structures for the ion $\mathrm{OCN^-}$ in which all atoms complete the octet.
2. b) Calculate the formal charges of each atom in the three structures and explain which of them makes the greatest contribution to the resonance hybrid, and which turns out to be the least favorable.

You can do this on paper and send a photo with your answer.

The nitrite anion ($\mathrm{NO_2^-}$) takes part in biogeochemical processes in soil. Data: atomic numbers $Z(\mathrm{N}) = 7$, $Z(\mathrm{O}) = 8$. Experimental bond lengths: typical $\mathrm{N\text{--}O}$ single bond: $140\,\text{pm}$; typical $\mathrm{N=O}$ double bond: $120\,\text{pm}$. X-ray crystallography reveals that in the nitrite ion the two nitrogen–oxygen bonds are identical and measure $124\,\text{pm}$.

1. a) Draw the two resonance Lewis structures of the ion $\mathrm{NO_2^-}$, indicating the lone pairs and formal charges of each atom.
2. b) Deduce the theoretical average bond order in the resonance hybrid, correlate it with the observed experimental length and rigorously refute the mistaken idea that the molecule oscillates periodically between a single and a double bond. Do not assume an exact linear relationship between bond order and bond length.

You can do this on paper and send a photo with your answer.

Ozone ($\mathrm{O_3}$) has distinctive physicochemical properties. Data: atomic number $Z(\mathrm{O}) = 8$. Experimental $\mathrm{O\text{--}O}$ bond lengths: in hydrogen peroxide ($\mathrm{H_2O_2}$) it is $148\,\text{pm}$; in molecular dioxygen ($\mathrm{O_2}$) it is $121\,\text{pm}$; in ozone, both $\mathrm{O\text{--}O}$ bonds are equivalent with a length of $128\,\text{pm}$, an angle of $117^\circ$ and a permanent dipole moment of $\mu = 0.53\,\text{D}$.

1. a) Write the two resonance Lewis forms of $\mathrm{O_3}$, deducing the formal charges for the central oxygen atom and for the two terminal atoms.
2. b) Calculate the average bond order, check that it is consistent with the interatomic distances given, and explain why a homonuclear molecule such as ozone has a non-zero net dipole moment. Do not assume an exact linear relationship between bond order and bond length.

Boron trifluoride ($\mathrm{BF_3}$) is a gaseous reagent frequently used as a catalyst in organic synthesis. Data: atomic numbers $Z(\mathrm{B}) = 5$, $Z(\mathrm{F}) = 9$.

1. a) Draw the Lewis structure of $\mathrm{BF_3}$ in which the three fluorine atoms form single bonds with the central boron atom and complete their respective octets.
2. b) Justify why the central boron atom is an exception to the octet rule (electron deficiency) and state the number of bonding and non-bonding pairs this atom has.

You can do this on paper and send a photo with your answer.

The marked electron deficiency of boron trifluoride gives it a high affinity for Lewis bases. When $\mathrm{BF_3}$ reacts with ammonia gas ($\mathrm{NH_3}$), the solid addition adduct $\mathrm{F_3B\text{--}NH_3}$ is formed. Data: atomic numbers $Z(\mathrm{H}) = 1$, $Z(\mathrm{B}) = 5$, $Z(\mathrm{N}) = 7$, $Z(\mathrm{F}) = 9$.

1. a) Draw the Lewis structures of the two individual reactants and of the adduct $\mathrm{F_3B\text{--}NH_3}$, specifying which is the donor atom and which is the acceptor in forming the boron–nitrogen bond.
2. b) Calculate the formal charges of boron and nitrogen in the isolated reactants and in the final product. From the results, explain how the fulfillment of the octet rule for boron changes after the reaction.