Problem 75 - Chemistry and Chemical Reactivity

Question

The cyanate ion, \(\mathrm{OCN}^{-}\), has the least electronegative atom, \(\mathrm{C}\), in the center. The very unstable fulminate ion, CNO \(^{-}\), has the same molecular formula, but the \(\mathrm{N}\) atom is in the center. (a) Draw the three possible resonance structures of \(\mathrm{CNO}^{-}\). (b) On the basis of formal charges, decide on the resonance structure with the most reasonable distribution of charge. (c) Mercury fulminate is so unstable it is used in blasting caps for dynamite. Can you offer an explanation for this instability? (Hint: Are the formal charges in any resonance structure reasonable in view of the relative electronegativities of the atoms?)

Step-by-Step Solution

Answer

The most stable resonance structure of \(\mathrm{CNO}^{-}\) has lower formal charges. Mercury fulminate's instability is due to mismatched formal charges and electronegativities.

Step 1: Identify Possible Resonance Structures

The given ion is \(\mathrm{CNO}^{-}\), which has three atoms: C, N, and O. Start by drawing the structures with different bonding between C, N, and O. Consider single, double, and triple bonds in various combinations, while ensuring that the total number of electrons adds up to the charge of the ion.

Step 2: Calculate Formal Charges

The formal charge on an atom is calculated as: \( \text{Formal Charge} = \text{(Valence electrons)} - \text{(Non-bonding electrons)} - \frac{1}{2}\text{(Bonding electrons)} \). For each resonance structure, calculate the formal charges for the carbon, nitrogen, and oxygen atoms.

Step 3: Evaluate Resonance Structures

Compare the calculated formal charges to determine which resonance structure offers the most stable distribution of charges. The resonance structure where atoms have formal charges closest to zero, especially on the more electronegative atoms, is considered most favorable. The least electronegative atom should have the more positive or least negative charge, while more electronegative atoms should carry negative charges.

Step 4: Assess Stability of the Ion

Given that mercury fulminate is highly unstable, consider the role of formal charges and electronegativity in its instability. Unstable ions often have significant formal charges on atoms, which are not matched with their electronegativities, leading to weaker structural integrity.

Key Concepts

Formal Charge Calculation

Formal charge calculation is a crucial part of determining the best resonance structure for a molecule. It helps us to understand how electrons are distributed within a molecule and how these distributions may contribute to the stability of the structure. When calculating the formal charge for an atom within a molecule, follow these steps:

• Identify the number of valence electrons for the atom in question.
• Count the number of non-bonding electrons (those that are not involved in bonds).
• Determine the number of bonding electrons (those involved in bonds) and take half of this value.

The formula to calculate the formal charge (\( ext{FC}\) ) is:\[\text{FC} = \text{(Valence electrons)} - \text{(Non-bonding electrons)} - \frac{1}{2}\text{(Bonding electrons)}\]This calculation helps identify which atoms bear charges, allowing us to pinpoint the most "natural" or energetically favored state of the molecule. It's especially significant when comparing resonance structures, as it directs us to the form with charges closely aligned with atom electronegativities.

Electronegativity

Electronegativity is a measure of how strongly an atom attracts electrons towards itself. It affects molecule stability, especially when evaluating resonance structures.In the cyanate ion, \( ext{CNO}^{-}\), different molecules vary in electronegativity:

• Oxygen is the most electronegative, meaning it attracts electrons more strongly.
• Nitrogen is less electronegative than oxygen but more so than carbon.
• Carbon, the least electronegative, attracts electrons the least.

In resonance structures, the preferred form has electronegative atoms such as oxygen carrying negative charges, as these atoms naturally "want" more electrons.A logical distribution of formal charges considers this trait. It prevents unlikely situations where a highly electronegative atom, like oxygen, ends up positively charged. Such mismatched distributions destabilize the molecule and are less preferable.

Molecular Stability

Molecular stability is guided largely by how resonance structures distribute electrons across the molecule. These structures can depict electrons shared through various bond types, like single, double, or triple bonds, involving atoms with varying electronegativities.For stability:

• Resonance structures where charges are minimal or zero are preferred.
• The charge arrangement should match electronegativities; for instance, negative charges should reside on electronegative atoms.

The cyanate ion \( ext{CNO}^{-}\) exhibits these principles. Resonance structures where oxygen—more capable of stabilizing negative charge—carries a negative charge tend to represent more stable forms.However, in molecules like mercury fulminate, significant formal charges on less electronegative atoms or highly electronegative atoms having positive charges contribute to instability. These result in a higher potential for bond breakage, leading to reactive or explosive characteristics. This perfectly illustrates why considering all aspects, including formal charge and electronegativity, is key for understanding why certain molecules are less stable, aiding in better predictions of molecular behavior.