Question

Considering both formal charge and bond polarities, predict on which atom or atoms the positive charge resides in the following cations: (a) \(\mathrm{H}_{3} \mathrm{O}^{+}\) (b) \(\mathrm{NH}_{4}^{+}\) (c) \(\mathrm{NO}_{2}^{+}\) (d) \(\mathrm{NF}_{4}^{+}\)

Short answer

The positive charge resides on oxygen in H3O+, and nitrogen in NH4+, NO2+, and NF4+.

Step-by-step solution

Understanding the Formal Charge

The formal charge of an atom in a molecule can be calculated using the formula: \( \text{Formal Charge} = \text{Valence Electrons} - (\text{Non-bonding Electrons} + \frac{1}{2} \text{Bonding Electrons}) \). We will use this to determine which atom carries the positive charge.

Analyzing the Molecule \( \mathrm{H}_{3} \mathrm{O}^{+} \)

In \( \mathrm{H}_{3} \mathrm{O}^{+} \), the oxygen atom originally has 6 valence electrons. In this ion, it has 1 non-bonding pair and forms 3 bonds with hydrogen. The formal charge on oxygen is calculated as follows: \( \text{Formal charge} = 6 - (2 + 3) = +1 \). Thus, the positive charge resides on the oxygen atom.

Analyzing the Molecule \( \mathrm{NH}_{4}^{+} \)

In \( \mathrm{NH}_{4}^{+} \), the nitrogen atom has 5 valence electrons and forms 4 bonds with hydrogen, with no lone pairs. The formal charge calculation for nitrogen is: \( \text{Formal charge} = 5 - (0 + 4) = +1 \). Therefore, the positive charge is on the nitrogen atom.

Analyzing the Molecule \( \mathrm{NO}_{2}^{+} \)

In \( \mathrm{NO}_{2}^{+} \), the nitrogen atom has 5 valence electrons. It forms 2 bonds with each of the oxygen atoms. Considering the double-bonded structure, the formal charge is: \( \text{Formal charge} = 5 - (0 + 4) = +1 \). Thus, the positive charge is on the nitrogen atom.

Analyzing the Molecule \( \mathrm{NF}_{4}^{+} \)

In \( \mathrm{NF}_{4}^{+} \), the nitrogen atom, with 5 valence electrons, forms 4 bonds with fluorine, leaving it with no lone pairs. The formal charge on nitrogen is: \( \text{Formal charge} = 5 - (0 + 4) = +1 \). Hence, the positive charge is on the nitrogen atom.

Key concepts

Bond Polarity

When we talk about bond polarity, we're discussing how electrons are shared between two atoms in a bond. Electrons can be shared equally or unequally, leading to either non-polar or polar bonds. This sharing depends mainly on the electronegativity of the atoms involved. Electronegativity is essentially an atom's ability to attract electrons.
- **Non-polar Bonds:** Here, atoms share electrons equally. Typically happens between atoms of the same element.
- **Polar Bonds:** Unequal sharing occurs when one atom is more electronegative compared to the other. This pulls electrons closer to itself, making it partially negative and the other atom partially positive.
In molecules like \( ext{H}_3 ext{O}^+\), oxygen is more electronegative than hydrogen. This difference causes polar bonds with the hydrogen atoms, giving oxygen a partial negative charge and hydrogen a partial positive charge. This gives insight into where the positive charge is distributed across the molecule, despite the formal charge calculations.

Molecular Structure

The molecular structure outlines the arrangement of atoms in a molecule. Understanding this helps us predict molecule properties like polarity, reactivity, and biological activity. Lewis structures are a simple way to represent molecular structures, showing how atoms connect and where lone pairs of electrons reside.
In tetrahedral molecules like \( ext{NH}_4^+\), nitrogen is at the center, bonded to four hydrogen atoms. Even without lone pairs, this symmetrical arrangement helps us confirm that nitrogen holds the positive charge.
Moreover, in molecules such as \( ext{NO}_2^+\), the structure is more nuanced with double bonds between nitrogen and oxygen. This results in a linear or bent configuration, directly influencing where charges might reside due to the relative electronegativities and presence of lone pairs.

Cation Charge Distribution

Cations have a net positive charge due to losing electrons. Understanding how this positive charge is distributed across the molecule involves evaluating both the formal charge and molecular arrangement. The formal charge helps identify specific atoms carrying the charge, especially when it doesn't evenly distribute.
Using \( ext{NF}_4^+\) as a reference, nitrogen carries the formal positive charge, since it has lost electrons relative to its usual valence electron count. With no lone pairs to redistribute, the single positive charge centers on the nitrogen atom.
For molecules like \( ext{H}_3 ext{O}^+\), the positive charge confined mainly to the central atom, oxygen, results from the combination of formal charge calculations and bond polarities with hydrogen atoms.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial for determining how atoms bond and interact. Counting these electrons helps us calculate formal charges and predict molecular behavior.
Consider the nitrogen atom in \( ext{NH}_4^+\): it has 5 valence electrons. When it forms bonds with four hydrogens, it uses all available valence electrons, leading to no remaining lone pairs. Consequently, calculating the formal charge helps us recognize it possesses a positive charge.
For oxygen in \( ext{H}_3 ext{O}^+\), its usual six valence electrons reduce due to bonding and lone pairs involvement, generating a formal charge of +1 when considering its lone electron pair. Understanding valence electrons ensures a deeper comprehension of charge distribution across atoms in a molecule.